Learning macroscopic internal variables and history dependence from microscopic models

Liu, Burigede; Ocegueda, Eric; Trautner, Margaret; Stuart, Andrew M.; Bhattacharya, Kaushik

doi:10.1016/j.jmps.2023.105329

Learning macroscopic internal variables and history dependence from microscopic models

Journal Article · Mon May 29 00:00:00 EDT 2023 · Journal of the Mechanics and Physics of Solids

DOI:https://doi.org/10.1016/j.jmps.2023.105329· OSTI ID:2417798

Liu, Burigede ^[1]; ^[2]; ^[2]; Stuart, Andrew M. ^[2]; ^[2]

Univ. of Cambridge (United Kingdom); OSTI
California Institute of Technology (CalTech), Pasadena, CA (United States)

This paper concerns the study of history dependent phenomena in heterogeneous materials in a two-scale setting where the material is specified at a fine microscopic scale of heterogeneities that is much smaller than the coarse macroscopic scale of application. Here, we specifically study a polycrystalline medium where each grain is governed by crystal plasticity while the solid is subjected to macroscopic dynamic loads. The theory of homogenization allows us to solve the macroscale problem directly with a constitutive relation that is defined implicitly by the solution of the microscale problem. However, the homogenization leads to a highly complex history dependence at the macroscale, one that can be quite different from that at the microscale. In this paper, we examine the use of machine-learning, and especially deep neural networks, to harness data generated by repeatedly solving the finer scale model to: (i) gain insights into the history dependence and the macroscopic internal variables that govern the overall response; and (ii) to create a computationally efficient surrogate of its solution operator, that can directly be used at the coarser scale with no further modeling. We do so by introducing a recurrent neural operator (RNO), and show that: (i) the architecture and the learned internal variables can provide insight into the physics of the macroscopic problem; and (ii) that the RNO can provide multiscale, specifically FE², accuracy at a cost comparable to a conventional empirical constitutive relation.

View Accepted Manuscript (DOE)

Research Organization:: Krell Institute, Ames, IA (United States)

Sponsoring Organization:: US Army Research Laboratory (USARL); US Army Research Office (ARO); USDOE Office of Science (SC)

Grant/Contract Number:: SC0021110

OSTI ID:: 2417798

Journal Information:: Journal of the Mechanics and Physics of Solids, Journal Name: Journal of the Mechanics and Physics of Solids Journal Issue: C Vol. 178; ISSN 0022-5096

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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