Machine learning of evolving physics-based material models for multiscale solid mechanics

In this work we present a hybrid physics-based and data-driven learning approach to construct surrogate models for concurrent multiscale simulations of complex material behavior. We start from robust but inflexible constitutive increase their expressivity by allowing subset parameters change in time according an evolution operator learned data. This leads flexible model combining encoder decoder. Apart introducing physics-motivated bias the resulting surrogate, internal variables decoder act as memory mechanism that allows path dependency arise naturally. demonstrate capabilities FNN with several plasticity decoders training reproduce macroscopic behavior fiber-reinforced composites. The are able provide reasonable predictions unloading/reloading while being trained exclusively on monotonic Furthermore, contrast traditional surrogates mapping strains stresses, specific architecture lossless dimensionality reduction straightforward enforcement frame invariance using strain invariants feature space encoder.