Nonlinear Finite Element Analysis for Elastomeric Materials under Finite Strain
AbstractIn 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.
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