Calculus of Variations and Geometric Measure Theory
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S. Conti - A. Garroni - S. Müller

Singular kernels, multiscale decomposition of microstructure, and dislocation models

created by garroni on 17 Feb 2010

[BibTeX]

Submitted Paper

Inserted: 17 feb 2010

Year: 2010

Abstract:

We consider a model for dislocations in crystals introduced by Koslowski, Cuitino and Ortiz, which includes elastic interactions via a singular kernel behaving as the H{12} norm of the slip. We obtain a sharp-interface limit of the model within the framework of Gamma-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitté and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound.

Keywords: non local energies, dislocations, microstructures


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