Calculus of Variations and Geometric Measure Theory

S. Cacace - A. Garroni

A multi-phase transition model for dislocations with interfacial microstructure

created by garroni on 02 Feb 2008


Submitted Paper

Inserted: 2 feb 2008

Year: 2008


We study, by means of Gamma-convergence, the asymptotic behavior of a variational model for dislocations moving on a slip plane. The variational problem is a two-dimensional multi-phase transition-type energy given by a nonlocal term and a nonlinear potential which penalizes noninteger values for the components of the phase. In the limit we obtain an anisotropic sharp interfaces model. The relevant feature of this problem is that optimal sequences in general are not given by a one dimensional profile, but they can create microstructure.

Keywords: Gamma-convergence, phase transitions, dislocations, MIcrostructure