Wave time-domain hypersingular integral applied to co-seismic slip of P- and S-waves from crack propagation

This work presents a wave time-domain hypersingular integral equation (WTD-HIE) method for modeling the 3D crack propagation problem of co-seismic slip under fully coupled electromagnetothermoelastic P- and S-wave fields through theoretical analysis and numerical simulations. First, the general extended displacement wave solutions are obtained by analyzing wave time-domains using the Green’s function method. Then, based on the wave time-domain boundary element method, the problem is reduced to solving a set of WTD-HIEs coupled with nonlinear boundary integral equations, in which the unknown functions are the general extended displacement discontinuity waves. The behavior of the general extended singular stress indices around the crack front terminating at the slip surface is analyzed by time-domain main-part analysis. The general extended singular stress waves and the extended dynamic stress intensity factors are obtained from closed-form solutions. In addition, a numerical method for the problem is proposed, in which the extended displacement discontinuity waves are approximated by the product of time-domain density functions and polynomials. Finally, the radiation distribution of near-field extended dynamic stress intensity factors for P- and S-waves at the crack surface are calculated, and the results are presented toward demonstrating the applicability of the proposed method.