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Solution of the incompatibility problem in linear three‐dimensional anisotropic media for an isotropic incompatibility tensor
Author(s) -
Michelitsch Th.,
Wunderlin A.
Publication year - 1996
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221950113
Subject(s) - isotropy , viscous stress tensor , tensor (intrinsic definition) , symmetric tensor , tensor density , anisotropy , cauchy stress tensor , hooke's law , tensor field , exact solutions in general relativity , elasticity (physics) , mathematical analysis , mathematics , linear elasticity , cartesian tensor , tensor contraction , symmetry (geometry) , cauchy elastic material , strain rate tensor , physics , geometry , constitutive equation , quantum mechanics , finite element method , thermodynamics
A solution of the incompatibility problem in three‐dimensional anisotropic elasticity is derived for the case that the incompatibility tensor has isotropic symmetry. To that end an infinitely extended linear elastic anisotropic medium is assumed. Under these conditions the internal stresses are obtained by pure differentiations from the corresponding fourth‐order stress function tensor. This result is then used to express the internal stress tensor as a convolution of the incompatibility tensor and the elastic Green's function tensor.