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Journal of Convex Analysis 24 (2017), No. 2, 547--570
Copyright Heldermann Verlag 2017

Renormalized Energy and Peach-Köhler Forces for Screw Dislocations with Antiplane Shear

Timothy Blass
Capital One Financial Corporation, Pier 1, The Embarcadero Bay 2, San Francisco, CA 94111, U.S.A.

Marco Morandotti
SISSA - International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy

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].

Keywords: Dislocations, variational methods, renormalized energy, Peach-Köhler force.

MSC: 70G75; 74B05, 49J99, 70F99

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