The problem on an edge dislocation running at superseismic velocity

V. M. Sadovskii, O. V. Sadovskaya

Institute of Computational Modeling of the Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, 660036 Russia

Abstract: As a model of shear rupture in the Earth’s crust at the depths of seismic activity, which grows with a velocity exceeding the velocity of longitudinal waves, we consider a Volterra edge dislocation moving in an infinite isotropic elastic medium under the action of preliminary tangential stresses. In the plane strain approximation, the equations of stationary motion of the medium around the dislocation are reduced to a hyperbolic system of equations for velocities and stresses, which is integrated by the method of characteristics. Using the invariant $J$–integral, an estimate of the energy released during the motion of dislocation is obtained, depending on the velocity, the value of tangential stress at infinity, the length of the fan adjacent to the vertex of dislocation, and on the nature of the distribution of the Burgers vector in the fan.

Keywords: shear rupture, dynamics, edge dislocation, method of characteristics, invariant integral.

UDC: 539.37

Received: 16.12.2024
Revised: 28.02.2025
Accepted: 26.03.2025

DOI: 10.33048/SIBJIM.2025.28.105

 English version: Journal of Applied and Industrial Mathematics, 2025, 19:1, 131–141