Finite element formulation and modeling of rate dependent response of natural and high damping rubbers

Abstract

Nonlinear rate-dependent responses of natural rubber (NR) and high damping rubber (HDR) are simulated by solving boundary value problems modelled with three dimensional 8-noded brick finite elements. The FE formulation has been obtained from the three-parameter Zener model as proposed recently in Amin et al 2006a by following the concept of nonlinear finite strain continuum mechanics. To this end Bernoulli's solution technique has been employed to obtain analytical solution of left Cauchy-Green deformation tensor of overstress part. The nonlinear rate- dependent behaviour of NR and HDR are simulated under compression, shear and their combinations. Explicit expressions for the second Piola-Kirchhoff stress tensor and the Cauchy stress tensor for the equilibrium and over-stress parts are made to formulate the finite element coding. The Lagrangian elasticity tensors for the equilibrium and over-stress parts are also formulated to implement in a general-purpose finite element code. The equilibrium and the over-stress response of NR and HDR under compression and shear have been simulated using the material parameters obtained from experimental observations. The relaxation responses under compression and shear have also been investigated. The simulation results are compared with published experimental findings. The conformity was found encouraging. The results are also in good agreement with the basic properties of NR and HDR. Finally, the FE formulation was utilized to solve the 3D laminated NR and HDR bearings under compression, shear and their combinations.