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Comparison of geometrically nonlinear LSFEM formulations based on different hyperelastic models
Author(s) -
Steeger Karl,
Schwarz Alexander,
Schröder Jörg,
Starke Gerhard,
Müller Benjamin
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310044
Subject(s) - hyperelastic material , interpolation (computer graphics) , mathematics , finite element method , nonlinear system , mathematical analysis , polynomial , weighting , structural engineering , classical mechanics , physics , engineering , motion (physics) , quantum mechanics , acoustics
This contribution deals with the solution of geometrically nonlinear elastic problems solved by the least‐squares mixed finite element method (LSFEM). The degrees of freedom (displacements and stresses) will be approximated using suitable spaces, namely W 1, p with p > 4 and H ( div ,Ω). In order to define the stress response of the material, different hyperelastic free energy functions will be presented. The residual forms ℛ I of the balance of momentum and the constitutive equation build a system of differential equations of first order. Choosing suitable weighting operators and applying L 2 ‐norms lead to a least‐squares functional ℱ( P,u ). The interpolation of the unknowns is accomplished using a standard polynomial interpolation for the displacements and vector‐valued Raviart‐Thomas functions for the approximation of the stresses. The formulations presented will be compared considering a uni‐axial spatial tension test. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)