Effective properties of magnetoelectroelastic interfaces weakened by micro‐cracks

Abstract

The effective properties of a microscopically damaged interface between two dissimilar magnetoelectroelastic materials are investigated using a micro‐statistical model. The interface is modeled as damaged by a periodic array of micro‐cracks. The micro‐cracks over a period interval of the interface are randomly generated and are either all (i) magnetically and electrically impermeable, or (ii) magnetically permeable and electrically impermeable, or (iii) electrically permeable and magnetically impermeable, or (iv) magnetically and electrically permeable. The conditions on the micro‐cracks are formulated in terms of hypersingular integro‐differential equations with the jumps in the elastic displacements, the electric potential and the magnetic potential across opposite micro‐crack faces being unknown functions to be determined. Once the unknown functions are determined, the effective properties of the microscopically damaged interface can be readily computed. The effects of the crack density and the material constants on the effective properties are investigated in detail.