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Incompatible deformations – plastic intermediate configuration
Author(s) -
Grammenoudis P.,
Tsakmakis Ch.
Publication year - 2008
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.200800015
Subject(s) - covariant transformation , finite strain theory , polar decomposition , curvature , continuum mechanics , context (archaeology) , mathematics , differential geometry , tensor (intrinsic definition) , manifold (fluid mechanics) , polar , classical mechanics , deformation (meteorology) , mathematical analysis , geometry , physics , finite element method , geology , engineering , paleontology , mechanical engineering , astronomy , meteorology , thermodynamics
There are many approaches in continuum mechanics involving incompatible deformations, one well‐known example being the polar decomposition of the deformation gradient tensor. Such deformations have in the past been regarded rather in the context of local configurations. In the present paper, we discuss incompatible deformations among others, also from the point of view of material lines. Related covariant derivatives and spatial differential operators are introduced and investigated. In particular, it is shown that components of curvature tensors, present in many gradient constitutive theories, may be expressed in terms of the difference between different connections for the same manifold. These issues are illustrated with reference to multiplicative decompositions of deformation gradient tensors into elastic and plastic parts. Two classes of model materials are addressed, non‐polar and micropolar ones.