Shear Oscillations, Rotations and Interactions in Asymmetric Continuum

Abstract

A concise asymmetric continuum theory including the relations between stresses, strains, interaction fields and defects is presented. In the presented theory, the motion equations for antisymmetric part of stresses replace the balance of angular momentum. Considering the symmetric stresses, we present a new form of the motion equations for the deviatoric part of strains, arriving at the definition of shear-twist motion as the oscillation of the axes of shears and their amplitudes. With the help of Dirac tensors we present an invariant form of these motions. The motions – displacement and rotations – generated in source processes, e.g., in an earthquake source, may be generated independently or with some phase shift due to the rebound processes; therefore, in the presented asymmetric continuum theory we introduce the phase shift index between the strains and rotations. The presented invariant system of motion equations makes it possible to obtain solutions with the simultaneous strains and rotation motion or those with the π/2 phase shift between them.

Further, we include in this asymmetric theory, besides the mechanical system, some interaction fields, e.g., thermal and electric interaction.terms. The presented interaction theory is equivalent to that given by Kröner, but it is practically much simpler and includes new solutions with the simultaneous strains and rotation motions or those with the phase shift between them.