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

TL;DR

This paper introduces a hybrid physics-based and data-driven approach to create surrogate models for multiscale solid mechanics, enabling path-dependent predictions and efficient dimensionality reduction.

Contribution

The work develops a flexible hybrid model combining physics-based and data-driven components, allowing for path dependency and invariance enforcement in multiscale material simulations.

Findings

Accurately predicts unloading/reloading behavior from monotonic data.

Enables lossless dimensionality reduction using strain invariants.

Combines physics-based bias with data-driven memory mechanisms.

Abstract

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