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On isotropic extension of anisotropic constitutive functions via structural tensors
Author(s) -
Xiao H.,
Bruhns O. T.,
Meyers A.
Publication year - 2006
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.200410226
Subject(s) - triclinic crystal system , isotropy , transverse isotropy , orthotropic material , anisotropy , tensor (intrinsic definition) , symmetry (geometry) , monoclinic crystal system , extension (predicate logic) , mathematics , mathematical analysis , pure mathematics , geometry , physics , computer science , optics , quantum mechanics , molecule , thermodynamics , finite element method , programming language
We demonstrate that any number of vectors and second order tensors can merely characterize and represent one of the cylindrical groups and the triclinic, monoclinic, rhombic crystal classes. This suggests that, for anisotropic functions relative to any anisotropic material symmetry group other than those just mentioned, the widely used isotropic extension method via structural tensors has to result in isotropic extension functions involving at least one structural tensor variable of order higher than two. The latter do not fall within the scope of the conventional isotropic functions of vector variables and second‐order tensor variables. In addition to the trivial case of the lowest material symmetry represented by the triclinic groups, isotropic extension functions in conventional sense would be possible only for a few limited cases, including transversely isotropic, orthotropic, monotropic functions, etc.