In the modeling of dislocations one is led naturally to energies concentrated on lines,where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may be identified with divergence free matrix-valued measures supported on curves or with 1-currents with multiplicity in a lattice. In this paper we develop the theory of relaxation for these energies and provide one physically motivated example in which the relaxation for some Burgers vectors is nontrivial and can be determined explicitly. From a technical viewpoint the key ingredients are an approximation and a structure theorem for 1-currents with multiplicity in a lattice.
Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity / Sergio, Conti; Garroni, Adriana; Annalisa, Massaccesi. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 54:(2015), pp. 1847-1874. [10.1007/s00526-015-0846-x]
Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity
GARRONI, Adriana
Membro del Collaboration Group
;
2015
Abstract
In the modeling of dislocations one is led naturally to energies concentrated on lines,where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may be identified with divergence free matrix-valued measures supported on curves or with 1-currents with multiplicity in a lattice. In this paper we develop the theory of relaxation for these energies and provide one physically motivated example in which the relaxation for some Burgers vectors is nontrivial and can be determined explicitly. From a technical viewpoint the key ingredients are an approximation and a structure theorem for 1-currents with multiplicity in a lattice.File | Dimensione | Formato | |
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