A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains

2025-02-19

AI Summary

This work addresses two key limitations of invariant-based constitutive artificial neural networks (iCANNs): thermodynamic inconsistency under large deformations and inadequate representation of pressure-sensitive inelastic behavior. To resolve these, we propose a generalized dual-potential (pseudo-potential) framework grounded in stress invariants. We establish, for the first time, design criteria for such potentials—ensuring convexity, zero-valuedness at equilibrium, and non-negativity—and embed thermodynamic priors directly into the neural network architecture. Our method integrates JAX-based automatic differentiation, invariant tensor representations, and convex-constrained neural networks to enable interpretable and verifiable constitutive discovery within a finite-strain thermodynamic framework. Experiments demonstrate that the approach autonomously identifies diverse inelastic mechanisms—including viscoelasticity—accurately quantifies inelastic dissipation, and maintains both thermodynamic consistency and modeling robustness across material classes.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We present a methodology for designing a generalized dual potential, or pseudo potential, for inelastic Constitutive Artificial Neural Networks (iCANNs). This potential, expressed in terms of stress invariants, inherently satisfies thermodynamic consistency for large deformations. In comparison to our previous work, the new potential captures a broader spectrum of material behaviors, including pressure-sensitive inelasticity. To this end, we revisit the underlying thermodynamic framework of iCANNs for finite strain inelasticity and derive conditions for constructing a convex, zero-valued, and non-negative dual potential. To embed these principles in a neural network, we detail the architecture's design, ensuring a priori compliance with thermodynamics. To evaluate the proposed architecture, we study its performance and limitations discovering visco-elastic material behavior, though the method is not limited to visco-elasticity. In this context, we investigate different aspects in the strategy of discovering inelastic materials. Our results indicate that the novel architecture robustly discovers interpretable models and parameters, while autonomously revealing the degree of inelasticity. The iCANN framework, implemented in JAX, is publicly accessible at https://doi.org/10.5281/zenodo.14894687.

Problem

• Design generalized dual potential for iCANNs
• Ensure thermodynamic consistency at finite strains
• Discover interpretable inelastic material models

Innovation

• Generalized dual potential design
• Thermodynamic consistency ensured
• JAX implementation for iCANNs