Analysis of 3D fluid driven crack propagation problem in co-seismic slip under P- and S-waves by hybrid hypersingular integral method

This work reports a new and accurate way of theoretical and numerical description of the extended 3D fluid (electromagnetic and flow) driven crack progression in co-seismic slip under P- and S-waves. First, based on the viscous fluid flow reciprocal work theorem, the hybrid hypersingular integral equation (HIE) method proposed by the author was defined by combined with the coupled extended wave time-domain HIE and the extended diffused interface phase field method. The general extended 3D fluid flow velocity wave solutions are obtained by the extended wave time-domains Green’s function method. The 3D extended dynamic fluid driven crack modeling under fully coupled electromagnetothermoelastic P- and S-wave and flow field was established. Then, the problem is reduced to solving a set of extended hybrid HIEs coupled with nonlinear boundary domain integral equations, in which the unknown functions are the general extended flow velocity discontinuity waves. The behavior of the general extended singular stress indices around the crack front terminating is analyzed by hybrid time-domain main-part analysis. The general extended singular pore stress waves (SPSWs) and the extended dynamic stress intensity factors (DSIFs) on the fluid driven crack surface are obtained from closed-form solutions. In addition, a numerical method for the problem is proposed, in which the extended velocity discontinuity waves are approximated by the product of time-domain density functions and polynomials. The extended DSIFs and general extended SPSWs are calculated, and the results are presented toward demonstrating the applicability of the proposed method.