A novel singular integral operator technique for analyzing semipermeable four collinear cracks in a magneto-electro-elastic solid based on the EMPS model

This manuscript introduces a novel analytical technique using singular integral operators (SIOs) to study the strip electric-magnetic polarization saturation (EMPS) model with four collinear cracks, including two pairs of symmetrical unequal cracks, embedded in an infinite magneto-electro-elastic (MEE) solid. By applying the EMPS model and the distributed dislocation technique (DDT) while leveraging symmetry, we formulate singular integral equations for the coupled mechanical, electrical, and magnetic cracks based on their dislocation density functions. These equations are then transformed into Cauchy-type singular integral equations using nonlinear transformation. Since the reduced system of singular integral equations is defined over two disjoint intervals, an SIO-based technique is developed for the problem where Cauchy-type SIOs and inverse operators for each dislocation density function are defined, and then using their identities, the analytical solutions for the unknown dislocation density functions are derived after simplification. Iterative methods are employed to determine semipermeable crack-face conditions and the lengths of saturated zones. Numerical analysis shows that the distances between cracks and the crack length ratio significantly affect the lengths of saturated zones, crack tip opening potential (CTOP), crack tip opening induction (CTOI), crack opening displacement (COD), and the local stress intensity factor (LSIF), while inter-crack distance variations have a negligible impact on crack-face conditions. Validation of the results for the specific cases of the stated problem confirms the accuracy and efficacy of the developed SIO-based technique and the analytical solutions.