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Accelerated computational micromechanics

Zhou, Hao and Bhattacharya, Kaushik (2020) Accelerated computational micromechanics. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20201110-073310991

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Abstract

We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations that are typically second order in space and first order in time. This combination of nonlinearity and nonlocality makes such problems difficult to solve in parallel. However, this combination is a result of collapsing nonlocal, but linear and universal physical laws (kinematic compatibility, balance laws), and nonlinear but local constitutive relations. We propose an operator-splitting scheme inspired by this structure. The governing equations are formulated as (incremental) variational problems, the differential constraints like compatibility are introduced using an augmented Lagrangian, and the resulting incremental variational principle is solved by the alternating direction method of multipliers. The resulting algorithm has a natural connection to physical principles, and also enables massively parallel implementation on structured grids. We present this method and use it to study two examples. The first concerns the long wavelength instability of finite elasticity, and allows us to verify the approach against previous numerical simulations. We also use this example to study convergence and parallel performance. The second example concerns microstructure evolution in liquid crystal elastomers and provides new insights into some counter-intuitive properties of these materials. We use this example to validate the model and the approach against experimental observations.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2010.06697arXivDiscussion Paper
ORCID:
AuthorORCID
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:We are delighted to acknowledge many stimulating discussions with Pierre Suquet (concerning FFT algorithms) and Kenji Urayama (concerning LCEs). The latter also generously provided us with experimental data shown in Figure 13. We gratefully acknowledge the support of the US Air Force Office for Scientific Research through the MURI grant number MURI grant FA9550-16-1-0566. The computations presented here were performed at the High Performance Computing Center of California Institute of Technology.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0566
Record Number:CaltechAUTHORS:20201110-073310991
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201110-073310991
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106576
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Nov 2020 16:26
Last Modified:10 Nov 2020 16:26

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