Learning Physics-Consistent Material Behavior from Dynamic Displacements

2024-07-25

AI Summary

This work addresses unsupervised learning of thermodynamically consistent constitutive laws solely from dynamic displacement field data, eliminating reliance on boundary traction measurements. Method: We propose a novel physics-informed framework integrating the dynamic equilibrium equations with input-convex neural networks (ICNNs), rigorously enforcing thermodynamic consistency—including convexity of the strain energy density and frame-indifference—while enabling generalization across geometries. The model is trained on local displacement observations via domain decomposition and unsupervised physical constraints, primarily minimization of the strong-form equilibrium residual. Contributions/Results: The method robustly recovers hyperelastic constitutive laws under noise, converges to ground-truth material models as spatial resolution increases, and generalizes to unseen geometries. It is the first approach achieving dynamic displacement-driven, thermodynamically exact, force-free constitutive learning—without requiring any stress or traction data.

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• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
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Abstract

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed to learn the constitutive law from deformation data. Nonetheless, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on boundary force data for training which are unavailable in many in-situ scenarios. Here, we introduce a machine learning approach to learn physics-consistent constitutive relations solely from material deformation without boundary force information. This is achieved by considering a dynamic formulation rather than static equilibrium data and applying an input convex neural network (ICNN). We validate the effectiveness of the proposed method on a diverse range of hyperelastic material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations. It is, due to its design based on dynamics, particularly suited for applications to strain-rate-dependent materials and situations where constitutive laws need to be inferred from in-situ measurements without access to global force data.

Problem

• Learn physics-consistent material laws from deformation data.
• Address limitations of existing unsupervised machine learning methods.
• Enable constitutive law discovery without boundary force information.

Innovation

• Uses dynamic formulation for physics-consistent learning
• Applies input convex neural network (ICNN)
• Learns from deformation data without boundary forces