Methods to compute dislocation line tension energy and force in anisotropic elasticity

摘要

Aframe indifferent formulation of the energy and force on a dislocation in a line tension model in an anisotropic elasticity media is presented. This formulation is valid for any dislocation line direction and Burgers' vector and expresses the energy and force in terms of an integral for which no general analytical solution can be calculated. Three numerical methods are investigated to evaluate the energy and the force: direct numerical integration, spherical harmonics expansions and an interpolation table method. We analyze the convergence and computational cost of each method and compare them with a view to selecting the most appropriate for implementation in large scale dislocation dynamics codes.