Comparison of different least-squares mixed finite element formulations for hyperelasticity |
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Authors: | Alexander Schwarz Karl Steeger Maximilian Igelbüscher Jörg Schröder |
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Affiliation: | Institute for Mechanics, University of Duisburg-Essen, Universitätsstr. 15, 45141 Essen, Germany |
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Abstract: | The main goal of this contribution is the solution of geometrically nonlinear problems using the mixed least-squares finite element method (LSFEM). An investigation of a hyperelastic material law based on logarithmic deformation measures is performed. The basis for the proposed LSFEM is a div-grad first-order system consisting of the equilibrium condition and the constitutive equation, see e.g. Cai and Starke [1]. For the interpolation of the solution variables vector-valued Raviart-Thomas functions for the approximation of the stresses and standard Lagrange polynomials for the displacements are used. In order to show the performance of the presented formulations a numerical example is investigated, where we compare the different interpolation combinations used. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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