A computational framework to establish data-driven constitutive models for time- or path-dependent heterogeneous solids

Weijian Ge,Vito L Tagarielli

doi:10.1038/s41598-021-94957-0

Abstract

We propose and implement a computational procedure to establish data-driven surrogate constitutive models for heterogeneous materials. We study the multiaxial response of non-linear n-phase composites via Finite Element (FE) simulations and computational homogenisation. Pseudo-random, multiaxial, non-proportional histories of macroscopic strain are imposed on volume elements of n-phase composites, subject to periodic boundary conditions, and the corresponding histories of macroscopic stresses and plastically dissipated energy are recorded. The recorded data is used to train surrogate, phenomenological constitutive models based on neural networks (NNs), and the accuracy of these models is assessed and discussed. We analyse heterogeneous composites with hyperelastic, viscoelastic or elastic–plastic local constitutive descriptions. In each of these three cases, we propose and assess optimal choices of inputs and outputs for the surrogate models and strategies for their training. We find that the proposed computational procedure can capture accurately and effectively the response of non-linear n-phase composites subject to arbitrary mechanical loading.

Highlights

All solids display a heterogeneous microstructure and their mechanical response depends on complex mechanisms spanning multiple length- and time-scales
To assess the accuracy of the regressions performed by the Neural Networks (NNs) NNrIeg, NNrIeIg, NNrIeIgIσ,NNrIeIgIW, in addition to the final value of the loss function mean absolute error (MAE), we introduce an additional metric, to which we refer as path-wise stress error, Eσ ; this metric aims at capturing the effectiveness of a surrogate model in predicting macroscopic stress versus strain histories of a volume elements (VEs)
This can be explained by the fact that our training data is thermodynamically consistent and that the NN have an excellent agreement with this data at the end of the training

Summary

Introduction

All solids display a heterogeneous microstructure and their mechanical response depends on complex mechanisms spanning multiple length- and time-scales. To assess the accuracy of each surrogate model we generate 20 additional unseen loading cases, in the form of pseudo-random walks in true principal strain space, as described in “Generation of the training datasets”.

Results

Conclusion