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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
92/2003

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

Adriana Garroni and Stefan Müller

Abstract

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).

Received:
10.11.03
Published:
10.11.03
MSC Codes:
82B26, 31C15, 49J45
Keywords:
dislocations, phase transitions, capacity, gamma convergence

Related publications

inJournal
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