Transonic Edge Dislocation Problem

A Volterra edge dislocation moving in an infinite isotropic elastic medium under shear prestress is considered as a model of a shear rupture in the Earth’s crust formed at seismic depths and propagating at velocities in the range between the elastic shear and longitudinal wave velocities. In the plane strain approximation, the equations of stationary motion of the medium around the dislocation are reduced to an elliptic-hyperbolic system of equations for velocities and stresses, which is integrated using analytic functions of a complex variable and the method of characteristics. The invariant J-integral is used to estimate the deformation energy released during the dislocation motion depending on the velocity, shear stress at infinity, length of a fan adjacent to the dislocation tip, and Burgers vector distribution in the fan.