A time-domain viscoelastic model of nonlinear compression behavior under cyclic loading

Viscoelastic (VE) pads, commonly employed as passive damping components in damping devices to absorb and dissipate energy, present challenges in predicting the mechanical behavior under large deformation due to significant nonlinearity. This study introduces a novel nonlinear time-domain model to accurately characterize the response of VE pads subjected to cyclic loading across small, moderate, and large compressive deformations. Effects such as strain hardening, the Mullins effect, continuous stress softening, and residual deformation are incorporated into the model. The proposed model integrates hyperelastic, viscoelastic, and elastoplastic parts, arranged in parallel, each addressing distinct aspects of the mechanical behavior. The hyperelastic part captures the time-independent response, in particular strain hardening in nonlinear stiffness. The VE part accounts for the frequency-dependent damping behavior, focusing on the initial unloading stiffness, the shape and area of the hysteresis loop, and major residual deformations. The elastoplastic part models the frequency-dependent plasticity, adjusting residual deformation and determining the extent of Mullins effect and continuous stress softening. Model parameters are determined through fitting procedures using uniaxial quasi-static and cyclic compression test data, allowing for an accurate description of the nonlinear mechanical behavior in the time domain. To assess the prediction capacity and applicability of the proposed model, the simulation results are comparatively evaluated by error analysis. The sensitivity analysis is further performed to investigate the influence of individual parameters. The proposed model demonstrates high accuracy and robustness in representing the mechanical behavior of VE pads across small, moderate, and large compressive deformations. The parameters in the hyperelastic, viscoelastic, and elastoplastic parts have accurate interpretations, providing distinct roles and contributions to the overall mechanical behavior.