The concept of Eshelby's energy–momentum tensor was briefly reconsidered here with respect to material defects in solid mechanics. This was 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, the kinetics were formulated in a statistical sense using Boltzmann's principle. For efficient numerical treatment, a semi-analytical method via a finite element formalism was suggested. Within this numerical technique, no restrictions on the elastic anisotropy of the material were made. The theory was applied in the situation of a two-phase system.

A Computational Concept for the Kinetics of Defects in Anisotropic Materials. S.Kolling, R.Mueller, D.Gross: Computational Materials Science, 2003, 26, 87-94