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Numerical Analysis of Properties of Dislocations in Anisotropic Media within the Range of Linear Elasticity
Author(s) -
Malén K.
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.19700380125
Subject(s) - dislocation , hypergeometric function , mathematical analysis , anisotropy , mathematics , elasticity (physics) , transformation (genetics) , integral equation , geometry , physics , optics , condensed matter physics , chemistry , biochemistry , gene , thermodynamics
The analysis of a curved dislocation in an anisotropic medium must be done numerically. The fields can be expressed in various line integral forms. In the analysis used in this paper the basic data are derived from data for straight dislocations. For comparison some other line integral expressions are given. The explicit expressions for the roots to the sextic equation in terms of hypergeometric functions do not seem to have advantages over a direct iterative solution of the equation. The angular derivatives of field quantities for straight dislocations can be found using the transformation properties of the elastic constants. A simple example is given of the use of an integration over angle using data for straight dislocations to estimate the force on a dislocation.