Mixed mode analysis of multiple cracks in magneto-electro-elastic plane

Abstract

In this paper, the mixed mode problem for a magneto-electro-elastic (MEE) material containing multiple cracks under in-plane magneto-electro-mechanical loads is analyzed. First, the solution to an generalized dislocation is obtained in the infinite MEE plane. The Fourier transform is employed to derive closed-form expressions for the stress, electric displacement and magnetic induction components. The solution to the problem is consequently reduced to derive singular integral equations for dislocation density functions on the surfaces of cracks. The equations are then solved numerically to determine field intensity factors for cracks. At the final step, the numerical results of calculated field intensity factors are presented for multiple curved cracks under certain ratios of the applied magnetical and electrical loads to mechanical loads. Also, the field intensity factors are calculated for various crack patterns with different geometries. Moreover, the analysis can be applied for any number of cracks with arbitrary arrangement in the MEE regions under in-plane condition.