Nonlinear Finite Element Analysis for Elastomeric Materials under Finite Strain


In this paper the finite element methodis used as a numerical techniquetoinvestigatethe three-dimensional elastomeric materials (rubber or rubber-likematerials) under finite, or large, strains analysis.The non-linear element equations forthe displacement and pressure field parameters are formulated using the minimizedvariational approach. Essentially, approximate solutions for the displacement andpressure field parameters are obtained from the solutions of the two correspondingsets of non-linear simultaneous equations via the nonlinear Newton-Raphson iterativeprocedure. The basic iterative solution procedure convergence is further improved viabreaking the applied load down into load incrementwith optimized incremental steps.Additionally,a complete finite element formulation is reported and detailed in thiswork,and the mathematical complexities conjoined with such kinds of analysis aresimplified as possible.Solving some numerical examples and comparing the results with that obtainedfrom some available results and ANSYS 12.0 showed that the current formulation ofthe finite element methods is correctand the resulted program is capable for solvingincompressible elastomeric materials under finite strain. The formulation used for thefinite element derivations for large strain analysis gave satisfactory results ascompared with that of available results.