Propagation of a Transverse Wave through the Interface of Elastic-Plastic Bodies with Dislocations

The problem of passage of a plane harmonic wave through the interface of elastic-plastic bodies with dislocations is considered. The continuum model obtained in the framework of the Lagrangian formalism and gauge dislocation theory is used to describe the studied bodies. According to this model, the shear wave in an elastic-plastic body with dislocations propagates in the form of coupled waves of transverse displacements and shear components of the plastic distortion tensor. Using the asymptotic method of slowly varying amplitude and the dispersion relations of the wave under consideration, analytical expressions are found for the reflection and refraction coefficients under various boundary conditions in the simplest case of the normal incidence of the primary wave. The dependences of the Fresnel coefficients on the frequency of the wave incident on the interface of the elastic-plastic bodies under condition of their ideal contact, sliding, viscous friction, and imperfect contact are calculated. The influence of the elastic parameters of the model and the constants of the dislocations continuum on the processes of shear waves passing through the interface of the elastic-plastic bodies under the considered boundary conditions is analyzed.