Top Plate is fixed.

Displacement of Bottom Plate

𝒖𝟐(𝒕) are applied.

Experimental Data : S. Tamrakar, R.

Ganesh, S. Sockalingam, B. Z.

Haque, J. W. Gillespie . 2017

The recent years have seen a surge in research on material

and structural response of composites using homogenization

based hierarchical modeling method. Conventionally, periodic

boundary condition (PBC) is applied on the RVE boundary. The

micromechanical results are inputted to a homogenized-based

constitutive model to give a macro-scale description. However,

when the heterogeneous microstructure is under very high strain

rate loading conditions (103 𝑠−1~106 𝑠−1), PBC do not

represent the accurate effect of stress wave propagation. Thus, it

will reduce the accuracy of the calibrated tensor field in the

multiscale model.

In order to increase the accuracy of the homogenization

model, this study introduces a new space-time dependent

boundary condition (STBC) for 3D microscopic RVE subjected

to high strain rate deformation in explicit FEM simulation. The

advantages of the STBC are discussed by comparing with time-

dependent averaging results of examples using PBC. The

proposed STBC offers significant advantages over conventional

PBC in the RVE-based analysis of heterogeneous materials.

[K. A. Brown. 2010]

Micromechanics Analysis of Damage and Failure in Heterogeneous Composite

Subject to High Strain Rate Impact and Blast

Zhiye Li1, Somnath Ghosh2 , Daniel J. O’Brien3 1Graduate Research Assistant; 2 Michael G. Callas Chair Professor, sghosh20@jhu.edu, Johns Hopkins University

3Composite and Hybrid Materials Branch, U.S. Army Research Laboratory

Research was sponsored by the Army Research Laboratory and was accomplished

under Cooperative Agreement Number W911NF-12-2-0022. The views and

conclusions contained in this document are those of the authors and should not be

interpreted as representing the official policies, either expressed or implied, of the

Army Research Laboratory or the U.S. Government. The U.S. Government is

authorized to reproduce and distribute reprints for Government purposes

notwithstanding any copyright notation herein.

ACKNOWLEDGEMENT

INTRODUCTION

MULTI-SCALE STUDY OF

COMPOSITE

………………….

EXPRTIMENT

VALIDATION

MICROSCOPIC

FEM MODEL

• Material (VUMAT)

Rate dependent elastic with

Nonlocal CDM

• Interface debonding

(VUEL)

Rate dependent CZM

• Periodic B.C.

HOMOGENIZED

MODEL

• Space Time B.C. (new)

• Unidirectional fibers

RVE

Give precise

prediction and

upgrade

model for

MAT162 （LS-DYNA）

Von Mises Stress Configuration from

FEM Calibration Result

DEVELOPING A CONTINUUM

DAMAGE MODEL FROM

EXPERIMENTS ON DER353

MICROMECHANICAL SPACE-TIME

DEPENDENT BOUNDARY

CONDITION ( STBC )

STBC (continued)

Comment:

• When the heterogeneous microstructure is under very high

strain rate loading conditions (higher than 104𝑠−1), periodic

boundary condition (PBC) do not represent the accurate effect

of stress wave propagation. Space-Time dependent Boundary

Condition (STBC) can give a more accurate prediction for

higher strain rate.

• Apply 1-D solution based STBC on 3D RVE and

calibrated averaged wave speed c from the 3D simulation.

Average wave speed c is a function of volume fraction.

Main idea: In order to increase the accuracy of

the homogenization model, this study introduces

a new space-time dependent boundary condition

(STBC) for 3D microscopic RVE subjected to

high strain rate deformation in explicit FEM

simulation by using characteristics method of

traveling waves.

1×1

1×5

Figure: Deformed local stress contour, volume averaged effective strain and volume

averaged von-Mises stress of 1 × 1 RVE with STBC and PBC for shear simulation.

Comment:

• Homogenization equations consolidates the objective that, the

single fiber RVE can be used in substitute of homogenized

properties of multiple fibers RVEs in order to maintain

accuracy and save computational resources.

HOMOGENIZED PROPERTIES OF

MICROSCOPIC MODEL

Example: 3D FEM 𝑑11= 2 × 106 𝑠−1, uniaxial tension. RVE1 RVE2 RVE3

1×1

1×5

• Effects of adiabatic heating:

∆T=𝛽

𝜌𝑐𝑊 𝐷𝑓(𝑘)

𝑒 𝑉 (𝑘)𝑒

𝑊 𝐷𝑓(𝑘)𝑒 is the dissipative

energy density of the k-th

element in donut. 𝑉 (𝑘)𝑒 is the

volume of the k-th element.

Uniaxial Compression Tests:

• ¼ symmetric model

• Coefficients of friction between

donut and two plate are the

same. (μ= 0.01 )

Deformed stress contour

Material value rate picture reference

Polycarbonate

(PC) polymer

0.5~0.6 1200/s~2200/s

(SHPB)

Z. Li

and J.

Lambros

2000

epoxy resin ~0.45 0.001/s and

300~2500/s

compression

Z. Pan,

B. Sun, V.

P.W. Shim,

B. Gu 2016

PMMA

poly(methyl

methacrylate)

~0.45 1e-2/s ~1e-1/s

SHPB

G. Shao, S.

Zhu,

Y. Wang, Q.

Zhao 2017

PC

(polycarbonate)

~0.8 >1000/s

SHPB

M. Garg

A. D.

Mulliken

M. C.

Boyce 2008

thermoset

epoxy (EPON

862/W)

0.4~0.6 >1000/s

SHPB

glass/epoxy

woven ply

0.4~0.6 visualization

of the portion of

dissipated energy

caused by matrix

cracking

T. Lisle,

C.Bouvet,

M. L.Pastor,

T. Rouault,

P.Margueres

2016

𝛽 is the Taylor-Quinney coefficient. Many experiments

observe that it depends on temperature, strain and strain

rate. A literature review of experiment calibrated 𝛽 value

• Cruciform experiment

[N. Getinet , D. J. O'Brien]

• Droplet experiment

[Sockalingam, et al., 2014]

• DER 353 donut

experiment

[Tamrakar, et al., 2017]

• U-D ply tensile

experiment

[Shokrieh and Omidi, 2009]