A computational concept for the kinetics of defects in anisotropic materials

In this paper, the idea of Eshelby’s energy–momentum tensor is briefly reconsidered with respect to material defects in solid mechanics. This is used to obtain the thermodynamic driving forces acting on centers of dilatation, dislocations and interfaces of two-phase materials. A simple constitutive kinetic law relates this force with the velocity of the defect. Alternatively, we formulate the kinetics in a statistical sense from Boltzmann’s principle. For an efficient numerical treatment we suggest a semi-analytical method via a finite element formalism. Within this numerical technique, no restrictions on the elastic anisotropy of the material are made. The theory is applied in the situation of a two-phase system.