Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)

TL;DR

This paper introduces Thermodynamics-based Artificial Neural Networks (TANN), a novel multiscale modeling approach that efficiently predicts inelastic material behavior with complex microstructures, reducing computational costs while maintaining high accuracy.

Contribution

The paper presents TANN, integrating thermodynamics-aware neural networks and dimensionality reduction to autonomously identify constitutive laws and internal variables for inelastic microstructured materials.

Findings

TANN accurately predicts stress-strain responses and energy dissipation.

TANN identifies internal state variables characterizing inelastic deformation.

The homogenized model with TANN shows excellent agreement with microstructural calculations.

Abstract

The mechanical behavior of inelastic materials with microstructure is very complex and hard to grasp with heuristic, empirical constitutive models. For this purpose, multiscale, homogenization approaches are often used for performing reliable, accurate predictions of the macroscopic mechanical behavior of solids and structures. Nevertheless, the calculation cost of such approaches is extremely high and prohibitive for real-scale applications involving inelastic materials. Here, we propose the so-called Thermodynamics-based Artificial Neural Networks (TANN) for the constitutive modeling of materials with inelastic and complex microstructure. Our approach integrates thermodynamics-aware dimensionality reduction techniques and thermodynamics-based deep neural networks to identify, in an autonomous way, the constitutive laws and discover the internal state variables of complex inelastic materials. The efficiency and accuracy of TANN in predicting the average and local stress-strain response, the free-energy and the dissipation rate is demonstrated for both regular and perturbed two- and three-dimensional lattice microstructures in inelasticity. TANN manage to identify the internal state variables that characterize the inelastic deformation of the complex microstructural fields. These internal state variables are then used to reconstruct the microdeformation fields of the microstructure at a given state. Finally, a double-scale homogenization scheme (FEMxTANN) is used to solve a large scale boundary value problem. The high performance of the homogenized model using TANN is illustrated through detailed comparisons with microstructural calculations at large scale. An excellent agreement is shown for a variety of monotonous and cyclic stress-strain paths.