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Translational Conservation and Balance Laws in the Gauge Theory of Dislocations
Abstract We present the translation gauge theory of moving dislocations which is mathematically analogue to the Maxwell theory of electromagnetic fields. Such a theory describes dislocations in an incompatible elastic continuum. The physical state quantities in the dislocation gauge theory are the physical velocity vector, the elastic distortion tensor, the dislocation density tensor and the dislocation current tensor. We use gauge-principles like minimal replacement known from field theories. We derive the equations of motion of dislocations. We give the isotropic as well as the anisotropic constitutive relations for the present theory. Translational conservation and balance laws are derived. We give the canonical as well as the gauge-invariant currents. We show that the dynamical Peach—Koehler force is mathematically analogous to the Lorentz force in Maxwell's theory of electromagnetic fields.
Translational Conservation and Balance Laws in the Gauge Theory of Dislocations
Abstract We present the translation gauge theory of moving dislocations which is mathematically analogue to the Maxwell theory of electromagnetic fields. Such a theory describes dislocations in an incompatible elastic continuum. The physical state quantities in the dislocation gauge theory are the physical velocity vector, the elastic distortion tensor, the dislocation density tensor and the dislocation current tensor. We use gauge-principles like minimal replacement known from field theories. We derive the equations of motion of dislocations. We give the isotropic as well as the anisotropic constitutive relations for the present theory. Translational conservation and balance laws are derived. We give the canonical as well as the gauge-invariant currents. We show that the dynamical Peach—Koehler force is mathematically analogous to the Lorentz force in Maxwell's theory of electromagnetic fields.
Translational Conservation and Balance Laws in the Gauge Theory of Dislocations
Lazar, Markus (Autor:in) / Anastassiadis, Charalampos (Autor:in)
01.01.2009
13 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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