Finite electro-elasticity with physics-augmented neural networks

TL;DR

This paper introduces a physics-augmented neural network model for finite electro-elasticity that ensures stability and thermodynamic consistency, demonstrating high accuracy and generalization in modeling complex electro-mechanical materials.

Contribution

It proposes a convex neural network-based constitutive model that respects physical laws and can handle various material behaviors and symmetries, advancing data-driven electro-elasticity modeling.

Findings

Model fulfills polyconvexity, ensuring stability.

Demonstrates excellent generalization on complex materials.

Applicable to various material symmetries and behaviors.

Abstract

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated as a convex neural network. In this way, the model fulfills the polyconvexity condition which ensures material stability, as well as thermodynamic consistency, objectivity, material symmetry, and growth conditions. Depending on the considered invariants, this physics-augmented machine learning model can either be applied for compressible or nearly incompressible material behavior, as well as for arbitrary material symmetry classes. The applicability and versatility of the approach is demonstrated by calibrating it on transversely isotropic data generated with an analytical potential, as well as for the effective constitutive modeling of an analytically homogenized, transversely isotropic rank-one laminate composite and a numerically homogenized cubic metamaterial. These examinations show the excellent generalization properties that physics-augmented neural networks offer also for multi-physical material modeling such as nonlinear electro-elasticity.