Strain Incompatibility in Single Crystals: Kröner’s Formula Revisited

In this paper we prove under precise working assumptions a famous relation originally due to Ekkehart Kröner (Physiques des défauts, Les Houches session XXXV, 1980 ) relating linear elastic strain incompatibility and dislocation and disclination densities. The 3 D case with a set of isolated skew (s...

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Bibliographic Details
Published in:Journal of elasticity 2011-03, Vol.103 (1), p.95-111
Main Author: Van Goethem, Nicolas
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Classroom Note
Physics
Physics and Astronomy
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Summary:In this paper we prove under precise working assumptions a famous relation originally due to Ekkehart Kröner (Physiques des défauts, Les Houches session XXXV, 1980 ) relating linear elastic strain incompatibility and dislocation and disclination densities. The 3 D case with a set of isolated skew (skew lines are lines which do not intersect but are not parallel either) defect lines in a single crystal is considered according to a mathematical approach taking into account the combined effects of field multivaluedness and concentration properties.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-010-9275-4