2008/04/11 by Markus Lazar, Charalampos Anastassiadis · 28 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Classical mechanics #Conservation law #Dislocation #Elasticity and Material Modeling #Gauge symmetry #Gauge theory #Geometry #Isotropy #Lagrangian #Law #Mathematical physics #Mathematics #Microstructure and mechanical properties #Noether's theorem #Nonlocal and gradient elasticity in micro/nano structures #Physics #Quantum mechanics #Tensor (intrinsic definition) #Translational symmetry #cond-mat.mtrl-sci
paper · pdf · doi:10.1080/14786430802255653
published in The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics 88(11), 1673-1699 (Taylor & Francis) · 28 pages
openalex publication_date 2008/04/11 · arxiv created 2008/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.