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

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 ( R 2) of 0.9995, with 99.4% of the curves reaching R 2 ≥ 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.