Semi-permeable crack analysis in a 2D magnetoelectroelastic medium based on the EMPS model

• The semi-permeable crack in EMPS model of magnetoelectroelastic media is studied.
• Extended dislocation theory is used to obtain the non-linear analytical solution.
• A uniquely iterative method is adopted in solving the nonlinear problem.
• Different boundary conditions on crack face have great influence on the solution.
• Electric and magnetic saturated properties have great influence on the solution.

For a crack in a magnetoelectroelastic plane under the electrically and magnetically semi-permeable boundary condition, we derive the non-linear analytical solution of the strip electric–magnetic polarization saturation (EMPS) model. Using the extended dislocation theory and integral equation method, we obtain the electric and magnetic yielding zones, as well as the field intensity factor and local J-integral. Adapting an iterative method, numerical examples were performed to analyze the effect of different boundary conditions and the electric–magnetic saturated properties on the electric displacement and magnetic induction in the crack cavity, electric and magnetic yielding zones, stress intensity factor and local J-integral.