Variational Evolution of Dislocations in Single Crystals

In this paper, we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem consists of a polyconvex stored elastic energy plus a dislocation energy and some higher-order terms. The dislocations are modeled by...

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Bibliographic Details
Published in:Journal of nonlinear science 2019-02, Vol.29 (1), p.319-344
Main Authors: Scala, Riccardo, Van Goethem, Nicolas
Format: Article
Language:English
Subjects:
Analysis
Classical Mechanics
Crystals
Dislocations
Economic Theory/Quantitative Economics/Mathematical Methods
Energy dissipation
Evolution
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Single crystals
Theoretical
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Summary:In this paper, we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem consists of a polyconvex stored elastic energy plus a dislocation energy and some higher-order terms. The dislocations are modeled by means of integral one-currents. Moreover, we discuss a novel dissipation structure for such currents, namely the flat distance, that will serve to drive the evolution of the dislocation clusters.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-018-9488-4