Geodesic
Renormalized Energy and Peach-Köhler Forces for Screw Dislocations with Antiplane Shear
Journal of convex analysis, Tome 24 (2017) no. 2, pp. 547-57
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We present a variational framework for studying screw dislocations subject to antiplane shear. Using a classical model developed by P. Cermelli and M. E. Gurtin [The motion of screw dislocations in crystalline materials undergoing antiplane shear: glide, cross-slip, fine cross-slip, Arch. Ration. Mech. Anal. 148 (1999) 3--52], methods of Calculus of Variations are exploited to prove existence of solutions, and to derive a useful expression of the Peach-Köhler forces acting on a system of dislocation. This provides a setting for studying the dynamics of the dislocations, which is done in another paper of T. Blass, I. Fonseca, G. Leoni and M. Morandotti [Dynamics for systems of screw dislocations, SIAM J. Appl. Math. 75 (2015) 393--419].
Classification : 70G75, 74B05, 49J99, 70F99
Mots-clés : Dislocations, variational methods, renormalized energy, Peach-Köhler force 
@article{JCA_2017_24_2_JCA_2017_24_2_a12,
     author = {T. Blass and M. Morandotti},
     title = {Renormalized {Energy} and {Peach-K\"ohler} {Forces} for {Screw} {Dislocations} with {Antiplane} {Shear}},
     journal = {Journal of convex analysis},
     pages = {547--57},
     year = {2017},
     volume = {24},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a12/}
}
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T. Blass; M. Morandotti. Renormalized Energy and Peach-Köhler Forces for Screw Dislocations with Antiplane Shear. Journal of convex analysis, Tome 24 (2017) no. 2, pp. 547-57. http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a12/