Physics – Condensed Matter – Materials Science
Scientific paper
2008-06-05
Philosophical Magazine 88, Issue 11 (2008), 1673-1699
Physics
Condensed Matter
Materials Science
28 pages
Scientific paper
10.1080/14786430802255653
We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. 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 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 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. Also we give the conservation and balance laws corresponding to the gauge symmetry and the addition of solutions. From the addition of solutions we derive a reciprocity theorem for the gauge theory of dislocations. Also, we derive the conservation laws for stress-free states of dislocations.
Anastassiadis Charalampos
Lazar Markus
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