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.
Scala, R., Van Goethem, N. (2019). Variational evolution of dislocations in single crystals. JOURNAL OF NONLINEAR SCIENCE, 29(1), 319-344 [10.1007/s00332-018-9488-4].
Variational evolution of dislocations in single crystals
Scala R;
2019-01-01
Abstract
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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https://hdl.handle.net/11365/1087432