A Creator-Inspector multi-agent LLM pipeline for constitutive artificial neural networks increases the rate of models satisfying all nine physical constraints to 100% or 56% depending on the LLM backbone.
Modeling isotropic polyconvex hyperelasticity by neural networks -- sufficient and necessary criteria for compressible and incompressible materials
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abstract
This work investigates different sufficient and necessary criteria for hyperelastic, isotropic polyconvex material models, focusing on neural network implementations for compressible and incompressible materials. Furthermore, the expressiveness, accuracy, simplicity as well as the efficiency of those models is analyzed. This also enables an assessment of the practical applicability of the models. Convex Signed Singular Value Neural Networks (CSSV-NNs) are applied to compressible materials and tailored to incompressibility (inc-CSSV-NNs), resulting in a universal approximation for frame-indifferent, isotropic polyconvex energies for the compressible as well as incompressible case. While other existing approaches also guarantee frame-indifference, isotropy and polyconvexity, they impose too restrictive constraints and thus limit the expressiveness of the model. This is further substantiated by numerical examples of several, well-established classical models (Neo-Hooke, Mooney-Rivlin, Gent and Arruda-Boyce) and Treloar's experimental data. Moreover, the numerical examples include an explicitly constructed energy function that cannot be approximated by neural networks constrained by Ball's criterion for polyconvexity. This substantiates that Ball's criterion, though sufficient, is not necessary for polyconvexity.
years
2026 2representative citing papers
Polyconvexity implies true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity, which is enforced in four PANN architectures that show varying extrapolation behavior on experimental data.
citing papers explorer
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LLM-driven design of physics-constrained constitutive models: two agents are better than one
A Creator-Inspector multi-agent LLM pipeline for constitutive artificial neural networks increases the rate of models satisfying all nine physical constraints to 100% or 56% depending on the LLM backbone.
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Concurrent enforcement of polyconvexity and true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity: application to neural network constitutive models
Polyconvexity implies true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity, which is enforced in four PANN architectures that show varying extrapolation behavior on experimental data.