A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains

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.

40 pages, 19 figures

References in corpus (23)

• Thermodynamics-based Artificial Neural Networks for constitutive modeling
• A new family of Constitutive Artificial Neural Networks towards automated model discovery
• Unsupervised discovery of interpretable hyperelastic constitutive laws
• Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)
• Neural networks meet hyperelasticity: A guide to enforcing physics
• Automated discovery of generalized standard material models with EUCLID
• Artificial intelligence adoption in the physical sciences, natural sciences, life sciences, social sciences and the arts and humanities: A bibliometric analysis of research publications from 1960-2021
• On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling
• Discovering plasticity models without stress data
• Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers
• FE${}^{\text{ANN}}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining
• Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations
• Theory and implementation of inelastic Constitutive Artificial Neural Networks
• Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs
• Finite electro-elasticity with physics-augmented neural networks
• Automated identification of linear viscoelastic constitutive laws with EUCLID
• Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID
• Multiscale topology optimization of functionally graded lattice structures based on physics-augmented neural network material models
• Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics
• I-FENN for thermoelasticity based on physics-informed temporal convolutional network (PI-TCN)
• Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling
• A topology optimisation framework to design test specimens for one-shot identification or discovery of material models
• Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies

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