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.
