Dispersion relations for the linearized field equations of dislocation dynamics
The field equations for a Yang-Mills type gauge theory of dislocations are obtained that describe the anelastic behavior of a partially (hyper) elastic material, due to the presence of dislocation fields. Dispersion relations are calculated for an infinitely extended space-time domain and for the first order approximation (linear) to the field equations. Dispersion of both the longitudinal and transverse elastic waves is observed for sufficiently large wavelengths. Realization of the dispersion curves in a laboratory experiment could result in an actual measurement of the additional material constants, needed for a full description of the constitutive behavior of a deformable body with dislocations, according to the predictions of the theory.
decomposition of distortion into elastic and anelastic parts
asymptotic expansion of full nonlinear set of field equations
Yang-Mills type gauge theory of dislocations
scientific article; zbMATH DE number 4083106