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MiS Preprint

$\Gamma$-limit of a phase-field model of dislocations

Adriana Garroni and Stefan Müller


We study, by means of $\Gamma$-convergence, the asymptotic behaviour of a variational problem modeling a dislocation ensemble moving on a slip plane through a discrete array of obstacles. The variational problem is a two dimensional phase transition type energy given by a non local term and a non linear potential which penalizes non integer values. In this paper we consider a regime corresponding to a diluted distribution of obstacles. In this case the leading term of the energy can be described by means of a cell problem formula defining an appropriate notion of capacity (that we call dislocation capacity).

MSC Codes:
82B26, 31C15, 49J45
dislocations, phase transitions, capacity, gamma convergence

Related publications

2005 Repository Open Access
Adriana Garroni and Stefan Müller

Gamma-limit of a phase-field model of dislocations

In: SIAM journal on mathematical analysis, 36 (2005) 6, pp. 1943-1964