Surrogate Model for Rubber Spring and Damping Elements Based on High-fidelity Simulations of Cyclically Loaded Vulcanizates

Abstract

This paper presents a surrogate modeling approach for predicting the cyclic stiffness characteristics of rubber spring and damping elements (RSDE) used in vibration isolation systems. The methodology is based on high-fidelity finite element (FE) simulations that incorporate geometry-dependent assembly effects and advanced material modeling of filled vulcanizates subjected to cyclic loading. The constitutive framework combines the Modified Extended Tube Model (METM) with Advanced Mullins Damage Modeling (AMDM), providing a physically motivated description of hyperelasticity, stress softening, and steady-state hysteretic behavior. The resulting three-dimensional FE implementation was realized as an Abaqus user material subroutine and validated against experimental measurements of commercial RSDEs. Simulated torque-angle characteristics showed excellent agreement with experiments, with peak torque deviations below ±3%.

To enable rapid engineering predictions, a parameterized FE model covering representative RSDE geometries was used to generate a design-of-experiments dataset. The simulated loading characteristics were condensed into three physically interpretable parameters describing cyclic stiffness behavior and subsequently approximated using multi-linear response surface regression models. The surrogate model links six geometric design variables to the non-linear torque-angle response, achieving high predictive accuracy with adjusted coefficients of determination R²_adj up to 0.977. Analysis of the regression model reveals the influence of rubber cord dimensions and profile geometry on stiffness evolution under torsional loading. Comparison with independent test cases demonstrates that the surrogate model reliably reproduces FE predictions within the considered design space. The proposed surrogate model enables real-time estimation of geometry- and material-dependent cyclic stiffness characteristics, supporting efficient design and optimization of customized RSDE applications without testing.