Variational approach in dislocation theory

Abstract

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke's law the variational framework gives the same field equations as Kröner's theory. However, the variational method proposed allows to study many other problems like dislocation core regularisation, role of elastic anharmonicity and dislocation--solute atom interaction. The aim of the paper is to demonstrate that these problems can be handled on a systematic manner.

16 pages, 4 figures. Minor changes in the text and few numerical corrections. Few references also added

References in corpus (2)

• Defect-induced incompatibility of elastic strains: dislocations within the Landau theory of martensitic phase transformations
• Evolution of the correlation functions in 2D dislocation systems

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• Continuum dynamics of the formation, migration and dissociation of self-locked dislocation structures on parallel slip planes
• Semi-discrete modeling of systems of wedge disclinations and edge dislocations via the Airy stress function method
• Abnormal subgrain growth in a dislocation-based model of recovery
• Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement
• Plasticity as Spontaneous Breaking of Symmetry
• Variational approach to determine the properties of dislocations at finite deformation