The gauge theory of dislocations: conservation and balance laws

Markus Lazar (1) , Charalampos Anastassiadis (2)

1 Heisenberg Research Group [Darmstadt]
2 TUD

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie's-infinitesimal invariance criterion we obtain conserved translational and rotational currents for the total Lagrangian density made up of an elastic and dislocation part. We calculate the broken scaling current. Looking only on one part of the whole system, the conservation laws are changed into balance laws. Because of the lack of translational, rotational and dilatation invariance for each part, a configurational force, moment and power appears. The corresponding path-independent J, L and M integrals are obtained. Only isotropic and homogeneous materials are considered and we restrict ourselves to a linear theory. We choose constitutive laws for the most general linear form of material isotropy.

Mots clés: Physical Sciences

Markus Lazar, Charalampos Anastassiadis. The gauge theory of dislocations: conservation and balance laws. Philosophical Magazine, 2008, 88 (11), pp.1673-1699. ⟨10.1080/14786430802255653⟩. ⟨hal-00513919⟩