From Large-Scale Elastomer Data to Engineering Simulation: A Generalizable Skip-Connected Physics-Informed Neural Network for Hyperelastic Constitutive Modeling

Ziyuan Li; Qiang Zhang; Peng Li; Jun Yang; Yonglai Lu; Fanzhu Li; Liqun Zhang

doi:10.1016/j.eng.2026.08.024

Engineering ›› :202608024 DOI: 10.1016/j.eng.2026.08.024

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From Large-Scale Elastomer Data to Engineering Simulation: A Generalizable Skip-Connected Physics-Informed Neural Network for Hyperelastic Constitutive Modeling

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Abstract

Hyperelastic constitutive models (HCMs) are essential for accurately describing elastomeric mechanical responses and supporting the structural optimization of engineering rubber products. However, existing empirical parametric and neural-network HCMs often face a trade-off between fitting accuracy and material stability. Here, a skip-connected physics-informed neural network (SC-PINN) was developed as a generalizable, accurate, and stable hyperelastic constitutive modeling framework. The strain energy potential is represented by an invariant-based polyconvex energy neural network, embedding thermodynamic consistency, material objectivity, isotropy, and material stability by construction. A dual skip-connected module is introduced as a physically admissible complementary component. Its output skip pathway can be interpreted as contributing a trainable Mooney–Rivlin-like term corresponding to the first-order terms of the Rivlin polynomial expansion, while the nonlinear backbone provides higher-order-like corrections. The SC-PINN was evaluated on 25 249 experimental uniaxial tensile stress–strain curves and benchmarked against six representative HCMs: Neo-Hookean, Mooney–Rivlin, Ogden, Zhang–Li, unconstrained PINN, and no-skip PINN. This network achieved an average coefficient of determination (R²) of 0.9995, with 99.4% of the curves reaching R² ≥ 0.99, while maintaining 100% material stability through its polyconvex architecture. Furthermore, the trained SC-PINN was implemented in Abaqus/Standard through a customized UHYPER material subroutine. The implementation was validated across cases ranging from standard specimens to engineering components, including a scaled non-pneumatic tire and the suspension bearings of a heavy-duty truck, with static-stiffness errors below 5.0%. The SC-PINN combines high fitting accuracy, architecture-enforced material stability, and large-scale generalizability. This combination advances hyperelastic constitutive modeling beyond empirical curve fitting toward a physics-grounded, data-driven framework that bridges material characterization and finite-element simulation of engineering elastomeric structures.

Keywords

Hyperelasticity / Physics-informed neural networks / Polyconvexity / UHYPER subroutine / Finite element analysis

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Ziyuan Li, Qiang Zhang, Peng Li, Jun Yang, Yonglai Lu, Fanzhu Li, Liqun Zhang. From Large-Scale Elastomer Data to Engineering Simulation: A Generalizable Skip-Connected Physics-Informed Neural Network for Hyperelastic Constitutive Modeling. Engineering 202608024 DOI:10.1016/j.eng.2026.08.024

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