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Three-dimensional finite elements for large deformation micropolar elasticity. (English) Zbl 1231.74399

Summary: In this paper, we propose a three-dimensional finite element formulation for micropolar elasticity dealing with large displacements and small strains (or equivalently small strains and finite rotations). A comprehensive outline of the theory’s characteristical features is given and we try to elucidate the set-up of a possible non-linear finite element implementation. One focus of the present study is on a sound verification process, featuring the construction of an enhanced Patch Test and the assessment of quadratic asymptotic rates of convergence. Aspects of performance and validity are discussed at a set of numerical examples. We show that, the proposed model is able to reproduce the transition between micropolar and classical continua highly accurate. Finally, we present results underlining the implementation’s applicability in the realm of finite deformation with arbitrarily large rotations.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
74A35 Polar materials
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