We study, by means Gamma-convergence, the asymptotic behavior of a variational model for dislocations moving on a slip plane. The variational functional 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.
A multi-phase transition model for dislocations with interfacial microstructure / Cacace, Simone; Garroni, Adriana. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - 11:2(2009), pp. 291-316. [10.4171/ifb/212]
A multi-phase transition model for dislocations with interfacial microstructure
CACACE, SIMONE;GARRONI, Adriana
2009
Abstract
We study, by means Gamma-convergence, the asymptotic behavior of a variational model for dislocations moving on a slip plane. The variational functional 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.| File | Dimensione | Formato | |
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