A set of collinear electrically and magnetically permeable cracks between two piezoelectromagnetic materials

Abstract

The plane strain problem for the bimaterial space consisting of two piezoelectromagnetic half-spaces with a finite set of cracks along the material interface is considered. It is assumed that the edges of the crack are electrically and magnetically permeable, and a mixed mechanical load and electric and magnetic fields can be set at infinity. The presentations of electro-magneto-mechanical quantities through a piecewise analytical vector function are constructed with the use of constitutive equations for piezoelectromagnetic materials. By means of these presentations the problem of linear relationship is formulated and solved analytically. Using the obtained solution, all the necessary mechanical, electrical, and magnetic components along the material interface as well as the energy release rate for all crack tips are found analytically. The asymptotic presentations of all fields around the crack tips and the crack closure integral method were used. Numerical results are obtained for different loads, location of the cracks, their number and lengths. A significant increase in energy release rates was demonstrated because of cracks converge, especially for the tips located closest to each other.