We study, by means of ?-convergence, the asymptotic behavior 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 nonlocal term and a nonlinear potential which penalizes noninteger 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).
Gamma-limit of a phase field model of dislocations / Garroni, Adriana; S., Muller. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 36:(2005), pp. 1943-1964. [10.1137/S003614100343768X]
Gamma-limit of a phase field model of dislocations
GARRONI, Adriana;
2005
Abstract
We study, by means of ?-convergence, the asymptotic behavior 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 nonlocal term and a nonlinear potential which penalizes noninteger 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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
