A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains

2025-10-05

AI Summary

This study addresses the challenge of modeling anisotropic inelastic materials under finite strains. Methodologically, it proposes a physics-informed neural constitutive framework featuring: (i) a dual-potential structure that rigorously enforces the dissipation inequality without requiring convexity assumptions; (ii) invariant-based input representation encoding elastic, inelastic, and structural tensor information; and (iii) a synergistic architecture combining input-monotonic neural networks with recurrent liquid time-constant networks to ensure stable time integration. The key contribution is the first integration of input monotonicity constraints with the dual-potential thermodynamic structure—thereby simultaneously ensuring physical consistency and expressive capacity. Experiments demonstrate high accuracy, robust numerical stability, and strong generalization across diverse boundary conditions, both at the material-point and structural scales. The implementation is publicly available.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently incorporates anisotropy, and-unlike conventional convex formulations-satisfies the dissipation inequality without requiring convexity. Our neural network architecture employs invariant-based input representations in terms of mixed elastic, inelastic and structural tensors. It adapts Input Convex Neural Networks, and introduces Input Monotonic Neural Networks to broaden the admissible potential class. To bypass exponential-map time integration in the finite strain regime and stabilize the training of inelastic materials, we employ recurrent Liquid Neural Networks. The approach is evaluated at both material point and structural scales. We benchmark against recurrent models without physical constraints and validate predictions of deformation and reaction forces for unseen boundary value problems. In all cases, the method delivers accurate and stable performance beyond the training regime. The neural network and finite element implementations are available as open-source and are accessible to the public via https://doi.org/10.5281/zenodo.17199965.

Problem

• Modeling anisotropic inelasticity at finite strains using neural networks
• Incorporating material principles to ensure physical consistency in predictions
• Developing stable neural architectures for finite strain regime simulations

Innovation

• Augments neural networks with material principles
• Employs dual potential satisfying dissipation inequality
• Uses recurrent Liquid Neural Networks for stability