Calculus of Variations and Geometric Measure Theory
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R. Scala - N. Van Goethem

Variational evolution of dislocations in single crystals

created by scala on 04 Dec 2018


Accepted Paper

Inserted: 4 dec 2018
Last Updated: 4 dec 2018

Journal: Journal of Nonlinear Science
Year: 2018


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.


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