MULTISCALE DEFORMATION AND FRACTURE IN MATERIALS

AND STRUCTURES

SOLID MECHANICS AND ITS APPLICATIONSVolume 84

Series Editor: G.M.L. GLADWELLDepartment of Civil EngineeringUniversity of WaterlooWaterloo, Ontario, Canada N2L 3GI

Aims and Scope of the Series

The fundamental questions arising in mechanics are: Why?, How?, and How much?The aim of this series is to provide lucid accounts written by authoritative researchersgiving vision and insight in answering these questions on the subject of mechanics as itrelates to solids.

The scope of the series covers the entire spectrum of solid mechanics. Thus it includesthe foundation of mechanics; variational formulations; computational mechanics;statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids andstructures; dynamical systems and chaos; the theories of elasticity, plasticity andviscoelasticity; composite materials; rods, beams, shells and membranes; structuralcontrol and stability; soils, rocks and geomechanics; fracture; tribology; experimentalmechanics; biomechanics and machine design.

The median level of presentation is the first year graduate student. Some texts are mono-graphs defining the current state of the field; others are accessible to final year under-graduates; but essentially the emphasis is on readability and clarity.

Multiscale Deformationand Fracture in Materialsand StructuresThe James R. Rice 60th Anniversary Volume

Edited by

T.-J. ChuangNational Institute of Standards & Technology,Gaithersburg, U.S.A.

and

J. W. RudnickiNorthwestern University,Evanston, Illinois, U.S.A.

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Editors’ Preface

The work of J. R. Rice has been central to developments in solid mechanics over the lastthirty years. This volume collects 21 articles on deformation and fracture in honor of J.R.Rice on the occasion of his 60th birthday.Contributors include students (P. M. Anderson,G. Beltz, T.-J. Chuang, W.J. Drugan, H. Gao, M. Kachanov, V. C. Li, R. M. McMeeking,S. D. Mesarovic, J. Pan, A. Rubinstein, and J. W. Rudnicki), post-docs (L. B. Sills, Y.Huang, J.Yu, J.-S. Wang), visiting scholars (B. Cotterell, S. Kubo, H. Riedel) andco-authors (R. M. Thomson and Z. Suo). These articles provide a window on the diverseapplications of modern solid mechanics to problems of deformation and fracture and insightinto recent developments.

The last thirty years have seen many changes to the practice and applications ofsolid mechanics. Some are due to the end of the Cold War and changes in the economy.The drive for competitiveness has accelerated the need to develop new types of materialswithout the costly and time-consuming process of trial and error. An essential element isa better understanding of the interaction of macroscopic material behavior with microscaleprocesses, not only mechanical interactions, but also chemical and diffusive mass transfer.Unprecedented growth in the power of computing has made it possible to attack increasinglycomplex problems. In turn, this ability demands more sophisticated and realistic materialmodels. A consistent theme in modern solid mechanics, and in this volume, is the effort tointegrate information from different size scales. In particular, there is an increasingemphasis on understanding the role of microstructural and even atomistic processes onmacroscopic material behavior. Despite the great advances in computational power, currentlevels do not approach that needed to employ atomic level formulations in practicalapplications. Consequently, idealized problems that link behavior at small, even atomic,size scales to macroscopic behavior remain essential.

It would be presumptuous to hope that the articles here are as original, rigorous,clear and as strongly connected to observations as the work of the man they are meant tohonor. Nevertheless, we hope that they do reflect the high standards that he has set. Thatthey do is in no small measure a consequence of the interaction, both formal and informal,of the authors with J. R. Rice and the inspiration that his work has provided.

The articles in this volume are grouped into sections on Deformation and Fracturealthough, obviously, there is some overlap in these topics. As is evident by reading thetitles, the scope and subjects of the articles are diverse. This reflects not only the extensiveimpact of Rice’s work but also the broad applicability of certain fundamental tools of solidmechanics.

vi EDITORS’ PREFACE

FRACTURE: Arguably, Rice’s most well-known contribution is theintroduction of the J-integral in 1968 and its application to problems of fracture. Becauseof its path-independent property, the integral has become a standard tool of fracturemechanics that makes it possible to link processes at the crack-tip to applied loads. Threeof the papers in the Fracture section discuss this J-integral (and several others use it). Kubogives a concise catalog of various versions of the integral and related extensions. Lidiscusses applications of the J-integral to characterization and tailoring of cementitiousmaterials. A special feature of these materials is the presence of fibers or aggregateparticles that transmit tractions across the crack-faces behind the tip. In his 1968 paper,Rice showed that the J-integral is equal to the energy released per unit area of crack advancefor elastic materials. Consequently, this energy or the value of J could be used as criterionfor fracture. Haug and McMeeking use the J-integral to study the effect of an extrinsicsurface charge on the energy release rate for a piezoelectric compact tension specimen.They find that the presence of the free charge diminishes the effect of the electric field andsuggest that this will complicate attempts to infer the portions of the crack tip singularitythat are due to stress and to the electric field. A related path-independent integral, theM-integral, is used by Banks-Sills and Boniface to determine the stress intensity factors fora crack on the interface between two transversely isotropic materials. A finite elementanalysis is used to determine the asymptotic near-field displacements needed to evaluate theM-integral.

Interpretation of the J-integral as an energy release is rigorous only for nonlinearelastic materials. But much of its usefulness arises from applications to elastic-plasticmaterials whose response, for proportional loading paths, is indistinguishable from ahypothetical nonlinear elastic one. For significant deviations from proportional loading, theinterpretation of J in terms of fracture energy is approximate. Cotterell et al. present amethod for accounting for the extra work arising from deviations from proportional loadingdue to significant crack growth in elastic plastic materials.

Crack growth is affected not only by mechanical loading (or coupled piezoelectricloading as considered by Haug and McMeeking) but also by chemical processes. Numericalsimulations by Tang et al. show that the presence of chemical activity at the crack tip canlead to blunting, stable steady crack growth or unstable sharpening of the crack tip. In thesteady state regime, the computed crack velocity as a function of applied load agreesqualitatively with experiments but uncertainties in material parameters make quantitativecomparison difficult. Consistent with previous studies, Tang et al. find the existence of athreshold stress level that leads to sharpening and fracture, but, contrary to previous studies,this threshold depends not only on the mechanical driving force, but also on the chemicalkinetics.

A classic problem of material behavior is to delineate the conditions for whichmaterials fail ductilely or brittlely. Rice and Thomson addressed this problem byconsidering the interaction of a dislocation with a sharp crack-tip and arguing that ductilebehavior occurred when the energetics of the interaction favored emission of a dislocation.In a concise analysis, Beltz and Fischer extend this formulation to consider the effect of theT-stress, that is , the non-singular portion of the crack-tip stress field. They show that the

EDITORS’ PREFACE vii

effect of this stress can be significant for small cracks, with lengths on the order of 100atomic spacings.

Klein and Gao present an innovative approach to the problem of dynamic fractureinstability. They suggest that the discrepancy between predictions and observations couldbe resolved by including non-linear deformations near the crack-tip. They do this by acohesive potential model that bridges the gap between continuum scale and atomistic scalecalculations. Using as a measure of failure the loss of strong ellipticity, they suggest thatcrack branching may be associated with a loss of stiffness in biaxial stretching near thecrack-tip.

Several pioneering papers by Rice have considered the problem of determining thestress and deformation fields near the tip of a crack in a ductile material. The chapter byDrugan extends consideration to the case of a crack propagating along the interface of twoductile (elastic-ideally plastic) materials. An interesting by-product of the analysis foranti-plane deformation of bimaterials is a family of admissible solutions for homogeneousmaterials (including the well-known Chitaley -McClintock solution). Analysis reveals thatbeyond a certain level of material mismatch (ratio of yield stresses) a single term of theasymptotic expansion is not sufficient to characterize accurately the near-tip field. Thissuggests that the number of terms required will depend on some microstructural distance.

Yu and Cho present detailed observations of the crack-tip fields in plasticallydeforming copper single crystals and compare them with fields predicted by Rice(Mechanics of Materials, 1987). They suggest that discrepancies could be due to absenceof latent hardening in the elastic ideally plastic model analyzed by Rice.

Rubinstein presents the results of numerical calculations based on a complexvariable formulation for a variety of micromechanical models of composites. Though thecalculations are elastic, they take explicit account of various reinforcing fibers, particles,etc. and, as a result the solutions depend on the ratio of fiber size to spacing, an importantdesign variable.

DEFORMATION: Another major contribution of Rice has been thedevelopment of shear localization theory as a model of failure in ductile materials. Incontrast to fracture, where the stress intensification caused by acute geometry plays adominant role, the approach of shear localization is based on the constitutive description ofhomogeneous deformation. The constitutive relation developed by Gurson, under Rice’sdirection, has seen much application in this context because it includes softening due to thenucleation and growth of micro-voids, an important microscale feature of ductile metaldeformation. Chen et al. discuss modifications of the Gurson model that are necessary todescribe the anisotropy of aluminum sheets. A related chapter by Chien et al. uses a threedimensional finite element analysis of a unit cell to confirm the accuracy of aphenomenological anisotropic yield condition for porous metal and apply thephenomenological condition to analyze failure in a fender forming operation. The chapterby Rudnicki discusses shear localization of porous materials in a quite different context: theeffects of coupling between pore fluid diffusion and deformation on the development ofshear localization in geomaterials.

viii EDITORS’ PREFACE

Although the constitutive model developed by Gurson and those used by Chien etal., Chen et al. and Rudnicki are more complex than classic elastic-plastic relations, theyinclude microstructural information simply by means of the void volume fraction orporosity. The paper by Riedel and Blug presents an example of the type of sophisticatedconstitutive model needed for implementation in a finite element code to model a complextechnology, solid state sintering. Application of the model to silicon carbide demonstratesthe level of detail and accuracy this kind of material modelling combined with finite elementanalysis can bring to technological processes.

Elastic-plastic contact is an example of the fruitful application of continuummechanics to microscale processes. Applications include indentation hardness testing,atomic force microscopy, powder compaction, friction and wear. Mesarovic reviews andsummarizes the current understanding in this area and identifies a number of problems inneed of further work. Recent computational advances have improved understanding butfurther work is needed in several areas.

Hydrogen is an element whose presence on an interface or at a crack-tip can leadto embrittlement. In an elegant analysis that combined thermodynamics and fracturemechanics and extended the introduction of surface energy into fracture analysis by Griffith,Rice showed how the presence and mobility of segregants can alter the surface energy.Wangreviews the analysis of Rice and co-workers and shows that the predictions are consistentwith observations of hydrogen embrittlement in iron single crystals.

Anderson and Xin address the classic problem of the stress needed to drive adislocation. In particular, they examine how this stress is affected by a welded interfaceusing a model that allows them to vary independently the unstable stacking fault energy gus,the peak shear strength and the slip at peak shear. Using a numerical solution, they find thatthe critical resolved shear stress increases with gus, but is relatively insensitive to themaximum shear strength.

Suo and Lu present a model for the growth of a two-phase epilayer on an elasticsubstrate. By means of a linear perturbation analysis and numerical computations, theyshow that the competition between phase coarsening, due to phase boundary energy, andphase refining, due to concentration dependent surface stress, can lead to a variety of growthpatterns, including a stable periodic structure.

The chapter by Kachanov et al. gives a complete solution for the problem oftranslation and rotation of ellipsoidal inclusions in an elastic space. Although they do notpursue applications of the solution, the solution is relevant to deformation around hardparticles in a matrix, motion of embedded anchors, etc.

Thomson et al. present a percolation theory approach to addressing the inevitableinhomogeneous deformation on the microscale. They show how it can be used to constructstress/ strain response and give insight into processes of microlocalization.

We consider it an honor and privilege to have had the opportunity to edit thisvolume. In the preparation of the biography, H. Gao, W. Drugan and Y. Ben-Zion providedextra needed information. Jim himself provided autobiographical source material andhelped proofread it to assure its correctness and completeness. We are grateful to theindividual authors for their contributions and timely cooperation, and to the technical review

EDITORS’ PREFACE ix

board members who enhanced the quality of the volume by providing critical reviews on thearticles.

Our special thanks are due to Kluwer Academic Publishers, Dordrecht Office andits professional staff for their editing and production, and for their agreement to publish theVolume given even when it was still unwritten, but existed simply as a proposal in the formof a list of authors and titles. Financial support and encouragement from NIST managementteam, S. Freiman, G. White and E. R. Fuller, Jr. are gratefully acknowledged. Finally, wewould like to express our appreciation to Drs. W. Luecke, X. Gu and J. Guyer for their helpin the editing of this book.

T-J. CHUANG, Gaithersburg, MD25 August 2000

J. W. RUDNICKI, Evanston, IL

TABLE OF CONTENTS

xv

Editors’ Preface v

Biography of James R. RiceT.-J. Chuang and J. W. Rudnicki

List of Publications by James R. Rice xxvii

List of Contributors xli

PART I: DEFORMATION

Approximate Yield Criterion for Anisotropic Porous Sheet Metals and itsApplications to Failure Prediction of Sheet Metals under Forming ProcessesW. Y. Chien, H.-M. Huang, J. Pan and S. C. Tang

A Dilatational Plasticity Theory for Aluminum SheetsB. Chen, P. D. Wu, Z. C. Xia, S. R. MacEwan, S. C. Tang and Y. Huang

Internal Hydrogen-Induced Embrittlement in Iron Single CrystalsJ.-S. Wang

A Comprehensive Model for Solid State Sintering and its Applicationto Silicon CarbideH. Riedel and B. Blug

Mapping the Elastic-Plastic Contact and AdhesionS. Dj. Mesarovic

The Critical Shear Stress to Transmit a Peierls Screw Dislocationacross a Non-Slipping InterfaceP. M. Anderson and X.J. Xin

1

17

31

49

71

87

xii TABLE OF CONTENTS

Self-Organizing Nanophases on a Solid SurfaceZ. Suo and W. Lu

Elastic Space Containing a Rigid Ellipsoidal InclusionSubjected to Translation and RotationM. Kachanov, E. Karapetian, and I. Sevostianov

Strain Percolation in Metal DeformationR. M. Thomson, L. E. Levine and Y. Shim

Diffusive Instabilities in Dilating and Compacting GeomaterialsJ. W. Rudnicki

107

123

145

159

183

205

223

237

243

275

311

PART II: FRACTURE

Fracture Mechanics of an Interface Crack between a Special Pair ofTransversely Isotropic MaterialsL. Banks-Sills and V. Boniface

Path-Independent Integrals Related to the J-Integral and Their EvaluationsS. Kubo

On the Extension of the JR Concept to Significant Crack GrowthB. Cotterell, Z. Chen and A. G. Atkins

Effect of T-Stress on Edge Dislocation Formation at a Crack Tip underMode I LoadingG. E. Beltz and L. L. Fischer

Elastic-Plastic Crack Growth along Ductile/Ductile InterfacesW. J. Drugan

Study of Crack Dynamics Using Virtual Internal Bond MethodP. A. Klein and H. Gao

Crack Tip Plasticity in Copper Single CrystalsJ. Yu and J. W. Cho

TABLE OF CONTENTS

Numerical Simulations of SubCritical Crack Growthby Stress Corrosion in an Elastic SolidZ. Tang, A. F. Bower and T.-J. Chuang

Energy Release Rate for a Crack with Extrinsic Surface Chargein a Piezoelectric Compact Tension SpecimenA. Haug and R. M. McMeeking

Micromechanics of Failure in Composites-An Analytical StudyA. A. Rubinstein

J-Integral Applications to Characterization and Tailoringof Cementitious MaterialsV. C. Li

Author Index

Subject Index

xiii

331

349

361

385

407

415

James R. Rice

Biography of James R. Rice

James Robert Rice (JRR) was born on 3 December 1940 in Frederick, Maryland to DonaldBlessing Rice and Mary Celia (Santangelo) Rice. Located some 50 miles northwest of thenation’s capital, Frederick was then a small city of about 20,000 people, set in a rural,farming area. Commemorated in Whittier’s poem about Dame Barbara Fritchie’s patriotism,Frederick was a crossroads for troop movements during the Civil War (1861-1865) and thebirthplace of Francis Scott Key who wrote the American National Anthem. JRR’s motherMary was the child of a Sicilian immigrant family and now resides in Adamstown,Maryland. The family of JRR’s father, Donald, had long lived in that part of the USA.Donald, who died in 1987, operated a gasoline station, served 3 terms as alderman and aterm as mayor of Frederick City in the early 1950s, later founded a successful tire company,and, like Mary, was highly active in Frederick community affairs.

JRR was raised in Frederick, and was the second of three children. His olderbrother, Donald Blessing Rice Jr., served as corporate CEO of several companies (such asthe RAND Corporation) in the private sector and one term as Secretary of the U.S. AirForce under the Bush Administration. He now resides in Los Angeles. JRR’s youngerbrother, Kenneth Walter Rice, continues to live in Frederick and runs the business startedby his father.

JRR attended primary and secondary school at St. John’s Literary Institute, a localparish school in Frederick. He played baseball and basketball, worked part-time deliveringnewspapers and in his father’s businesses, and read a lot. Influenced by his high schoolteachers of math and physics, recruited from Fort Dieterich, a local army base, JRR’s earlyinterest in auto mechanics gradually evolved into an interest in mechanical engineering.Armed with several scholarships, he began undergraduate studies in that subject at LehighUniversity in Bethlehem, PA, in 1958, one year after the launch of Sputnik propelled theU.S. into a keen competition in outer space with the then-USSR.

During his undergraduate studies at Lehigh, JRR realized his particular interest wasin theoretical mechanics, especially fluid and solid mechanics, and applied mathematics.Under the influence of inspiring teachers including Ferdinand Beer, Fazil Erdogan, PaulParis, Jerzy Owczarek, George Sih, and Gerry Smith, he did his subsequent studies in theengineering mechanics and applied mechanics programs. Paul Paris has said that for thecourses JRR took from him, half of Paul’s preparation for each lecture consisted ofanswering the questions JRR had posed during the previous class meeting. Because of hisproficiency in math and physics, JRR earned all his academic degrees, from B.S. to Ph.Din only six years (1958-1964), the shortest time in Lehigh’s record. Ferdinand Beer directedJRR’s M.S. and Ph.D. theses on stochastic processes, specifically on the statistics of highlycorrelated noise. The results were summarized in 1964 in his Ph.D. thesis, entitled“Theoretical Prediction of Some Statistical Characteristics of Random Loadings Relevant

xvi BIOGRAPHY OF J. R. RICE

to Fatigue and Fracture”. At the same time, he continued working with George Sih on thesubject of his undergraduate research project, elastic stress analysis of cracks along a bi-material interface. He independently developed a simple elastic-plastic crack model, whichturned out to be the same as D. S. Dugdale had already published, and then extended themodel to the case of cyclic loads. His work on “The Mechanics of Crack Tip Deformationand Extension by Fatigue” was published in ASTM STP 415 in 1967, and was awarded theASTM Charles B. Dudley Medal in 1969.

In the late 1950s, fracture mechanics was still in the early stages of development.Egon Orowan of MIT and George Irwin of Naval Research Laboratory were beginning toadvocate using stress analysis of cracks to solve fracture and fatigue problems inconventional metals and metal alloys. Motivated by the problems encountered whileworking at Boeing in the summers, Paul Paris was especially keen to work in this field.Together Paris, George Sih and Erdogan offered the first graduate course on fracturemechanics, which JRR took in his senior year. In addition, they recruited bright graduatestudents, including JRR, to do thesis research in this area. This environment cultivatedJRR’s interest in fracture mechanics, which became a major focus of his teaching andresearch.

After JRR’s graduation from Lehigh in 1964, his advisor, Ferdinand Beer,suggested he accept an offer from Daniel C. Drucker to be a post-doctoral research fellowin the Solid Mechanics Group of the Division of Engineering at Brown University. Brownwas (and still is) well known internationally in the solid mechanics community. At that timemany world-renowned researchers in solid mechanics were members of the faculty. Theyincluded, among others, Daniel C. Drucker, Morton E. Gurtin, Harry Kolsky, JosephKestin, Alan C. Pipkin, Ronald S. Rivlin, Richard T. Shield, and Paul S. Symonds.

At Brown, JRR, armed with enthusiasm, energy, and innovative ideas, pursued hisresearch on many critical fronts in fracture mechanics. He continued to collaborate with hisformer professors on the unfinished work from Lehigh, including characterization of fatigueloadings, plastic yielding at a crack tip and stress analysis of cracks and notches in elasticand work-hardening plastic materials under longitudinal shear loading. At Lehigh, he hadalso obtained some results for determining energy changes due to material removal, suchas cracking or cavitation, in a linear elastic solid. At Brown, Drucker opened his eyes to theimportance of generalizing these results to the widest possible class of materials; thus, JRRdeveloped this work into a procedure for calculating energy changes in a general class ofsolids. This work led to JRR’s discovery of the well-known J-integral a few years later.With these impressive achievements, he was offered a tenure-track faculty job as AssistantProfessor in 1965.

As an assistant professor at Brown, JRR devoted his energy and efforts not onlyto research but also to teaching. He always believed that a good professor must excel inteaching and research. He offered many courses in applied mechanics. He developed hisown lecture notes in each course without relying on specific text books. During lecturingin a typical class, he memorized every important piece of information and used theblackboard to convey the concepts to students. He was an excellent and effective

BIOGRAPHY OF J. R. RICE xvii

communicator. Students were always welcome and encouraged to ask questions or engagein discussions. Copies of his lecture notes highlighting the key information includingmethods of derivations and final resulting formulae were distributed to his students.

In research, he obtained federal funding from agencies such as NSF, DARPA,NASA, ONR, and the DOE to support project initiatives on mechanics of deformation andfracture. At this time, fracture mechanics was still in the early stages of development. JRRseized the opportunity to work out many unsolved problems in stress and deformation fieldsaround a crack in various materials systems, mostly in 2D. Some examples are: elastic-plastic mechanics of crack extension, stresses in an infinite strip containing a semi-infinitecrack, plane-strain deformation near a crack in a power-law hardening material (with G.F.Rosengren), energy changes in stressed bodies due to void and crack growth (with D.C.Drucker), a path independent integral and the approximate analysis of strain concentrationby notches and cracks. At the invitation of H. Liebowitz, this work was summarized in aclassic review article entitled “Mathematical Analysis in the Mechanics of Fracture”, whichappeared in 1968 as Chapter 3, in Volume 2, Mathematical Fundamentals of Fracture, ofthe book series, Fracture: An Advanced Treatise.

Of particular significance was the discovery of a path-independent integralresulting from his prior probe into energy variations due to cracking of a nonlinear elasticsolid. He named this particular integral the “J-Integral” with the upper case letter “J”inadvertently coinciding with his nickname “big Jim” respectfully used by his students. Thisintegral turned out to coincide with a 2D version of the general 3D energy momentum tensorproposed by J. D. Eshelby in England in 1956. A similar concept was also developed byCherepanov in Russia at about the same time as Rice’s J-integral, but JRR exploited theintegral’s usefulness more fully in fracture analysis, especially by focusing on aspectsrelating to path-independence. Because of its path independence, the J-integral is a powerfultool to evaluate energy release due to cracking, bypassing the difficulties arising from strainconcentration at the crack-tip. Using the procedure he developed with Drucker, JRR showedthat the J-Integral is identical to the rate of reduction of potential energy with respect tocrack extension. In addition, JRR, together with the late Göran F. Rosengren, showed in1968 that the J-integral plays the role of a single unique parameter that governs theamplitude of the nonlinear deformation and stress fields inside the plastic zone near a cracktip. This result established criticality of the J-integral as a criterion for fracture even for anelastic-plastic material and made possible its use for practical engineering applications.Simultaneously, John Hutchinson at Harvard also derived a similar result. Based on theirstudies, the nonlinear stress distribution in the crack tip zone is now referred to as the“Huchinson-Rice-Rosengren” or “HRR” field. Over the next decade, criticality of the J-Integral was adopted as the major design criterion against failure. It is used in the ASMEPressure Vessel and Piping Design Code, and in general purpose finite element codes suchas ABAQUS and ANSYS. JRR’s paper on the J-integral, which appeared in the Journal ofApplied Mechanics in 1968, received the ASME Henry Hess Award in 1969 and hasbecome a classic, attracting more than 1000 citations and references. The J-Integral formsan essential part of the subject matter contained in any textbook on fracture mechanics.

xviii BIOGRAPHY OF J. R. RICE

Because of this and other contributions, JRR was promoted to Associate Professor inEngineering in 1968 and received the ASME Pi Tau Sigma Gold Medal Award foroutstanding achievement in mechanical engineering within 10 years following graduationin 1971.

As Associate Professor at Brown, JRR extended his research interests frommechanics to the physics and thermodynamics aspects of fracture phenomena. He workedwith his student N. Levy on the prediction of temperature rise by plastic deformation at amoving or stationary crack-tip. When applied to a set of aluminum and mild steel alloys, thiswork helped to explain the experimentally observed relationship between the temperature-dependent toughness and the loading rate. Other accomplishments included his work withhis student Dennis Tracey on the ductile void growth in a triaxial stress field. This workclarified the mechanism of void growth under applied stress in ductile metals. The role oflarge crack tip geometry changes in plane strain fracture was quantified in a paper with M.Johnson. He also actively participated in the development of formulations for finite elementcomputations. He directed Ph.D. thesis research in computational fracture mechanics byDennis Tracey. He interacted with Pedro Marcal, a faculty colleague and the foundingdeveloper of the MARC finite element code, and with Dave Hibbitt, Marcal’s graduatestudent and the co-developer of the ABAQUS code. Together, they developed anappropriate numerical algorithm to compute large strains and large displacements in thefinite element code. This scheme has been implemented in many general purpose finiteelement codes such as MARC, ABAQUS and ANSYS.

With another faculty colleague, Joseph Kestin, JRR worked on the application ofthermodynamics to strained solids. For example, although the chemical potential is well-defined in fluids, the proper definition in solids is not clear. A paper by Kestin and Ricehelped to clarify the concept and served as a starting point to extend JRR’s developinginterest in high temperature fracture, namely, creep and creep rupture.

In 1970, JRR was promoted to Full Professor of Engineering. With financialsupport from federal funding agencies such as the National Aeronautic and SpaceAdministration (NASA), Office of Naval Research (ONR), DARPA, National ScienceFoundation (NSF) and Atomic Energy Commission (AEC, the predecessor of ERDA andthe Department of Energy (DOE)), he was directing a research team of 7 Ph.D. graduatestudents. The team participated in the Materials Research Laboratory, a large-scale,interdisciplinary research program, funded by DARPA and NSF, and in a program of theAEC Basic Sciences Division directed by Joseph Gurland. JRR’s students worked in awide range of areas in the mechanics of solids and fracture: Dennis Tracey, Dave Parks, andBob McMeeking in (1) theoretical and computational fracture mechanics; Art Gurson in (2)constitutive relationships in metals and metallic alloys; Glenn Brown and (Jerry) T.- j.Chuang in (3) creep and creep rupture in the high temperature range; and Mike Cleary in(4) mechanics of geomaterials. Representative work in (1) included an alternativeformulation of Bueckner’s (1970) weight function method to evaluate the stress intensityfactor KI of a given 2D linear elastic cracked solid subject to arbitrary loading, based on anyknown solution to the same geometry; a finite element analysis of small scale yielding near

BIOGRAPHY OF J. R. RICE xix

a crack in plane-strain (with N. Levy, P.V. Marcal and W.J.Ostergren); an approximatemethod for analysis of a part-through surface crack in an elastic plate (with N. Levy); and3D elastic-plastic stress analysis for fracture mechanics (with N. Levy and P. V. Marcal).In (2) JRR worked out the fundamental structure for the time-dependent stress-strainrelationship of a metal in the plastic deformation range and proposed an internal variabletheory for the inelastic constitutive relations in metal plasticity.

In 1971-72, JRR took a year of sabbatical leave with support from a NSF SeniorPostdoctoral Fellowship. He spent the year at the Department of Applied Mathematics andTheoretical Physics of the University of Cambridge, where he was affiliated with ChurchillCollege under the support of a Churchill College Overseas Fellowship. At Cambridge, heworked with a number of people, including Rodney Hill, one of the pioneers in classicalplasticity, Andrew C. Palmer in soil mechanics, and John Knott and his student Rob Ritchieon elastic-plastic fracture. With Hill, JRR developed a general structure of inelasticconstitutive relations assuming the existence of elastic potentials, and gave a specialimplementation for elastic/plastic crystals at finite strain. In the latter case, crystallographicslip along a set of active slip planes was considered as the sole deformation mechanismresponsible for the inelastic behavior. This theory successfully explained various aspects ofplasticity such as strain hardening, the existence of a flow rule and normality. With Knottand Ritchie, JRR proposed a relationship between the critical tensile stress and the fracturetoughness of mild steel. The analysis predicts the observed temperature dependence of KICin the brittle to ductile transition range. With Andrew Palmer, JRR used his newlydeveloped J-integral to develop a mode-II “shear crack” model for the growth of slipsurfaces in over-consolidated clay slopes.

Returning to Brown in 1972, JRR continued to pursue research on many aspectsof fracture mechanics. John Landes and Jim Begley of the Westinghouse R&D Centerbecame keen advocates of using the J-Integral as a design criterion in the nuclear energybusiness, and in a paper with Landes and Paul Paris, JRR developed an elegantly simpleprocedure to estimate the value of J-Integrals from experiments. Eventually, this procedurebecame the ASTM standard and part of the ASME Pressure Vessels and Piping design code.Besides analysis on the continuum level, JRR strongly felt that there was a need to studyfracture at the microstructural level in order to bridge the atomic and engineering scales.One important area that required such a treatment is high temperature creep and creeprupture where mass transport plays an important role. At that time, a group at Harvard ledby Mike Ashby was also interested in this topic. As a result, there was much interactionbetween Harvard and Brown during 1972-74: JRR and Ashby and their students madefrequent mutual visits to give seminars and to exchange ideas. One important result, jointlydeveloped in 1973 with his student, T.- J. Chuang, was the discovery of creep crack-likecavity shapes induced by surface diffusion. This type of cavity, referred to as a Chuang-Ricecrack-like cavity, is frequently observed at the grain boundaries of a ruptured tensilespecimen. This work defines the boundary conditions at the cavity apex and satisfactorilyexplained non-linear stress dependence on cavity growth rate. The degree of non-linearitydepends on the deformability of the grains, and JRR obtained solutions for the stress

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dependence on creep cavity growth in rigid grains (with Chuang, Kagawa, Sills and Sham),in elastic grains (with Chuang) and in plastic grains (with Needleman). The predicted stressdependence was verified experimentally by Bill Nix and his students at Stanford in the late1970s using implanted water vapor cavities at grain boundaries in pure silver and nickel-tinalloys. Later in the 1980s and 90s, this work was used by many researchers to predict cavitygrowth induced by electromigration in aluminum interconnect wires.

In 1973, JRR was offered a Chair by the Brown President, Donald Hornig with thetitle L. Herbert Ballou Professor of Theoretical and Applied Mechanics. This privileged titleis an honor comparable to a University Professorship, which is the highest rank of teachingprofessors at Brown.

In physical metallurgy, it had become well-known that dislocations at the atomiclevel are fully responsible for the room temperature plastic behavior in metals. Since theearly 1960s, many researchers (such as Hirth, Lothe, Mura and Weertman) devoted theirefforts to this area and helped to build the foundation of dislocation theory. JRR was amongthose cutting edge scholars who excelled in mathematical dislocation theory. In 1972, hemet Robb Thomson of SUNY-Stony Brook at a conference and they puzzled over theductile versus brittle transition phenomenon in crystals. Since dislocation movement leadsto ductility and rapid crack growth leads to catastrophic failure, they believed theinteractions of both must play a dominant role in ductile/brittle behavior. They proposedthat the ability to emit dislocations from a pre-existing sharp crack tip is the source ofductility in metals. On the other hand, the resistance of a crack tip to dislocation emissionleads to brittleness in ionic or covalent crystals like ceramics. By analyzing the energeticforces between a dislocation and a crack, they derived an important parameter that governsthe ductility. If this parameter, which is shear modulus times Burgers vector over surfaceenergy, exceeds 8.5 to 10, then the crystal exhibits intrinsically brittle behavior. If less, itis generally ductile. The Rice -Thomson theory has become a classic in the Science CitationIndex with more than 200 citations. In the late 1970’s, Mike Ohr of Oak Ridge NationalLaboratory provided direct experimental evidence for the theory by observing emission ofdislocations from the crack tip in a variety of metal specimens in situ under TEM.

In another noteworthy work, JRR helped his student Art Gurson to develop in 1975the plasticity theory of porous media, in which yield criteria and flow rules were predictedin stress space using 2D or 3D unit cell models. The model predicts the effect of porosityon the plastic behavior of ductile materials and has come to be known as the “Gurson”model. It is well-known in the metallurgy and mechanics communities and is one of themajor yield criteria adopted in the commercial general purpose finite element codes forassessing inelastic behavior of metallic materials.

Motivated by his studies of shear bands with Andrew Palmer, JRR becameinterested in the fundamental question of why deformation would localize in a narrow zone.A basic premise of fracture mechanics, going back to the ideas of Griffith, is that thepresence of flaws in a material causes a local elevation of the stress and leads to propagationof the flaw and, eventually, to failure. Although this process provides a satisfactoryexplanation of failure in many materials, it does not explain why macroscopically uniform

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deformation should give way to localized deformation in very ductile materials or underconditions of compressive stress that suppress flaw propagation. Based on antecedents inthe work of Hadamard, Hill, Thomas and Mandel, JRR and his student Rudnicki treated theinitiation of localized deformation as a bifurcation from homogeneous deformation andshowed that its onset was promoted by certain subtle features of the constitutive behavior.This work, which was published in the Journal of the Mechanics and Physics of Solids in1975, received the Award for Outstanding Research in Rock Mechanics from the U. S.National Committee on Rock Mechanics in 1977. Although this work was originallyintended to describe fault formation in rock, JRR extended the approach to considerlocalized necking in thin sheets (with S. Storen), strain localization in ductile single crystals(with R. J. Asaro), and limits to ductility in sheet metal forming (with A. Needleman). Hesummarized the state of the subject in a keynote lecture on “The Localization of PlasticDeformation” at the 14th International Congress on Theoretical and Applied Mechanics inDelft in 1976. The printed version of this lecture is a widely-cited classic.

In the early 1970’s, there were many reports of observations precursory toearthquakes that were attributed to the coupling of deformation with the diffusion of porefluid. A series of papers, by JRR with students (Cleary and Rudnicki) and Don Simons, anAssistant Professor at Brown, analyzed the effects of this coupling on models for earthquakeinstability and for quasi-statically propagating creep events. One of these papers (“Somebasic stress-diffusion solutions for fluid-saturated elastic porous media with compressibleconstituents”, with M. P. Cleary, Rev. Geophys. Space Phys., 14, pp. 227-241, 1976)reformulated, in a particularly insightful way, the equations first derived by Biot for a linearelastic, porous, fluid-infiltrated solid. This version of the equations has proven soadvantageous that it is now the standard form. The models of the earthquake instabilityformulated to study these effects were among the first in which the instability was notpostulated but arose in a mechanically consistent way from the interaction of the fault zonematerial behavior and the surroundings.

JRR’s interest in the mechanics of earthquakes proved durable and became a majorbranch of his work. With Florian Lehner and Victor Li, he worked on time-dependenteffects due to coupling of the shallow, elastic portion of the Earth’s lithosphere with deeperviscoelastic portions. This work was based on a generalization of an earlier thin plate modelby Elsasser. This work demonstrated that the viscous deformation of the lower crust andupper mantle following large earthquakes could affect surface deformation for decades andprovided a new model for the interpretation of increasingly detailed surface deformationmeasurements. In the early 90s, JRR used the finite element code ABAQUS together withYehuda Ben-Zion, Renata Dmowska, Mark Linker, and Mark Taylor to explore thebehavior of this model in 3D and to compare model predictions with geophysicalobservations. JRR’s growing interest in the mechanics of earthquakes complemented nicelythe interests of his spouse, Renata Dmowska, a seismologist. Together, Renata's analysisof data and JRR’s mathematical models have been combined in several papers on aspectsof earthquakes, particularly in subduction zones.

JRR’s interest in the mechanics of earthquakes soon led to a study of frictional

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stability. Stick-slip is a widely observed phenomenon and has long been regarded as aphysical analog for the earthquake instability. But the standard constitutive description,static and dynamic friction, was inconsistent with the steady sliding often observed andcontained no mechanism for restrengthening that would allow repeated events on the samesurface. Based on experimental observations of Dieterich at the U.S. Geological Survey,JRR and his student Andy Ruina formulated a rate- and state-dependent constitutiverelationship for sliding on a frictional surface. By examining the stability of a one degree-of-freedom system with this relationship, they were able to predict the variety of behaviorsobserved in rock friction experiments: steady sliding, damped oscillations, stick-slip andsustained periodic oscillations. Other papers with Tse and Gu examined the dynamics andnonlinear stability of these systems. JRR and his student Tse showed that when this type ofrelationship was applied on a surface between two elastic solids and modified to include adepth dependence appropriate for the temperature and pressure dependence in the earth, thecalculations produced periodic events with a depth dependence remarkably similar to thatof observed earthquakes.

In the late 1970s and early 1980s, JRR also continued to work on many aspects ofinelasticity and fracture. With Joop Nagtegaal and Dave Parks, he developed a numericalscheme to improve the accuracy of finite element computations in the fully plastic range.With Bob McMeeking, he worked out the proper finite element formulation in the largeelastic-plastic deformation regime. With a colleague at Brown, Ben Freund, and a student,Dave Parks, he helped solve the problem of a running crack in a pressurized pipeline. Inmaterials science, he studied stress corrosion and hydrogen embrittlement problems.

He also orchestrated a remarkable multidirectional attack on the problem of quasi-static crack growth in elastic-plastic materials. This began with a paper with Paul Sorensenin 1978 that proposed an elegant way of using near-tip elastic-plastic fields to derivetheoretical predictions for crack growth resistance curves (JR curves). Then, he and hisstudent Walt Drugan derived asymptotic analytical elastic-ideally plastic solutions for thestress and deformation fields near a plane strain growing crack which showed the necessityof an elastic unloading sector in the near-tip field. [Independent work by L. I. Slepyan inthe then-USSR and Y. C. Gao in China also addressed this problem, for incompressiblematerial and steady-state conditions.] The detailed numerical finite element elastic-plasticgrowing crack solutions of JRR’s student T-L. Sham confirmed the analytical predictions,and in a 1980 paper with Drugan and Sham, JRR combined the method proposed earlierwith Sorensen, with the new analytical asymptotic solutions and Sham’s numerical results,to produce a comprehensive and fundamentals-based model of stable ductile crack growthand predictions of plane strain crack growth resistance curves. Then, with LawrenceHermann, JRR conducted and analyzed “plane strain” crack growth tests and showed thatthis theory was indeed capable of describing the experimentally-measured crack growthresistance curves under contained yielding conditions.

The asymptotic analysis of elastic-ideally plastic growing crack fields, involvingthe assembling of different possible types of near-tip solution sectors into complete near-tipsolutions, prompted JRR and Drugan to inquire more fundamentally about what continuity

BIOGRAPHY OF J. R. RICE xxiii

and jump conditions are required across quasi-statically propagating surfaces in elastic-plastic materials by the fundamental laws of continuum mechanics and broad, realisticconstitutive constraints (such as the maximum plastic work inequality). Their resultingrestrictions (published in the D. C. Drucker Anniversary Volume), and the latergeneralization of these to dynamic conditions by Drugan and Shen, have been utilizedrepeatedly in elastic-plastic crack growth studies. Not surprisingly, perhaps the mostimportant applications of these discontinuity results are due to JRR himself, in hisfundamental studies of stationary and growing crack fields in ductile single crystals, whereinJRR showed that a precise understanding of possible discontinuity types is absolutelyessential in deriving correct solutions. Beginning in 1985 with his student R. Nikolic on theanti-plane shear crack problem, and in a landmark, pioneering 1987 paper on plane straintensile cracks, JRR produced fascinating analytical solutions for the near-tip fields inelastic-ideally plastic ductile single crystals. These fields differ dramatically from crackfields in isotropic (i.e., polycrystalline) ductile materials, being characterized bydiscontinuous displacements and stresses for stationary cracks, discontinuous velocities forquasi-statically growing cracks, and, in another fascinating paper with Nikolic in 1988, JRRshowed that the near-tip field for a dynamically propagating anti-plane shear crack in aductile single crystal must involve shock surfaces across which stress and velocity jump.JRR and his student M. Saeedvafa generalized the stationary crack ductile single crystalsolutions to incorporate Taylor hardening, revealing even more complex near-tip behavior.

Other major work in the late 1970s and early 1980s included two important paperswith visiting faculty members: one on the crack tip stress and deformation fields for a crackin a creeping solid, with Hermann Riedel; and another heavily-cited paper on crack curvingand kinking in elastic materials, with Brian Cotterell.

For his significant contributions to sciences and engineering, JRR was elected toFellow grade of the American Academy of Arts and Sciences in 1978, Fellow of theAmerican Society of Mechanical Engineers and Membership in the National Academy ofEngineering in 1980, and membership in the National Academy of Sciences in 1981.

The next move was to Harvard University in September 1981. A Gordon McKayChaired Professorship in Engineering Sciences and Geophysics was created for JRR, jointlyin the Division of Applied Sciences and the Department of Earth and Planetary Sciences.He further expanded the scope of his research activities along two major branches inmechanics, namely, fracture of engineering materials and geological materials. At Harvard,he recruited many bright students from all over the world to work on topical fractureproblems in engineering and geology. He directed Peter Anderson to study constrainedcreep cavitation and the Rice-Thomson model, supervised Huajian Gao on threedimensional crack problems, worked with Jwo Pan, Ruzica Nikolic and Maryam Saeedvafaon inelastic behaviors of cracks in single crystal metals, and collaborated with RenataDmowska, Victor Li, Paul Segall, Andy Ruina, Yehuda Ben-Zion, G. Perrin, J.-c. Gu, MarkLinker, Simon T. Tse , G. Zheng, and F. K. Lehner in developing friction laws and shearcrack models of geological faults as related to earthquake events in seismology.

JRR’s recent work on earthquakes has focused on several important aspects of the

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process. One issue is the origin of earthquake complexity, that is, the distribution of eventsof various sizes, as described by the well-established Gutenberg-Richter relationship. Oneprevious explanation was that fault slip, as modeled by friction between two elastic solids,was an inherently chaotic process. In a series of papers that combine elegant analysis andprodigious calculations, JRR and his post-doc, Yehuda Ben-Zion, showed that the chaoticbehavior predicted in these models was the subtle result of numerical discretization andoversimplification of the frictional constitutive relation. Other work was motivated byobservations that slip during an earthquake does not propagate in the fashion predicted byclassical dynamic fracture mechanics with most of the surface slipping for the entireduration of the event. Instead, slip is pulse-like and any point on the surface slips only fora short time. Papers with Zheng and Perrin showed that only certain types of frictionalconstitutive relations were consistent with these observations. Another, very influentialpaper, “Fault Stress States, Pore pressure Distributions and the Weakness of the SanAndreas Fault” addresses a long-standing paradox in earthquake mechanics: A variety ofmeasurements indicate that the San Andreas fault in southern California is much weaker,both in an absolute sense and relative to the surrounding crust, than would be expected froma straightforward interpretation of laboratory friction experiments. JRR showed that thediscrepancy could be resolved by high fluid pressures within the fault zone and summarizeda variety of evidence for this possibility. Another mechanism that can explain thediscrepancy and produce slip in a pulse-like form is dynamic rupture along a bi-materialinterface. JRR has been studying this problem recently together with his student K. Ranjithand Post-Doc A. Cochard, following earlier works of Weertman, Adams, and Andrews andBen-Zion, thus returning to a subject he investigated statically as an undergrad at Lehigh.

In the mid-1980’s, JRR and other faculty members including John Hutchinson andBernie Budiansky formed a joint research team with Tony Evans at the University ofCalifornia at Santa Barbara to study mechanical behavior and toughening mechanisms ofceramics. Between 1988 and 1994, faculty and students at Harvard regularly visited andexchanged ideas with Tony Evans and his research group at UCSB. The Harvard-UCSBcollaboration generated tremendous research output. During this period, JRR worked withJohn Hutchinson, Jian-Sheng Wang, Mark E. Mear and Zhigang Suo on crack growth onor near a bi-material interface. With Jian-Sheng Wang, he developed a model of interfacialembrittlement by hydrogen and solute segregation. This model has been referred to as theRice-Wang Model which provided a basis for the materials community in pursuit of betterdesign of steels. Between 1989 and 1995, JRR worked with Glenn Beltz, Y. Sun and L.Truskinovsky to reformulate the Rice-Thomson model in terms of interactions between acrack and a Peierls dislocation being emitted from the crack tip. This study eliminated theneed to define a core cut-off radius for dislocations and instead established unstable stackingfault energy as the new physical parameter governing the intrinsic ductility of crystals.Rice’s new model caused an instant sensation among materials scientists and physicists andis now used as the new paradigm for understanding brittle-ductile transition of crystals.

Separate from his other activities at Harvard, JRR began to develop a growinginterest in three dimensional crack problems, starting around 1984. Together with Huajian

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Gao, the first of his graduate students at Harvard to work on 3-D crack problems, hedeveloped a series of ingenious methods of analysis based on the idea of 3-D weightfunctions, generalizing a 2-D concept he and Hans Bueckner had developed in the early1970’s. These methods were used to study configurational stability of crack fronts, crackinteraction with dislocation loops and transformation strains, and trapping of crack frontsby tough particles. In 1987, he began to work with K. S. Kim, who spent a year of sabbaticalat Harvard, to generalize these methods to model dynamically propagating 3-D crack fronts.This then led to a burst of his interests in the following years in the spontaneous dynamicsof 3-D tensile crack propagation and of slip ruptures in earthquake dynamics. He directeda number of graduate students, post-docs and visiting scientists on those areas, including K.S. Kim, Yehuda Ben-Zion, G. Perrin, G. Zheng, Phillipe Geubelle, A. Cochard, J. W.Morrissey, and Nadia Lapusta. He also encouraged other leading scientists such as JohnWillis and Daniel Fisher to work in this field. An example of significant discoveries comingout of these activities is a new kind of wave which propagates along the crack front at avelocity different from the usual body and surface elastic wave speeds. JRR continues todayto lead an international research effort in crack and fault dynamics. Needless to say, theoutput of his research group is of the highest quality and generates significant impact on theengineering, materials science and geophysics communities.

As a result of his contributions to science and engineering, JRR received numerousawards and recognitions by professional societies and academic institutions. In 1981, he waselected to Fellow of AAAS. Next year in 1982, he received the George R. Irwin Medalfrom ASTM Committee E-24, shared with John Hutchinson, for “significant contributionsto the development of nonlinear fracture mechanics”. In 1985, he was one of the recipientsof an Honorary Doctor of Science Degree at his alma mater, Lehigh University. In 1988, hewas elected Fellow of the American Geophysical Union, and received the William PragerMedal from the Society of Engineering Science for his “outstanding achievements in solidmechanics”. Two years later, he was elected Fellow of the American Academy ofMechanics and the Royal Society of Edinburgh. In 1992, he received an award from AAMfor “Distinguished Service to the Field of Theoretical and Applied Mechanics”. Thefollowing year he served as Francis Birch Lecturer on “Problems on Earthquake SourceMechanics” at the American Geophysics Union. The next year he received the ASMETimoshenko Medal with the following citation: “for seminal contributions to theunderstanding of plasticity and fracture of engineering materials and applications in thedevelopment in the computational and experimental methods of broad significance inmechanical engineering practice”. In 1996, he was elected as a Foreign Member of theRoyal Society of London for his work on “earthquakes and solid mechanics” and receivedan honorary degree from Northwestern University. In addition, he received the ASMENadai Award for major contributions to the fundamental understanding of plastic flow andfracture processes in engineering and geophysical materials and for the invention of the J-Integral which forms the basis for the practical application of nonlinear fracture mechanicsto the development of standards for the safety of structures. He also received the Francis J.Clamer Medal from the Franklin Institute for Advances in Metallurgy with the citation: “for

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development of the J-Integral for the accurate prediction of elastic-plastic fracture behaviorin metal from easily obtained data”. In 1997, he received an honorary Doctor of Sciencedegree from Brown University. In 1998, a donation from David Hibbitt and Paul Sorensenof HKS, Inc. established the Rice Professorship at Brown in his honor. Recently, he wasawarded the Blaise Pascal Professorship by the Region Ile-de-France for the 1999 calendaryear for research on “Rupture Dynamics in Seismology and Materials Physics”, and he wasthe recipient of an Honorary Doctoral Degree at the University of Paris VI in March 1999.He was elected a Foreign Member (Associé Étrager) of the French Academy of Sciencesin April 2000.

There is no need to place complimentary words here on the impact of his work.The recognitions described in the previous paragraph speak for themselves. His standardsof scholarship and intellectual honesty are the highest. He is always ready to appreciate thegood work of other colleagues, and to give them proper credit. On the other hand, he doesnot hesitate to dispense candid criticism of inconsistent or misguided thinking, though in agentle rather than harsh manner -- as some oral comments in conferences or written bookreviews testify.

A man is as young as he thinks. JRR enjoys long walks, whether in urban ormountain settings, reads broadly in science, history and social commentary, and likeslistening to classical and folk music in his spare time.. He has an excellent sense of humor,a razor-sharp wit and a cheerful disposition. His wife Renata Dmowska, in addition to beinga regular and important scientific collaborator, is an excellent influence on Jim. Renata isan enthusiastic polymath with a warm and cheerful personality and a seemingly endlessarray of interests. She insists that he take much-deserved breaks from his research to attendconcerts, to visit art museums, to travel, to read literature, and to socialize with their largecircle of friends. JRR is increasingly active in his research, full of curiosity, creativity andpersistence. As his students can attest, he is also an excellent teacher in the classroom. Hegives lectures in a humorous, but comprehensive way that can be easily digested by hisaudience. As a thesis advisor, he defines the scope of a research area in which he sees thepotential for advancement. He inspires and encourages, but does not push his students.When a student heads in a wrong direction or reaches a dead end, he wastes no time to steerhim or her back to the right track. His good qualities as an advisor were recognized by hisrecent Excellence in Mentoring Award conferred by the Graduate Student Council ofHarvard University in April 1999.

JRR recently returned from his full year sabbatical leave (January 1999 to January2000) in Paris, France, working in the Département Terre Atmosphère Océan of ÉcoleNormale Supérieure, and also part time at École Polytechnique in Paliseau. His flow ofpublications shows no sign of diminishing and his friends and colleagues surely will hopethat the short legend “J. R. Rice” will appear again and again in the scientific literature formany years to come.

TZE-JER CHUANGGaithersburg, MD

JOHN W. RUDNICKIEvanston, IL

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G. C. Sih and J. R. Rice, “The Bending of Plates of Dissimilar Materials withCracks”, Journal of Applied Mechanics, 31, (1964), pp. 477-482.J. R. Rice and E. J. Brown, “Discussion of ‘Random Fatigue Failure of a MultipleLoad Path Redundant Structure’ by Heller, Heller and Freudenthal”, in Fatigue:An Interdisciplinary Approach (eds. J. Burke, N. Reed and V. Weiss), SyracuseUniversity Press, (1974), pp. 202-206.J. R. Rice and F. P. Beer, “On the Distribution of Rises and Falls in a ContinuousRandom Process”, Transactions ASME (Journal of Basic Engineering), 87D,(1965), pp. 398-404.J. R. Rice and G. C. Sih, “Plane Problems of Cracks in Dissimilar Materials”,Journal of Applied Mechanics, 32, (1965), pp. 418-423.J. R. Rice, F. P. Beer and P. C. Paris, “On the Prediction of Some RandomLoading Characteristics Relevant to Fatigue”, in Acoustical Fatigue in AerospaceStructures (eds. W. Trapp and D. Forney), Syracuse University Press, (1965), pp.121-144.J. R. Rice, “Starting Transients in the Response on Linear Systems to StationaryRandom Loadings”, Journal of Applied Mechanics, 32, (1965) pp. 200-201.J. R. Rice, “Plastic Yielding at a Crack Tip”, in Proceedings of the 1stInternational Conference on Fracture, Sendai, 1965 (eds. T. Yokobori, T.Kawasaki, and J. L. Swedlow), Vol. I, Japanese Society for Strength and Fractureof Materials, Tokyo, (1966), pp. 283-308.J. R. Rice, “An Examination of the Fracture Mechanics Energy Balance from thePoint of View of Continuum Mechanics”, in Proceedings of the 1st InternationalConference on Fracture, Sendai, 1965 (eds. T. Yokobori, T. Kawasaki, and J. L.Swedlow),Vol. I, Japanese Society for Strength and Fracture of Materials, Tokyo,(1966) pp. 309-340.J. R. Rice and F. P. Beer, “First Occurrence Time of High Level Crossings in aContinuous Random Process”, Journal of the Acoustical Society of America, 39,(1966) pp. 323-335.J. R. Rice, “Contained Plastic Deformation Near Cracks and Notches UnderLongitudinal Shear”, International Journal of Fracture Mechanics, 2, (1966) pp.426-447.J. R. Rice and D. C. Drucker, “Energy Changes in Stressed Bodies due to Voidand Crack Growth”, International Journal of Fracture Mechanics, 3, (1967) pp.19-27.J. R. Rice, “Stresses due to a Sharp Notch in a Work Hardening Elastic-PlasticMaterial Loaded by Longitudinal Shear”, Journal of Applied Mechanics, 34,(1967), pp. 287-298.

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J. R. Rice, “The Mechanics of Crack Tip Deformation and Extension by Fatigue”,in Fatigue Crack Propagation, Special Technical Publication 415, ASTM,Philadelphia, (1967), pp. 247-311.J. R. Rice, “Discussion of ‘Stresses in an Infinite Strip Containing a Semi-InfiniteCrack’ by W.G. Knauss”, Journal of Applied Mechanics, 34, (1967), pp. 248-250.J. R. Rice, “A Path Independent Integral and the Approximate Analysis of StrainConcentration by Notches and Cracks”, Journal of Applied Mechanics, 35, (1968),pp. 379-386.J. R. Rice and G. F. Rosengren, “Plane Strain Deformation Near a Crack in aPower Law Hardening Material”, Journal of the Mechanics and Physics of Solids,16, (1968), pp. 1-12.J. R. Rice, “The Elastic-Plastic Mechanics of Crack Extension”, InternationalJournal of Fracture Mechanics, 4, (1968), pp. 41-49 (also published inInternational Symposium on Fracture Mechanics, Wolters-Noordhoff Publ.,Groningen, 1968,41-49).J. R. Rice, “Mathematical Analysis in the Mechanics of Fracture”, Chapter 3 ofFracture: An Advanced Treatise (Vol. 2, Mathematical Fundamentals) (ed. H.Liebowitz), Academic Press, N.Y., (1968), pp. 191-311.J. R. Rice and N. Levy, “Local Heating by Plastic Deformation at a Crack Tip”,in Physics of Strength and Plasticity (ed. A. S. Argon), M.I.T. Press, Cambridge,Mass., (1969), pp. 277-293.J. R. Rice and D. M. Tracey, “On the Ductile Enlargement of Voids in TriaxialStress Fields”, Journal of the Mechanics and Physics of Solids, 17, (1969), pp.201-217.D. C. Drucker and J. R. Rice, “Plastic Deformation on Brittle and DuctileFracture”, Engineering Fracture Mechanics, 1, (1970), pp. 577-602.J. Kestin and J. R. Rice, “Paradoxes in the Application of Thermodynamics toStrained Solids”, in A Critical Review of Thermodynamics (eds. E.G. Stuart, B.Gal-Or and A.J. Brainard), Mono Book Corp., Baltimore, MD (1970), pp. 275-298.H. D. Hibbitt, P. V. Marcal and J. R. Rice, “A Finite Element Formulation forProblems of Large Strain and Large Displacement”, International Journal of Solidsand Structures, 6, (1970), pp. 1069-1086.J. R. Rice, “On the Structure of Stress-Strain Relations for Time-Dependent PlasticDeformation in Metals”, Journal of Applied Mechanics, 37, (1970), pp. 728-737.J. R. Rice and M. A. Johnson, “The Role of Large Crack Tip Geometry Changesin Plane Strain Fracture”, in Inelastic Behavior of Solids (eds. M. F. Kanninen, etal.), McGraw-Hill, N.Y., (1970), pp. 641-672.N. Levy, P. V. Marcal, W. J. Ostergren and J. R. Rice, “Small Scale Yielding Neara Crack in Plane Strain: A Finite Element Analysis”, International Journal ofFracture Mechanics, 7, (1971), pp. 143-156.

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J. R. Rice and N. Levy, “The Part-Through Surface Crack in an Elastic Plate”,Journal of Applied Mechanics, 39, (1972), pp. 185-194.N. Levy, P. V. Marcal and J. R. Rice, “Progress in Three-Dimensional Elastic-Plastic Stress Analysis for Fracture Mechanics”, Nuclear Engineering and Design,17, (1971), pp. 64-75.J. R. Rice, “Inelastic Constitutive Relations for Solids: An Internal VariableTheory and Its Application to Metal Plasticity”, Journal of the Mechanics andPhysics of Solids, 19, (1971), pp. 433-455.J. R. Rice, “Some Remarks on Elastic Crack Tip Stress Fields”, InternationalJournal of Solids and Structures, 8, (1972), pp. 571-578.J. R. Rice and D. M. Tracey, “Computational Fracture Mechanics”, in Numericaland Computer Methods in Structural Mechanics (eds. S. J. Fenves et al.),Academic Press, N.Y., (1973), pp. 585-623.B. Budiansky and J. R. Rice, “Conservation Laws and Energy-Release Rates”,Journal of Applied Mechanics, 40, (1973), pp. 201-203.J. R. Rice and M. A. Chinnery, “On the Calculation of Changes in the Earth’sInertia Tensor due to Faulting”, Geophysical Journal of the Royal AstronomicalSociety, 29, (1972), pp. 79-90.R. J. Bucci, P. C. Paris, J. D. Landes and J. R. Rice, “J Integral EstimationProcedures”, in Fracture Toughness, Special Technical Publication 514, Part 2,ASTM, Philadelphia, (1972), pp. 40-69.J. R. Rice, “The Line Spring Model for Surface Flaws”, in The Surface Crack:Physical Problems and Computational Solutions (ed. J.L. Swedlow), ASME,N.Y., (1972), pp. 171-185.R. Hill and J. R. Rice, “Constitutive Analysis of Elastic/Plastic Crystals atArbitrary Strain”, Journal of the Mechanics and Physics of Solids, 20, (1972), pp.401-413.J. R. Rice, “Elastic-Plastic Fracture Mechanics (Remarks for Round TableDiscusison on Fracture at the 13th International Congress of Theoretical andApplied Mechanics, Moscow, 1972)“, Engineering Fracture Mechanics, 5, (1973),pp. 1019-1022.A. C. Palmer and J. R. Rice, “The Growth of Slip Surfaces in the ProgressiveFailure of Overconsolidated Clay”, Proceedings of the Royal Society of London,A 332, (1973), pp. 527-548.J. R. Rice, “Plane Strain Slip Line Theory for Anisotropic Rigic/Plastic Materials”,Journal of the Mechanics and Physics of Solids, 21, (1973), pp. 63-74.J. R. Rice, P. C. Paris and J. G. Merkle, “Some Further Results of J-IntegralAnalysis and Estimates”, in Progress in Flaw Growth and Fracture ToughnessTesting, Special Tech. Publication 536, ASTM, Philadelphia, PA (1973), pp. 231-245.

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R. Hill and J. R. Rice, “Elastic Potentials and the Structure of InelasticConstitutive Laws”, SIAM Journal of Applied Mathematics, 25, (1973), pp. 448-461.J. R. Rice, “Continuum Plasticity in Relation to Microscale DeformationMechanisms”, in Metallurgical Effects at High Strain Rate (eds. R.W. Rohde etal.), Plenum Press, (1973), pp. 93-106.J. R. Rice, “Elastic-Plastic Models for Stable Crack Growth”, in Mechanics andMechanisms of Crack Growth (ed. M.J. May), British Steel Corporation PhysicalMetallurgy Centre Publication, April 1973 (issued 1975), pp. 14-39.T.- J. Chuang and J. R. Rice, “The Shape of Intergranular Creep Cracks Growingby Surface Diffusion”, Acta Metallurgica, 21, (1973), pp. 1625-1628.R. O. Ritchie, J. F. Knott and J. R. Rice, “On the Relationship Between CriticalTensile Stress and Fracture Toughness in Mild Steel”, Journal of the Mechanicsand Physics of Solids, 21, (1973), pp. 395-410.L. B. Freund and J. R. Rice, “On the Determination of Elastodynamic Crack TipStress Fields, International Journal of Solids and Structures, 10, (1974), pp. 411-417.J. R. Rice, “Limitations to the Small Scale Yielding Approximation for Crack TipPlasticity”, Journal of the Mechanics and Physics of Solids, 22, (1974), pp. 17-26.J. R. Rice and R. M. Thomson, “Ductile vs. Brittle Behavior of Crystals”,Philosophical Magazine, 29, (1974), 73-97.J. R. Rice, “The Initiation and Growth of Shear Bands”, in Plasticity and SoilMechanics (edited by A. C. Palmer), Cambridge University EngineeringDepartment, Cambridge, (1973) pp. 263-274.J. C. Nagtegaal, D. M. Parks and J. R. Rice, “On Numerically Accurate FiniteElement Solutions in the Fully Plastic Range”, Computer Methods in AppliedMechanics and Engineering, 4, (1974) pp. 153-177.J. R. Rice, “Continuum Mechanics and Thermodynamics of Plasticity in Relationto Microscale Deformation Mechanisms”, Chapter 2 of Constitutive Equations inPlasticity (ed. A. S. Argon), M.I.T. Press, (1975), pp. 23-79.R. M. McMeeking and J. R. Rice, “Finite-Element Formulations for Problems ofLarge Elastic-Plastic Deformation”, International Journal of Solids and Structures,11, (1975), pp. 601-616.J. R. Rice, “On the Stability of Dilatant Hardening for Saturated Rock Masses”,Journal of Geophysical Research, 80, (1975), pp. 1531-1536.J. R. Rice, “Discussion of ‘The Path Independence of the J-Contour Integral’ by G.G. Chell and P. T. Heald”, International Journal of Fracture, 11, (1975), pp. 352-353.J. W. Rudnicki and J. R. Rice, “Conditions for the Localization of Deformation inPressure-Sensitive Dilatant Materials”, Journal of the Mechanics and Physics ofSolids, 23, (1975) pp. 371-394.

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S. Storen and J. R. Rice, “Localized Necking in Thin Sheets”, Journal of theMechanics and Physics of Solids, 23, (1975), pp. 421-441.J. R. Rice, “Some Mechanics Research Topics Related to the HydrogenEmbrittlement of Metals” (discussion appended to paper by J. P. Hirth and H. H.Johnson); Corrosion, 32, (1976), pp. 22-26.J. R. Rice and M. P. Cleary, “Some Basic Stress-Diffusion Solutions for Fluid-Saturated Elastic Porous Media with Compressible Constituents”, Reviews ofGeophysics and Space Physics, 14, (1976), pp. 227-241.J. R. Rice, “Hydrogen and Interfacial Cohesion”, in Effect of Hydrogen onBehavior of Materials (eds. A.W. Thompson and I.M. Bernstein), MetallurgicalSociety of AIME, (1976), pp. 455-466.L.B. Freund, D.M. Parks and J. R. Rice, “Running Ductile Fracture in aPressurized Line Pipe”, in Mechanics of Crack Growth, Special TechnicalPublication 590, ASTM, Philadephia, (1976), pp. 243-262.J. R. Rice, “The Localization of Plastic Deformation”, in Theoretical and AppliedMechanics (Proceedings of the 14th International Congress on Theoretical andApplied Mechanics, Delft, 1976, ed. W.T. Koiter), Vol. 1, North-HollandPublishing Co., (1976), 207-220.J. R. Rice and D. A. Simons, “The Stabilization of Spreading Shear Faults byCoupled Deformation-Diffusion Effects in Fluid-Infiltrated Porous Materials”,Journal of Geophysical Research, 81, (1976), pp. 5322-5334.J. R. Rice, “Elastic-Plastic Fracture Mechanics”, in The Mechanics of Fracture(ed. F. Erdogan), Applied Mechanics Division (AMD) Volume 19, AmericanSociety of Mechanical Engineers, New York, (1976), pp. 23-53.J. R. Rice, “Mechanics Aspects of Stress Corrosion Cracking and HydrogenEmbrittlement”, in Stress Corrosion Cracking and Hydrogen Embrittlement ofIron Base Alloys_ (eds. R. W. Staehle et al.), National Association of CorrosionEngineers, Houston, (1977), pp. 11-15.A. P. Kfouri and J. R. Rice, “Elastic/Plastic Separation Energy Rate for CrackAdvance in Finite Growth Steps”, in Fracture 1977 (eds. D.M.R. Taplin et al.),Vol. 1, Solid Mechanics Division Publication, University of Waterloo, Canada,(1977), pp. 43-59.R. J. Asaro and J. R. Rice, “Strain Localization in Ductile Single Crystals”, Journalof the Mechanics and Physics of Solids, 25, (1977), pp. 309-338.J. R. Rice, “Pore Pressure Effects in Inelastic Constitutive Formulations forFissured Rock Masses”, in Advances in Civil Engineering Through EngineeringMechanics (Proceedings of 2nd ASCE Engineering Mechanics Division SpecialtyConference, Raleigh, N.C., 1977), American Society of Civil Engineers, NewYork, (1977), pp. 295-297.

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J. R. Rice, “Fracture Mechanics Model for Slip Surface Propagation in Soil andRock Masses”, in Advances in Civil Engineering Through Engineering Mechanics(Proceedings of 2nd ASCE Engineering Mechanics Division Specialty Conference,Raleigh, N.C., 1977), American Society of Civil Engineers, New York, NY(1977), pp. 373-376.J. R. Rice, J. W. Rudnicki and D. A. Simons, “Deformation of Spherical Cavitiesand Inclusions in Fluid-Infiltrated Elastic Materials”, International Journal ofSolids and Structures, 14, (1978), pp. 289-303.A. Needleman and J. R. Rice, “Limits to Ductility Set by Plastic FlowLocalization”, in Mechanics of Sheet Metal Forming (Proceedings of GeneralMotors Research Laboratories Symposium, October 1977, ed. D.P. Koistinen andN.-M. Wang), Plenum Press, (1978), pp. 237-267.J. R. Rice, “Some Computational Problems in Elastic-Plastic Crack Mechanics”,in Numerical Methods in Fracture Mechanics (Proceedings of the FirstInternational Conference on Numerical Methods in Fracture Mechanics, Swansea,Wales, 1978; eds. A. R. Luxmoore and D. R. J. Owen), Department of CivilEngineering, University College of Swansea, Wales, (1978), pp. 434-449.J. R. Rice, “Thermodynamics of the Quasi-Static Growth of Griffith Cracks”,Journal of the Mechanics and Physics of Solids, 26, (1978) pp. 61-78.J. R. Rice and E. P. Sorensen, “Continuing Crack Tip Deformation and Fracturefor Plane-Strain Crack Growth in Elastic-Plastic Solids”, Journal of the Mechanicsand Physics of Solids, 26, (1978), pp. 163-186.B. Budiansky and J. R. Rice, “On the Estimation of a Crack Fracture Parameter byLong-Wavelength Scattering”, Journal of Applied Mechanics, 45, (1978), pp. 453-454.V. N. Nikolaevskii and J. R. Rice, “Current Topics in Non-elastic Deformation ofGeological Materials”, in High-Pressure Science and Technology: Sixth AIRAPTConference, Volume 2: Applications and Mechanical Properties (ed. K.D.Timmerhaus and M.S. Barber), Plenum Press, New York, NY (1979), pp. 455-464.J. R. Rice, “Theory of Precursory Processes in the Inception of EarthquakeRupture”, in Proceedings of the Symposium on Physics of Earthquake Sources (atGeneral Assembly of International Association of Seismology and Physics of theEarth’s Interior, Durham, England, August 1977), Gerlands Beitrage zurGeophysik, 88, (1979), pp. 91-127.J. R. Rice and J. W. Rudnicki, “Earthquake Precursory Effects due to Pore FluidStabilization of a Weakening Fault Zone”, Journal of Geophysical Research, 84,(1979), pp. 2177-2193.J. B. Walsh and J. R. Rice, “Local Changes in Gravity Resulting fromDeformation”, Journal of Geophysical Research, 84, (1979) pp. 165-170.

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T.- J. Chuang, K. I. Kagawa, J. R. Rice and L. B. Sills, “Non-equilibrium Modelsfor Diffusive Cavitation of Grain Interfaces”, Acta Metallurgica, Overview PaperNo. 2, 27, (1979), pp. 265-284.J. R. Rice, R. M. McMeeking, D. M. Parks and E. P. Sorensen, “Recent FiniteElement Studies in Plasticity and Fracture Mechanics”, in Proceedings of theFENOMECH '78 Conference (Stuttgart, edited by K.S. Pister et al.), North-Holland Publ. Co., Vol. 2, (1979), pp. 411-442; also, Computer Methods inApplied Mechanics and Engineering, 17/18, (1979), pp. 411-442.W. Kohn and J. R. Rice, “Scattering of Long Wavelength Elastic Waves formLocalized Defects in Solids”, Journal of Applied Physics, 50, (1979), pp. 3346-3353.J. R. Rice, “The Mechanics of Quasi-static Crack Growth”, in Proceedings of the8th U.S. National Congress of Applied Mechanics (at U.C.L.A., June 1978; ed. R.E. Kelly), Western Periodicals Co., North Hollywood, California, (1979), pp. 191-216.B. Budiansky and J. R. Rice, “An Integral Equation for Dynamic Elastic Responseof an Isolated 3-D Crack”, Wave Motion, 1, (1979), pp. 187-192.J. R. Rice, “Plastic Creep Flow Processes in Fracture at Elevated Temperature”,in Time-Dependent Fracture of Materials at Elevated Temperature (ed. S.M.Wolf), U.S. Department of Energy Report CONF 790236 UC-25 (June 1979), pp.130-145.B. Budiansky, D. C. Drucker, G. S. Kino and J. R. Rice, “The Pressure Sensitivityof a Clad Optical Fiber”, Applied Optics, 18, (1979), pp. 4085-4088.B. Cotterell and J. R. Rice, “Slightly Curved or Kinked Cracks”, InternationalJournal of Fracture, 16, (1980), pp. 155-169.A. G. Evans, J. R. Rice and J. P. Hirth, “The Suppression of Cavity Formation inCeramics: Prospects for Superplasticity”, Journal of the American CeramicSociety, 63, (1980), pp. 368-375.J. R. Rice, “The Mechanics of Earthquake Rupture”, in Physics of the Earth’sInterior (Proc. International School of Physics ‘Enrico Fermi’, Course 78, 1979;(ed. A. M. Dziewonski and E. Boschi), Italian Physical Society and North-HollandPubl. Co., (1980), pp. 555-649.J. R. Rice, “Discussion on ‘Outstanding Problems in Geodynamics: Mechanismsof Faulting"', in Physics of the Earth’s Interior (Proc. International School ofPhysics ‘Enrico Fermi’, Course 78, 1979; ed. A. M. Dziewonski and E. Boschi),Italian Physical Society and North-Holland Publ. Co., (1980) pp. 713-716.J. R. Rice and J. W. Rudnicki, “A Note on Some Features of the Theory ofLocalization of Deformation”, International Journal of Solids and Structures, 16,(1980), pp. 597-605.H. Riedel and J. R. Rice, “Tensile Cracks in Creeping Solids”, in FractureMechanics: Twelfth Conference (ed. P.C. Paris), Special Technical Publication700, ASTM, Philadelphia, (1980), pp. 112-130.

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J. R. Rice, W. J. Drugan and T. L. Sham, “Elastic-Plastic Analysis of GrowingCracks”, in Fracture Mechanics: Twelfth Conference (ed. P. C. Paris), SpecialTechnical Publication 700, ASTM, Philadelphia, PA (1980), pp. 189-221.A. Needleman and J. R. Rice, “Plastic Creep Flow Effects in the DiffusiveCavitation of Grain Boundaries”, Acta Metallurgica, Overview Paper No. 9, 28,(1980), pp. 1315-1332.J. P. Hirth and J. R. Rice, “On the Thermodynamics of Adsorption at Interfaces asit Influences Decohesion”, Metallurgical Transactions, 11A, (1980), pp. 1501-1511.L. Hermann and J. R. Rice, “Comparison of Theory and Experiment for Elastic-Plastic Plane-Strain Crack Growth”, Metal Science, 14, (1980), pp. 285-291.J. R. Rice, “Pore-Fluid Processes in the Mechanics of Earthquake Rupture”, inSolid Earth Geophysics and Geotechnology (ed. S. Nemat-Nasser), AmericanSociety of Mechanical Engineers, Appl. Mech. Div. Volume 42, New York, NY(1980), pp. 81-89.J. R. Rice, “Elastic Wave Emission from Damage Processes”, Journal ofNondestructive Evaluation, 1, (1980), pp. 215-224.J. R. Rice and T.- J. Chuang, “Energy Variations in Diffusive Cavity Growth”,Journal of the American Ceramic Society, 64, (1981), pp. 46-53.J. R. Rice, “Creep Cavitation of Grain Interfaces”, in Three-DimensionalConstitutive Relations and Ductile Fracture (ed. S. Nemat-Nasser), North-HollandPubl. Co., (1981), pp. 173-184.J. R. Rice, “Constraints on the Diffusive Cavitation of Isolated Grain BoundaryFacets in Creeping Polycrystals”, Acta Metallurgica, 29, (1981), pp. 675-681.F. K. Lehner, V. C. Li and J. R. Rice, “Stress Diffusion along Rupturing PlateBoundaries”, Journal of Geophysical Research, 86, (1981), pp. 6155-6169.J. R. Rice, “Elastic-Plastic Crack Growth”, in Mechanics of Solids: The RodneyHill 60th Anniversary Volume (ed. H.G. Hopkins and M.J. Sewell), PergamonPress, Oxford and New York, (1982), pp. 539-562.W. J. Drugan, J. R. Rice and T.-L. Sham, “Asymptotic Analysis of Growing PlaneStrain Tensile Cracks in Elastic-Ideally Plastic Solids”, Journal of the Mechanicsand Physics of Solids, 30, 1982, pp. 447-473; erratum, 31, (1983), p. 191.J. R. Rice and A. L. Ruina, “Stability of Steady Frictional Slipping”, Journal ofApplied Mechanics, 50, (1983), pp. 343-349.J. Pan and J. R. Rice, “Rate Sensitivity of Plastic Flow and Implications for YieldSurface Vertices”, International Journal of Solids and Structures, 19, (1983), pp.973-987.V. C. Li and J. R. Rice, “Pre-seismic Rupture Progression and Great EarthquakeInstabilities at Plate Boundaries”, Journal of Geophysical Research, 88, (1983), pp.4231-4246.

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V. C. Li and J. R. Rice, "Precursory Surface Deformation in Great Plate BoundaryEarthquake Sequences", Bulletin of the Seismological Society of America, 73,(1983), pp. 1415-1434J. R. Rice and J.-c. Gu, "Earthquake Aftereffects and Triggered SeismicPhenomena", Pure and Applied Geophysics, 121, (1983), pp. 187-219.J. R. Rice, "Constitutive Relations for Fault Slip and Earthquake Instabilities",Pure and Applied Geophysics, 121, (1983), pp. 443-475.J. R. Rice, "On the Theory of Perfectly Plastic Anti-Plane Straining", Mechanicsof Materials, 3, (1984), pp. 55-80.W. J. Drugan and J. R. Rice, "Restrictions on Quasi-Statically Moving Surfacesof Strong Discontinuity in Elastic-Plastic Solids", in Mechanics of MaterialBehavior (the D.C. Drucker anniversary volume, ed. G.J. Dvorak and R.T. Shield),Elsevier, (1984), pp. 59-73.J. R. Rice, "Shear Instability in Relation to the Constitutive Description of FaultSlip", in Rockbursts and Seismicity in Mines (ed. N.C. Gay and E.H. Wainwright),Symp. Ser. No. 6, S. African Inst. Mining and Metallurgy, Johannesburg, (1984),pp. 57-62.J.-c. Gu, J. R. Rice, A. L. Ruina and S.T. Tse, "Slip Motion and Stability of aSingle Degree of Freedom Elastic System with Rate and State DependentFriction", Journal of the Mechanics and Physics of Solids, 32, (1984), pp. 167-196.J. R. Rice, "Comments on 'On the Stability of Shear Cracks and the Calculation ofCompressive Strength' by J.K. Dienes", Journal of Geophysical Research, 89,(1984), pp. 2505-2507.J. R. Rice, "Shear Localization, Faulting and Frictional Slip: Discusser’s Report",in Mechanics of Geomaterials (Proc. IUTAM W. Prager Symp., Sept. 1983, ed.Z.P. Bazant), J. Wiley and Sons Ltd., (1985), Chp. 11, pp. 211-216.J. R. Rice, "Conserved Integrals and Energetic Forces", in Fundamentals ofDeformation and Fracture (Eshelby Memorial Symposium), ed. B.A. Bilby, K.J.Miller and J.R. Willis, Cambridge Univ. Press, (1985) pp. 33-56.P. M. Anderson and J. R. Rice, "Constrained Creep Cavitation of Grain BoundaryFacets", Acta Metallurgica, 33, (1985), pp. 409-422.J. R. Rice, "First Order Variation in Elastic Fields due to Variation in Location ofa Planar Crack Front", Journal of Applied Mechanics, 52, (1985), pp. 571-579.S. T. Tse, R. Dmowska and J. R. Rice, "Stressing of Locked Patches along aCreeping Fault", Bulletin of the Seismological Society of America, 75, (1985), pp.709-736.J. R. Rice and R. Nikolic, "Anti-plane Shear Cracks in Ideally Plastic Crystals",Journal of the Mechanics and Physics of Solids, 33, (1985), pp. 595-622.J. R. Rice, "Three Dimensional Elastic Crack Tip Interactions with TransformationStrains and Dislocations", International Journal of Solids and Structures, 21,(1985), pp. 781-791.

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J. R. Rice (Editor), Solid Mechanics Research Trends and Opportunities (Reportof the Committee on Solid Mechanics Research Directions of the AppliedMechanics Division, American Society of Mechanical Engineers), AppliedMechanics Reviews, 38, (1985), pp. 1247-1308; published simultaneously asAMD-Vol. 70, ASME Book No. I00198.J. R. Rice, "Fracture Mechanics", in Solid Mechanics Research Trends andOpportunities, ed. J. R. Rice, Applied Mechanics Reviews, 38, (1985), pp. 1271-1275; published simultaneously in AMD-Vol. 70, ASME Book No. I00198.J. R. Rice and S. T. Tse, "Dynamic Motion of a Single Degree of Freedom Systemfollowing a Rate and State Dependent Friction Law", Journal of GeophysicalResearch, 91, (1986), pp. 521-530.R. Dmowska and J. R. Rice, "Fracture Theory and Its Seismological Applications",in Continuum Theories in Solid Earth Physics (Vol. 3 of series "Physics andEvolution of the Earth's Interior"; ed. R. Teisseyre), Elsevier and Polish ScientificPublishers, (1986), pp. 187-255.H. Gao and J. R. Rice, "Shear Stress Intensity Factors for a Planar Crack withSlightly Curved Front", Journal of Applied Mechanics, 53, (1986), pp. 774-778.S. T. Tse and J. R. Rice, "Crustal Earthquake Instability in Relation to the DepthVariation of Frictional Slip Properties", Journal of Geophysical Research, 91,(1986), pp. 9452-9472.P. M. Anderson and J. R. Rice, "Dislocation Emission from Cracks in Crystals orAlong Crystal Interfaces", Scripta Metallurgica, 20, (1986), pp. 1467-1472.J.-S. Wang, P.M. Anderson and J. R. Rice, "Micromechanics of the Embrittlementof Crystal Interfaces", in Mechanical Behavior of Materials - V (Proceedings ofthe 5th International Conference, Beijing, 1987; ed. M.G. Yan, S.H. Zhang andZ.M. Zheng), Pergamon Press, (1987), pp. 191-198.J. R. Rice, "Mechanics of Brittle Cracking of Crystal Lattices and Interfaces", inChemistry and Physics of Fracture (proceedings of a 1986 NATO AdvancedResearch Workshop; edited by R.M. Latanision and R.H. Jones), Martinus NijhoffPublishers, Dordrecht, (1987), pp. 22-43.P. M. Anderson and J. R. Rice, "The Stress Field and Energy of a Three-Dimensional Dislocation Loop at a Crack Tip", Journal of the Mechanics andPhysics of Solids, 35, (1987), pp. 743-769.H. Gao and J. R. Rice, "Somewhat Circular Tensile Cracks", International Journalof Fracture, 33, (1987), 155-174.J. R. Rice, "Two General Integrals of Singular Crack Tip Deformation Fields",Journal of Elasticity, 20, (1988), pp. 131-142.H. Gao and J. R. Rice, "Nearly Circular Connections of Elastic Half Spaces",Journal of Applied Mechanics, 54, (1987) pp. 627-634.R. Hill and J. R. Rice, "Discussion of 'A Rate-Independent Constitutive Theory forFinite Inelastic Deformation' by M.M. Carroll", Journal of Applied Mechanics, 54,(1987), pp. 745-747.

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V. C. Li and J. R. Rice, "Crustal Deformation in Great California EarthquakeCycles", Journal of Geophysical Research, 92, (1987), pp. 11,533-11,551.J. R. Rice, "Tensile Crack Tip Fields in Elastic-Ideally Plastic Crystals",Mechanics of Materials, 6, (1987), pp. 317-335.J. W. Hutchinson, M. E. Mear and J. R. Rice, "Crack Paralleling an InterfaceBetween Dissimilar Materials", Journal of Applied Mechanics, 54, (1987), pp. 828-832.J. R. Rice and M. Saeedvafa, "Crack Tip Singular Fields in Ductile Crystals withTaylor Power-Law Hardening, I: Anti-Plane Shear", Journal of the Mechanics andPhysics of Solids, 36, (1988), pp. 189-214.J. R. Rice, "Elastic Fracture Mechanics Concepts for Interfacial Cracks", Journalof Applied Mechanics, 55, (1988), pp. 98-103.R. Dmowska, J. R. Rice, L.C. Lovison and D. Josell, "Stress Transfer and SeismicPhenomena in Coupled Subduction Zones During the Earthquake Cycle", Journalof Geophysical Research, 93, (1988), pp. 7869-7884.J. R. Rice, "Crack Fronts Trapped by Arrays of Obstacles: Solutions Based onLinear Perturbation Theory", in Analytical, Numerical and Experimental Aspectsof Three Dimensional Fracture Processes (eds. A. J. Rosakis, K. Ravi-Chandarand Y. Rajapakse), ASME Applied Mechanics Division Volume 91, AmericanSociety of Mechanical Engineers, New York, (1988), pp. 175-184.J. Yu and J. R. Rice, "Dislocation Pinning Effect of Grain Boundary SegregatedSolutes at a Crack Tip", in Interfacial Structure, Properties and Design (eds. M.H.Yoo, W.A.T. Clark and C.L. Briant), Materials Research Society Proc. Vol. 122,(1988), pp. 361-366.R. Nikolic and J. R. Rice, "Dynamic Growth of Anti-Plane Shear Cracks in IdeallyPlastic Crystals", Mechanics of Materials, 7, (1988), pp. 163-173.J. R. Rice, "Weight Function Theory for Three-Dimensional Elastic CrackAnalysis", in Fracture Mechanics: Perspectives and Directions (TwentiethSymposium), Special Technical Publication 1020, eds. R. P. Wei and R. P.Gangloff, ASTM, Philadelphia, (1989), pp. 29-57.H. Gao and J. R. Rice, "Application of 3D Weight Functions - II. The Stress Fieldand Energy of a Shear Dislocation Loop at a Crack Tip", Journal of the Mechanicsand Physics of Solids, 37, (1989), pp. 155-174.J. R. Rice and J.-S. Wang, "Embrittlement of Interfaces by Solute Segregation",Materials Science and Engineering, A107, (1989), pp. 23-40.M. Saeedvafa and J. R. Rice, "Crack Tip Singular Fields in Ductile Crystals withTaylor Power-Law Hardening, II: Plane Strain", Journal of the Mechanics andPhysics of Solids, 37, (1989), pp. 673-691.H. Gao and J. R. Rice, "A First Order Perturbation Analysis of Crack Trapping byArrays of Obstacles", Journal of Applied Mechanics, 56, (1989), pp. 828-836.J. R. Rice, D. E. Hawk and R. J. Asaro, "Crack Tip Fields in Ductile Crystals",International Journal of Fracture, 42, (1990), pp. 301-321.

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J. R. Rice, "Summary of Studies on Crack Tip Fields in Ductile Crystals", inYielding, Damage, and Failure of Anisotropic Solids (ed. J. P. Boehler),Mechanical Engineering Publications (London), (1990), pp. 49-52.P. M. Anderson, J.-S. Wang and J. R. Rice, "Thermodynamic and MechanicalModels of Interfacial Embrittlement", in Innovations in Ultrahigh-Strength SteelTechnology (eds. G. B. Olson, M. Azrin and E. S. Wright), Sagamore ArmyMaterials Research Conference Proceedings, Volume 34, (1990), pp. 619-649.J. R. Rice, Z. Suo and J.-S. Wang, "Mechanics and Thermodynamics of BrittleInterfacial Failure in Bimaterial Systems", in Metal-Ceramic Interfaces (eds. M.Rühle, A. G. Evans, M. F. Ashby and J. P. Hirth), Acta-Scripta MetallurgicaProceedings Series, Volume 4, Pergamon Press, (1990), pp. 269-294.Y. Sun, J. R. Rice and L. Truskinovsky, "Dislocation Nucleation Versus Cleavagein Ni3Al and Ni", in High-Temperature Ordered Intermetallic Alloys (eds. L. A.Johnson, D. T. Pope and J. O. Stiegler), Materials Research Society Proc. Vol.213, (1991) pp. 243-248.G. E. Beltz and J. R. Rice, "Dislocation Nucleation Versus Cleavage Decohesionat Crack Tips", in Modeling the Deformation of Crystalline Solids (eds. T. C.Lowe, A. D. Rollett, P. S. Follansbee and G. S. Daehn), The Minerals, Metals andMaterials Society (TMS), Warrendale, Penna., (1991), pp. 457-480.H. Gao, J. R. Rice and J. Lee, "Penetration of a Quasistatically Slipping Crack intoa Seismogenic Zone of Heterogeneous Fracture Resistance", Journal ofGeophysical Research, 96, (1991), 21535-21548J. R. Rice, "Fault Stress States, Pore Pressure Distributions, and the Weakness ofthe San Andreas Fault", in Fault Mechanics and Transport Properties in Rocks(eds. B. Evans and T.-F. Wong), Academic Press, (1992), pp. 475-503.J. R. Rice, "Dislocation Nucleation from a Crack Tip: An Analysis Based on thePeierls Concept", Journal of the Mechanics and Physics of Solids, 40, (1992), pp.239-271.G. E. Beltz and J. R. Rice, "Dislocation Nucleation at Metal/Ceramic Interfaces",Acta Metallurgica et Materiala, 40, Supplement, (1992), pp. s321-s331.J. R. Rice, G. E. Beltz and Y. Sun, "Peierls Framework for Analysis of DislocationNucleation from a Crack Tip", in Topics in Fracture and Fatigue (ed. A. S.Argon), Springer Verlag, (1992), Chapter 1, pp. 1-58.M. Saeedvafa and J. R. Rice, "Crack Tip Fields in a Material with ThreeIndependent Slip Systems: NiAl Single Crystal", Modelling and Simulation inMaterials Science and Engineering, 1, (1992), pp. 53-71.Y. Ben-Zion, J. R. Rice and R. Dmowska, "Interaction of the San Andreas FaultCreeping Segment with Adjacent Great Rupture Zones, and EarthquakeRecurrence at Parkfield, Journal of Geophysical Research, 98, (1993), pp. 2135-2144.

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J. R. Rice, "Mechanics of Solids", section of the article on "Mechanics", inEncyclopaedia Britannica (1993 printing of the 15th edition), volume 23, pp. 734-747 and 773, (1993).J. R. Rice, "Spatio-temporal Complexity of Slip on a Fault", Journal ofGeophysical Research, 98, (1993), pp. 9885-9907.Y. Sun, G. E. Beltz and J. R. Rice, "Estimates from Atomic Models of Tension-Shear Coupling in Dislocation Nucleation from a Crack Tip", Materials Scienceand Engineering A, 170, (1993), pp. 67-85.Y. Ben-Zion and J. R. Rice, "Earthquake Failure Sequences Along a Cellular FaultZone in a 3D Elastic Solid Containing Asperity and Non-Asperity Regions",Journal of Geophysical Research, 98, (1993), pp. 14,109-14,131.J. R. Rice and G. E. Beltz, "The Activation Energy for Dislocation Nucleation ata Crack", Journal of the Mechanics and Physics of Solids, 42, (1994), pp. 333-360.J. R. Rice, Y. Ben-Zion and K.-S. Kim, "Three-Dimensional Perturbation Solutionfor a Dynamic Planar Crack Moving Unsteadily in a Model Elastic Solid", Journalof the Mechanics and Physics of Solids, 42, (1994), pp. 813-843.G. Perrin and J. R. Rice, "Disordering of a Dynamic Planar Crack Front in aModel Elastic Medium of Randomly Variable Toughness", Journal of theMechanics and Physics of Solids, 42, (1994), pp. 1047-1064.Y. Ben-Zion and J. R. Rice, "Quasi-Static Simulations of Earthquakes and SlipComplexity along a 2D Fault in a 3D Elastic Solid", in The MechanicalInvolvement of Fluids in Faulting, Proceedings of June 1993 National EarthquakeHazards Reduction Program Workshop LXIII, USGS Open-File Report 94-228,Menlo Park, CA, (1994), pp. 406-435.Y. Ben-Zion and J. R. Rice, "Slip Patterns and Earthquake Populations alongDifferent Classes of Faults in Elastic Solids", Journal of Geophysical Research,100, (1995), pp. 12959-12983.G. Perrin, J. R. Rice and G. Zheng, "Self-healing Slip Pulse on a FrictionalSurface", Journal of the Mechanics and Physics of Solids, 43, (1995), pp. 1461-1495.P. H. Geubelle and J. R. Rice, "A Spectral Method for Three-DimensionalElastodynamic Fracture Problems", Journal of the Mechanics and Physics ofSolids, 43, (1995), pp. 1791-1824.J. R. Rice, "Text of Timoshenko Medal Speech", in Applied Mechanics Newsletter(ed. B. Moran), American Society of Mechanical Engineers, (Spring 1995), pp. 2-3.P. Segall and J. R. Rice, "Dilatancy, Compaction, and Slip Instability of a FluidInfiltrated Fault", Journal of Geophysical Research, 100, (1995), pp. 22155-22171.J. R. Rice and Y. Ben-Zion, "Slip Complexity in Earthquake Fault Models",Proceedings of the National Academy of Sciences USA, 93, (1996), pp. 3811-3818.

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R. Dmowska, G. Zheng and J. R. Rice, "Seismicity and Deformation at ConvergentMargins due to Heterogeneous Coupling", Journal of Geophysical Research, 101,(1996), pp. 3015-3029.M. A. J. Taylor, G. Zheng, J. R. Rice, W. D. Stuart and R. Dmowska, "CyclicStressing and Seismicity at Strongly Coupled Subduction Zones", Journal ofGeophysical Research, 101, (1996), pp. 8363-8381.G. Zheng, R. Dmowska and J. R. Rice, "Modeling Earthquake Cycles in theShumagins Subduction Segment, Alaska, with Seismic and Geodetic Constraints",Journal of Geophysical Research, 101, (1996), pp. 8383-8392.G. E. Beltz, J. R. Rice, C. F. Shih and L. Xia, "A Self-Consistent Model forCleavage in the Presence of Plastic Flow", Acta Materiala, 44, (1996), pp. 3943-3954.M. F. Linker and J. R. Rice, "Models of Postseismic Deformation and StressTransfer Associated with the Loma Prieta Earthquake", in U. S. Geological SurveyProfessional Paper 1550-D: The Loma Prieta, California, Earthquake of October17, 1989 - Aftershocks and Postseismic Effects, (1997), pp. D253-D275.A. Cochard and J. R. Rice, "A Spectral Method for Numerical ElastodynamicFracture Analysis without Spatial Replication of the Rupture Event", Journal of theMechanics and Physics of Solids, 45, (1997), pp. 1393-1418.Y. Ben-Zion and J. R. Rice, "Dynamic Simulations of Slip on a Smooth Fault inan Elastic Solid", Journal of Geophysical Research, 102, (1997), pp. 17771-17784.J. W. Morrissey and J. R. Rice, "Crack Front Waves", Journal of the Mechanicsand Physics of Solids, 46, (1998), pp. 467-487.M. A. J. Taylor, R. Dmowska and J. R. Rice, "Upper-plate Stressing andSeismicity in the Subduction Earthquake Cycle", Journal of Geophysical Research,103, (1998), pp. 24523-24542.G. Zheng and J. R. Rice, "Conditions under which Velocity-Weakening Frictionallows a Self-healing versus a Cracklike Mode of Rupture", Bulletin of theSeismological Society of America, 88, (1998), pp. 1466-1483.K. Ranjith and J. R. Rice, "Stability of Quasi-static Slip in a Single Degree ofFreedom Elastic System with Rate and State Dependent Friction", Journal of theMechanics and Physics of Solids, 47, (1999), pp. 1207-1218.J. R. Rice, "Foundations of Solid Mechanics", in Mechanics and Materials:Fundamentals and Linkages (eds. M. A. Meyers, R. W. Armstrong, and H.Kirchner), Chapter 3, Wiley, in press, (1999).J. W. Morrissey and J. R. Rice, "Perturbative Simulations of Crack Front Waves",Journal of the Mechanics and Physics of Solids, in press.

List of Contributors

Professor Peter M. Anderson, Department of Materials Science and Engineering, The OhioState University, 2041 College Road, Columbus, OH 43210-1179 U. S. A.

Professor A. G. Atkins, Department of Engineering, University of Reading, Reading,BG6 6AY, UK

Professor Leslie Bank-Sills, The Dreszer Fracture Mechanics Laboratory, Department ofSolid Mechanics, Materials and Structures, The Fleischman Faculty of Engineering, TelAviv University, 69978 Ramat Aviv, Israel

Dr. B Blug, Fraunhofer-Institut für Werkstoffmechanik,Wöhlerstr. 11,79108 Freiburg,Germany

Dr. Vinodkumar Boniface, The Dreszer Fracture Mechanics Laboratory, Department ofSolid Mechanics, Materials and Structures, The Fleischman Faculty of Engineering, TelAviv University, 69978 Ramat Aviv, Israel

Professor Allan F. Bower, Division of Engineering, Brown University, Providence, RI02912, U.S.A.

Dr. B. Chen,. Department of Mechanical and Industrial Engineering, University of Illinois,Urbana, IL 61801

Dr. Z. Chen, Institute of Materials Research and Engineering, 3 Research Link, Singapore117602

Dr. W. Y. Chien, Department of Mechanical Engineering and Applied Mechanics, TheUniversity of Michigan, Ann Arbor, MI 48109, USA

Dr.J. W. Cho, Technical Center, Deawoo Heavy Industries Co, Inchun, Korea

Dr. T.-J. Chuang, Ceramics Division, National Institute of Standards and Technology,Gaithersburg, MD 20899-8521, U. S. A.

Dr. Brian Cotterell, Institute of Materials Research and Engineering, 3 Research Link,Singapore 117602

x1ii LIST OF CONTRIBUTORS

Professor Walter W.Drugan, Department of Engineering Physics, University of Wisconsin,Madison, 1500 Engineering Drive, Madison, WI 53706

Professor Glenn E. Beltz, Department of Mechanical and Environmental Engineering,University of California, Santa Barbara, CA 93106-5070, USA

Professor Huajian Gao, Division of Mechanics and Computation, Department ofMechanical Engineering, Stanford University, Stanford, CA 94305-4040

Mr. Anja Haug, Materials Department, University of California, Santa Barbara, California93106 USA

Professor Young Huang, Department of Mechanical and Industrial Engineering, Universityof Illinois, Urbana, IL 61801

Mr. H.-M. Huang, Department of Mechanical Engineering and Applied Mechanics, TheUniversity of Michigan, Ann Arbor, MI 48109, USA

Professor Mark Kachanov, Department of Mechanical Engineering, Tufts University,Medford, MA 02155

Dr. E. Karapetian, Department of Mechanical Engineering, Tufts University, Medford, MA02155, U.S.A.

Dr.Patrick A Klein, Sandia National Laboratories, Mail Stop 9161,P.O. Box 0969,Livermore, CA 94551

Professor Shiro Kubo, Department of Mechanical Engineering and Systems, GraduateSchool of Engineering, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871Japan

Dr. L. L. Fischer, Department of Mechanical and Environmental Engineering, Universityof California,Santa Barbara, CA 93106-5070, USA

Dr. L. E. Levine, Maaterials Science and Engineering Lab., National Institute of Standardsand Technology, Gaithersburg, MD 20899

Professor Victor C. Li, Department of Civil and Environmental Engineering, Universityof Michigan, Ann Arbor, MI, 48109-2125

Mr. W. Lu, Mechanical and Aerospace Engineering Department and Materials Institute,Princeton University, Princeton, NJ 08544

LIST OF CONTRIBUTORS xliii

Dr. S. R. MacEwen, Alcan International Ltd., P.O. Box 8400, Kinston, Ontario, K7L 5L9,Canada

Professor Robert M. McMeeking, Department of Mechanical and EnvironmentalEngineering, University of Californi, Santa Barbara, California 93106, USA

Professor Sinisa Dj. Mesarovic, Department of Materials Science and Engineering,University of Virginia, Charlottesville, VA 22903 U. S. A.

Professor Joe Pan, Department of Mechanical Engineering and Applied Mechanics, TheUniversity of Michigan, Ann Arbor, MI 48109, USA

Dr. Hermann Riedel, Fraunhofer-Institut für Werkstoffmechanik,Wöhlerstr. 11,79108Freiburg, Germany

Professor Asher A. Rubinstein, Department of Mechanical Engineering, Tulane University,New Orleans, LA 70118, U. S. A.

Professor J. W .Rudnicki, Department of Civil Engineering, Northwestern University,2145 Sheridan Road, Evanston, IL 60208-3109

Dr. I. Sevostianov, Department of Mechanical Engineering, Tufts University, Medford,MA 02155

Dr. Y. Shim, Center for Simulational Physics, University of Georgia, Athens, GA 30602

Professor Z. Suo, Mechanical and Aerospace Engineering Department, and MaterialsInstitute, Princeton University, Princeton, NJ 08544

Dr. S. C. Tang, Ford Research Lab., P.O. Box 2053, MD3135/SRL, Dearborn, MI48121, U.S.A.

Mr. Zhibo Tang, Division of Engineering, Brown University, Providence, RI 02912

Dr. Robb M. Thomson, Maaterials Science and Engineering Lab., National Institute ofStandards and Technology, Gaithersburg, MD 20899

Dr. Jian-Sheng Wang, Northwestern University, Evanston, IL 60201, USA

Dr. P. D. Wu, Alcan International Ltd., P.O. Box 8400, Kinston, Ontario, K7L 5L9,Canada

Dr. Z. C. Xia, Ford Research Lab., P.O. Box 2053, MD3135/SRL, Dearborn, MI 48121

x1iv LIST OF CONTRIBUTORS

Dr. Xiao J. Xin, Department of Mechanical and Nuclear Engineering, Kansas StateUniversity, 338 Rathbone Hall, Manhattan, KS 66506-5205 U. S. A.

Professor Jin Yu, Department of Materials Science and Engineering,Korea AdvancedInstitute of Science and Technology, P.O. Box 201, Chongryang. Seoul, Korea