Finite Element Formulation of Three-dimensional Nonlinear Elasticity Problem

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https://userpages.umbc.edu/~sousedik/papers/vycichlo05.pdf

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UMBC Mathematics and Statistics Department

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https://orcid.org/0000-0002-8053-8956

Date

2005-04

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conference papers and proceedings
preprints
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Bedřich Sousedík, Pavel Burda: Finite element formulation of three-dimensional nonlinear elasticity problem, Proceedings of the Seminar of applied mathematics in commemoration of the 100th birthday of Prof. Vyčichlo, Faculty of Civil Engineering, Czech Technical University in Prague, Prague, Czech Republic, April 2005

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Abstract

The purpose of the present work is to give a brief description of the finite elasticity and of its approximation via finite element method. We formulate the problem for the case of compressible elasticity. Weak formulation allows to use any isotropic hyperelastic material model that satisfies polyconvexity assumptions. Discretization using FEM leads to systems of non-linear equations. Finally we also show the strategy of solving such systems of equations by modification of Newton’s method that can be used under some restrictions.