🤖 AI Summary
Conventional inverse hyperelastic modeling for heterogeneous materials relies heavily on pre-specified constitutive forms, limiting generalizability and introducing bias. Method: This paper proposes a model-free, physics-embedded end-to-end framework that reconstructs spatially varying constitutive mappings directly from full-field displacement data (e.g., DIC measurements). It integrates Fourier feature networks, neural ordinary differential equations (NODEs), and hypernetworks to inherently satisfy continuum mechanics constraints—namely, kinematic compatibility and local force balance. A physics-informed loss function is formulated using the strong-form equilibrium equations and Neumann boundary conditions, jointly optimized with multi-objective regularization to balance physical consistency and data fidelity. Results: The method demonstrates robustness across scenarios involving parameter heterogeneity, anisotropic transitions, synthetic noise, and real experimental data—significantly reducing reliance on prior constitutive assumptions while achieving superior accuracy compared to traditional inversion approaches.
📝 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.