Nonlinear Deformation Responses of Rubber Components by Finite Element Analysis

Abstract

Typically, rubber under the influence of mechanical loads exhibits strong nonlinear behavior due to both material and geometrical nonlinearities. Structural analysis of such material via finite element method is further complicated by three additional issues: (1) inappropriate elemnt formulation may induce locking phenomenon leading to erroneous results, (2) polynomial-form constitutive equations may cause material instability in the process of deformation analysis, and (3) use of low order elements can result in pressure instability. In this paper, several typical benchmark problems are analyzed to examine a few numerical issues: (1) convergence property of the iterative solution vs. the range of bulk modulus in the perturbed Lagrangian formulation, (2) criteria to insure material stability within the strain range of interest, and (3) alternative iterative techniques for both perfectly and nearly incompressible rubbers.