Presentation Summary:Design and Optimization Group

NSF/DOE/APC Workshop:

The Future of Modeling in Composites Molding Processes

June 9-10, 2004

VisionThe development and implementation of a comprehensive composites design environmentthat generates the geometric configuration, component materials, and processing schedule for industrial products. Designtool to be based on validated simulations, and address uncertainty in the product’s use, its processing, and models used to assess each, and provide desirable performance over its entire life cycle.

Composite Design AttributesComposite Design AttributesUsability

ExtendibilityDurability

Dimensional stabilityReliability

ManufacturabilityServiceabilityRecycle abilityDisposability

etc…

cradleto

gravelengthscale

Product Design

Process Design

Material Design

Product/Process Design ExampleIntegrated product and process design for short fiber reinforced Integrated product and process design for short fiber reinforced

polymer compositespolymer composites

• Stiffness and strength defined by fiber direction during manufacturingStiffness and strength defined by fiber direction during manufacturing

• IPPD enabling technologiesIPPD enabling technologies

mold fillingfiber orientation

material propertiesproduct performance

polymermelt flowanalysis

staticstress

analysis

modalanalysis

thermalstress

analysis

moldfilling

simulation

fiberorientationprediction

materialproperty

calculation

mold coolinganalysis

warpagesimulation

numericaloptimization

designsensitivityanalysis

multidisciplinarydesign

methodologies

structuraloptimization

State of the Art• Numerous software / algorithms available for numerical optimization

– VDoc/DOT, ISight, Hyperopt, LMS Optimus, Dakota, IMSL, Excel, Matlab, IMSL, Minpack, etc….

• Structural optimization well established– Sizing, Shape, and Topology

• Metamodeling techniques reduce cost of simulation-based design• Enterprise-Driven Multidisciplinary Design Optimization (MDO) developed

for niche applications, e.g., aeroelasticity, automotive body structure, etc…

• Non-deterministic approaches address uncertainty in design– Reliability Analysis Methods, Robust Design,

Reliability-Based Design, etc…• Optimization and design sensitivity analysis

methods developed for numerous manufacturing applications

MPP

f(u1, u2)

u1

u2

g=0

pdf

0

0.5

1

0

0.5

10

200

400

Perceived Gaps• Common language needed across materials scientists, product

designers, manufacturing process engineers, etc.• Validated models needed for all aspects of composites processing

– E.g., strength and stiffness prediction from flow simulation• Design sensitivities not developed to level of analyses

– Fiber orientation– Mechanical properties from process models– Non-isothermal flow, reactive flow

• Integrated design methodologies not available to end user• Optimal design applications are task or discipline focused

– I.e., Multidisciplinary design methods rarely not applied to composite molding problems

• Nondeterministic approaches not applied to composite molding problems

Future Research• Further develop/validate composite molding process/product models and

validate optimization results

• Development of language/representations for seamless communication

• Efficient optimization methods that incorporate multidisciplinary variable-fidelity simulation models

• Development of a user-oriented composites molding design environment– Incorporate design knowledge and experience– Further develop DSA methods for composites molding– Incorporate multidisciplinary design methodologies– Incorporate design under uncertainty tools– Include process control in optimal process design

• Application / Validation on industrial scale problems under distributed and collaborative design environment

1.1. Address clearly the heterogeneous nature Address clearly the heterogeneous nature of composite materialsof composite materials

2. Identify “defects” or “features” of interest for modeling and design

- porosity- texture

- interface imperfections - fiber clustering

- fiber misalignment

3. Develop “metamodels” expressing the effect of microstructure on “performance” or “properties”

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.4

0.5

0.6

0.7

0.8

0.9

1.0

n = 0.70

n = 0.12

Kef

f/Khe

x

(dm-D)/

hex

Multi-scale modeling and topology optimization

Experimental/modeling approach

• Evolve from experimentally-based empirical models physics-based models

• Reduce number of experiments required to validate models• Length scales for homogenization

Some Specific Topics• Micromechanics

– Process micromechanics: Effects of fiber content, length on the rheology and fiber orientation

– Micromechanics of materials: Homogenization accounts for interaction between constituents and defects

• Continuum mechanics: Need of constitutive models for– Fatigue– Time dependent behaviors (creep, relaxation,..)– Impact– Moisture– Crashworthiness

• Nonlinear behaviors– Minimization of damage– Improvement of durability (fatigue, creep)

Operation count Memory storage Traditional BEM assembly

O(N2)

O(N)

solution O(N3) (direct solver) O(N) (iterative solver)

O(N2)

= 2~3

Fast Multipole-Accelerated BEM assembly

NA

NA

Solution O(NlogN) (far field shift) O(N) (far + near shift)

O(N) *

The limiting factor for large scale BEM simulations is the memory requirement of O(N2), which easily becomes excessive as the problem size increases. Fast Multipole-Accelerated BEM can reduce both operation count and memory to O(N) level.

Specific numerical issues in BEM