A Physics-Augmented Machine Learning Constitutive Model for Damage in Solids

TL;DR

This paper introduces a physics-augmented, neural network-based constitutive model for damage in solids that ensures thermodynamic consistency, captures anisotropic damage effects, and is validated through numerical and experimental benchmarks.

Contribution

It presents a novel, data-driven damage model combining neural networks with physical principles, including polyconvexity and anisotropy, for improved accuracy and computational efficiency.

Findings

Model accurately predicts damage in various anisotropic materials.

Neural network parameterization ensures thermodynamic consistency.

Validated against experimental data and numerical benchmarks.

Abstract

We propose a data-driven constitutive framework for anisotropic damage mechanics based on the second-order damage tensor approach for both compressible and incompressible materials. The formulation is thermodynamically consistent and satisfies the Clausius-Duhem inequality. The strain energy density potentials are expressed as isotropic functions of the right Cauchy-Green deformation tensor, along with structural tensors that encode anisotropy either present in the virgin material or resulting from damage. To guarantee the polyconvexity condition, non-decreasing convex neural networks with inputs that ensure polyconvexity are used to parameterize the strain energy density potentials. The model vanishes in the undeformed state, fulfilling the normality condition. In contrast to classical [1-d] damage models, the expressiveness of the new data-driven model is enhanced by employing a family of nonlinear, convex, decreasing functions to capture the effect of damage. Damage evolution is governed through a damage potential, where the corresponding threshold is defined in terms of the damage conjugate forces. As a special case of the general formulation, a new anisotropic generic format is introduced to predict constitutive responses under damage-induced anisotropy in initially isotropic materials. To reduce the computational burden during training, a decoupled training scheme is introduced, and its accuracy is demonstrated in all numerical examples. These include benchmarks for incompressible isotropic, transversely isotropic, and compressible orthotropic materials. The framework is also validated against experimental data capturing anisotropic Mullins-type damage.