FE${}^\textbf{ANN}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

TL;DR

This paper introduces FE${}^ ext{ANN}$, a multiscale framework combining physics-constrained neural networks and autonomous data mining to efficiently simulate complex material behaviors with reduced microscale simulations.

Contribution

The novel framework integrates physics-informed ANNs with automated data collection, enabling efficient multiscale modeling of nonlinear anisotropic materials with minimal microscale computations.

Findings

Reduced number of microscale simulations needed

Accurate modeling of fiber reinforced composites

Framework applicable to nonlinear hyperelastic materials

Abstract

Herein, we present a new data-driven multiscale framework called FE${}^\text{ANN}$ which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous data mining process. Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. Thereby, we restrict ourselves to finite strain hyperelasticity problems for now. By using a set of problem specific invariants as the input of the ANN and the Helmholtz free energy density as the output, several physical principles, e.g., objectivity, material symmetry, compatibility with the balance of angular momentum and thermodynamic consistency are fulfilled a priori. The necessary data for the training of the ANN-based surrogate model, i.e., macroscopic deformations and corresponding stresses, are collected via computational homogenization of representative volume elements (RVEs). Thereby, the core feature of the approach is given by a completely autonomous mining of the required data set within an overall loop. In each iteration of the loop, new data are generated by gathering the macroscopic deformation states from the macroscopic finite element (FE) simulation and a subsequently sorting by using the anisotropy class of the considered material. Finally, all unknown deformations are prescribed in the RVE simulation to get the corresponding stresses and thus to extend the data set. The proposed framework consequently allows to reduce the number of time-consuming microscale simulations to a minimum. It is exemplarily applied to several descriptive examples, where a fiber reinforced composite with a highly nonlinear Ogden-type behavior of the individual components is considered.