Finite element modeling of nonlinear elastic response of natural and high damping rubber

Abstract

The monotonic response of natural rubber (NR) and high damping rubber (HDR) as revealed through recent experiments are critically examined and reported here in. In understanding the mechanical behavior of rubbers, attention is mostly paid to the compression and shear regime. In studying the mechanical test results in the compression and shear regime, the existence of Mullins' effect, strain-rate dependency, hystersis and residual strain effects in all the specimens was noted. In NR, the extent of these effects is found to have an inherent relation with the presence of microstructural voids. The presence of all these effects is also found to be significant in HDR. In addition, the strain-rate dependent high initial stiffness feature at low compressive strain levels was also evident. However, in considering a strainrate dependent response, equilibrium and instantaneous responses are defined rateindependent responses. In the constitutive model, these responses are uaually modelled using a hyperelasticity law. In this context, the current work is carried out using finite element modeling of the rate independent elastic behavior of NR and HDR subjected to compression, shear and their combinations. To this end, several constitutive models based on phenomenological motivation were thoroughly studied. An improved hyperelasticity model was utilized to formulate the finite element coding for representing the rate-independent nonlinear elastic responses including high initial stiffness characteristics of rubber materials. In doing this an explicit analytical expressions for the second Piola-Kirchhoff stress tensor and the Cauchy stress tensor have been formulated for the distortional part of the hyperelasticity model. The Lagrangian elasticity tensor has also been formulated for the distortional part of the hyperelasticity model to implement in a general-purpose finite element code. The elastic equilibrium and instantaneous responses of NR and HDR under compression and shear have been simulated using material parameters identified from the available experimental observations. The numerical simulation results have been compared with the available experimental observations to discuss the adequacy of the developed finite element procedure in simulating quasiincompressible response of NR and HDR under uniaxial compression and simple shear deformation. To this end, the simulation results have been verified with available analytical solution for the elastomeric rubber bearing with different shape factors. Numerical expeirments have been performed for simultaneous action of compression and shear. Finally, the possibility of modeling and analyzing the fullscale bridge seats and base isolation bearings have been investigated at different deformation modes by utilizing the developed finite element procedure. In this process, the numerical results have been compared with the available analytical results.