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On the Force Exerted upon Continuously Distributed Dislocations in a Cosserat Continuum
Author(s) -
Minagawa S.
Publication year - 1970
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.19700390123
Subject(s) - dislocation , classical mechanics , physics , tensor (intrinsic definition) , displacement (psychology) , force density , mathematics , condensed matter physics , geometry , psychology , psychotherapist
The force acting on distributed dislocations in a Cosserat continuum is studied and the expressions for the force and force density are given in tensorial form. The increase in the potential energy of the material body, caused by a displacement of distributed dislocations in a certain region of the body, is obtained. The force acting on those dislocations is deduced by differentiating it with respect to the distance through which the dislocations are displaced. The expression for the density of forces is given as follows:where s jni is the tensor of dislocation density, ∑ ij the symmetric part of stresses, M jni the couple‐stress tensor, and η ij the incompatibility tensor.