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Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p‐version finite elements
Author(s) -
AlKinani R.,
Hartmann S.,
Netz T.
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300155
Subject(s) - isotropy , anisotropy , transversal (combinatorics) , deformation (meteorology) , finite strain theory , multiplicative function , elasticity (physics) , mathematical analysis , mathematics , geometry , physics , finite element method , optics , meteorology , thermodynamics
In this article the multiplicative decomposition of the deformation gradient into one part constrained in the direction of the axis of anisotropy and one part describing the directional deformation is proposed. This leads to a clear division of the deformation and stress states in the direction of anisotropy and a remaining part. The decomposition is explained in detail and a constitutive model of hyper‐elasticity is proposed for the case of transversal isotropy, where the behavior of the model is investigated with the aid of simple analytical examples. The model is also investigated for inhomogeneous deformation states using high‐order finite elements based on hierarchical shape functions showing the sensitivity of the accuracy of the results in the case of anisotropic media.