Fully data-driven inverse hyperelasticity with hyper-network neural ODE fields

TL;DR

This paper introduces a fully data-driven neural network framework that identifies heterogeneous material properties from full-field displacement data, leveraging neural ODEs and hyper-networks to model complex constitutive behaviors without explicit equations.

Contribution

It presents a novel hyper-network neural ODE approach that captures heterogeneity and sharp gradients in material properties directly from experimental data.

Findings

Robust identification of heterogeneous materials from noisy data.

Effective modeling of spatial transitions from isotropy to anisotropy.

Successful application to experimental displacement measurements.

Abstract

We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image correlation (DIC), a continuous approximation of the strain field is obtained by training a neural network that incorporates Fourier features to effectively capture sharp gradients in the data. A physics-based data-driven method built upon ordinary neural differential equations (NODEs) is employed to discover constitutive equations. The NODE framework can represent arbitrary materials while satisfying constraints in the theory of constitutive equations by default. To account for heterogeneity, a hyper-network is defined, where the input is the material coordinate system, and the output is the NODE-based constitutive equation. The parameters of the hyper-network are optimized by minimizing a multi-objective loss function that includes penalty terms for violations of the strong form of the equilibrium equations of elasticity and the associated Neumann boundary conditions. We showcase the framework with several numerical examples, including heterogeneity arising from variations in material parameters, spatial transitions from isotropy to anisotropy, material identification in the presence of noise, and, ultimately, application to experimental data. As the numerical results suggest, the proposed approach is robust and general in identifying the mechanical properties of heterogeneous materials with very few assumptions, making it a suitable alternative to classical inverse methods.