On the Nonlinear Continuum Theory of Dislocations: A Gauge Field Theoretical Approach

摘要

A nonlinear continuum theory of material bodies with continuously distributed dislocations is presented, based on a gauge theoretical approach. Firstly, we derive the canonical conservation laws that correspond to the group of translations and rotations in the material space using Noether’s theorem. These equations give us the canonical Eshelby stress tensor as well as the total canonical angular momentum tensor. The canonical Eshelby stress tensor is neither symmetric nor gauge-invariant. Based on the Belinfante-Rosenfeld procedure, we obtain the gauge-invariant Eshelby stress tensor which can be symmetric relative to the reference configuration only for isotropic materials. The gauge-invariant angular momentum tensor is obtained as well. The decomposition of the gauge-invariant Eshelby stress tensor in an elastic and in a dislocation part gives rise to the derivation of the famous Peach-Koehler force.