Numerical solution technique for calculating interior crack condition parameters in the moving DBY‐EMPS model for semi‐permeable cracked magneto‐electro‐elastic materials

Abstract The choice of electric and magnetic boundary conditions on crack surfaces significantly impacts the analysis of crack problems in magneto–electro–elastic (MEE) materials. The semi‐permeable condition is deemed more realistic than impermeable or permeable conditions, yet literature lacks a comprehensive method for solving the interior electric displacement and magnetic induction in such scenarios. This paper proposes a novel approach, exemplified by a Yoffe‐type moving crack within a MEE layer featuring strip‐like zones of electrical saturation, magnetic induction, and mechanical yielding. Transforming the mixed boundary value problem using the Fourier transform and the Copson method, we derive a set of coupling Fredholm integral equations (FIEs) of the second kind. Numerical discretization and the Newton–Raphson method for solving nonlinear equations are employed to effectively solve for the crack's interior electric displacement and magnetic induction. Numerical results explore the relationships between external loads and crack‐face electric displacement and magnetic induction relative to zone lengths. Comparative analysis between semi‐permeable and impermeable crack conditions reveals that the interior magnetic displacement increases with magnetic load but decreases with electrical and mechanical load. Furthermore, the zone lengths are influenced by three loadings (i.e., mechanical, electrical, and magnetic loads), independent of the MEE layer's thickness or the size ratio between mechanical, electrical, and magnetic zone lengths. We outline the algorithmic flow (see (F)) and present illustrative examples to demonstrate the efficacy of our technique. This study provides a valuable reference for solving semi‐permeable crack problems in finite MEE materials with distinct strip‐like zones.