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On the reference‐state problem in the non‐linear elasticity theory of continua with dislocations
Author(s) -
Stojanovitch R.
Publication year - 1962
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.19620020506
Subject(s) - dislocation , elasticity (physics) , tensor (intrinsic definition) , linear elasticity , infinitesimal strain theory , mathematics , internal stress , ideal (ethics) , distribution (mathematics) , mathematical analysis , cauchy stress tensor , classical mechanics , physics , geometry , materials science , thermodynamics , condensed matter physics , finite element method , philosophy , epistemology , composite material
Abstract The problem of internal stresses in solids is discussed for a given distribution of dislocations (dislocation density tensor). The treatment is based on a system of coordinates which refers to the configuration of the ideal (undeformed) solid. Basic equations. which involve the non‐linear stress‐strain relations and admit the application of the Kröner‐Seeger iteration procedure, are derived under some restricting assumptions on the magnitude of strains.