Nonlinear Finite Element Analysis for Elastomeric Materials under Finite Strain

Abstract

In this paper the finite element methodis used as a numerical techniqueto investigatethe three-dimensional elastomeric materials (rubber or rubber-like materials) under finite, or large, strains analysis.The non-linear element equations for the displacement and pressure field parameters are formulated using the minimized variational approach. Essentially, approximate solutions for the displacement and pressure field parameters are obtained from the solutions of the two corresponding sets of non-linear simultaneous equations via the nonlinear Newton-Raphson iterative procedure. The basic iterative solution procedure convergence is further improved via breaking the applied load down into load incrementwith optimized incremental steps. Additionally,a complete finite element formulation is reported and detailed in this work,and the mathematical complexities conjoined with such kinds of analysis are simplified as possible. Solving some numerical examples and comparing the results with that obtained from some available results and ANSYS 12.0 showed that the current formulation of the finite element methods is correctand the resulted program is capable for solving incompressible elastomeric materials under finite strain. The formulation used for the finite element derivations for large strain analysis gave satisfactory results as compared with that of available results.

Keywords

• nonlinear fem
• finite strain
• large deformation
• elastomers
• rubber
• like materials