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Low‐order locking‐free mixed finite element formulation with approximation of the minors of the deformation gradient
Author(s) -
Kraus Alex,
Wriggers Peter,
Viebahn Nils,
Schröder Jörg
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6168
Subject(s) - hyperelastic material , finite element method , discretization , mathematics , mixed finite element method , mathematical analysis , extended finite element method , boundary knot method , nonlinear system , boundary value problem , finite strain theory , finite element limit analysis , geometry , boundary element method , physics , structural engineering , engineering , quantum mechanics
Summary In this work, a low‐order mixed finite element formulation for three‐dimensional nonlinear elastic problems is presented. The main goal of this paper is to develop a robust and efficient element formulation to overcome locking arising in the cases of hyperelastic bending, quasi‐incompressibility, and anisotropy. For this, a low‐order discretisation of a five‐field Hu‐Washizu functional written in terms of the minors of the Cauchy‐Green tensor is used. For the tested boundary value problems, the proposed element formulation is more accurate and computational efficient than comparable element formulations.