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The effect of crystal symmetries on the locality of screw dislocation cores. (English) Zbl 1428.35572

The aim of this article is to improve on the continuum linearized elasticity far-field description. The article focuses on screw dislocations under antiplane shear kinematics, in the cubic, hexagonal and body-centred-cubic lattices. The theoretical results are used to construct boundary conditions that lead to new supercell approximations. The resulting new numerical scheme is presented along with its convergence analysis. The analysis is carried out for short-ranged interatomic many-body potentials.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
49N60 Regularity of solutions in optimal control
70C20 Statics
74B20 Nonlinear elasticity
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74G65 Energy minimization in equilibrium problems in solid mechanics
74E15 Crystalline structure
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References:

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