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On the Physical Origin for the Geometric Theory of Continuum Mechanics
Author(s) -
Günther H.
Publication year - 1983
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19834950406
Subject(s) - continuum mechanics , affine transformation , classical mechanics , physics , continuum hypothesis , manifold (fluid mechanics) , tensor field , theoretical physics , tensor (intrinsic definition) , mathematics , geometry , quantum mechanics , exact solutions in general relativity , mechanical engineering , engineering
It is explained, that the basic notion for a geometric picture of continuum mechanics is a four dimensional material manifold. The four dimensional mechanical affinity is then the unified field for any defect distribution in the general time dependent case. The minimal number of geometric relations being valid for any continuum is formulated as a set of pure affine relations. The state variables of the theory are additional tensor fields as e.g. deformation defining a metric. A material with a well defined deformation has a Newton‐Cartan structure. Only if defects are included into the dynamical determination by additional equilibrium conditions, the theory has a pseudo relativistic structure.