The calculation of the glide force on a dislocation in finite elasticity requires a suitable description of the variation of the deformation due to dislocation motion. This was achieved here by extending the linear Somigliana-type dislocation model to finite strains. The core was modeled by a strip of finite width where the displacement jump continuously decreased with the distance to the dislocation tip. In the case of finite transformations, this distance could be defined in the deformed or in the undeformed state. By defining it in the undeformed natural state of the crystal, it was shown that the work dissipated by friction in the core region only depended upon the dislocation motion. Using the principle of virtual work, the equation of the dislocation motion and several alternative expressions for the glide force were derived. The obtained force may be interpreted as a generalization of Eshelby's configurational forces for a non-coherent singular surface. In the linear case, the glide force of Peach and Koehler as well as the well-known expression of the self-force due to De Wit and Koehler were retrieved.

The Glide Force on a Dislocation in Finite Elasticity. B.Fedelich: Journal of the Mechanics and Physics of Solids, 2004, 52[1], 215-47