Dynamic response of cracked non‐homogeneous magneto‐electro‐elastic layer sandwiched by two dissimilar orthotropic layers

Abstract

AbstractThis paper is concerned with the transient response of cracked functionally graded magneto‐electro‐elastic layer (FGMEE) bonded between dissimilar orthotropic layers under impacts. Fourier and Laplace transforms are employed to obtain the analytical solution of a dynamic magneto‐electro‐elastic dislocation with time‐dependent Burgers' vector at the FGMEE layer. Expressions for stress, electric displacement, and magnetic inductions in the vicinity of the magneto‐electro‐elastic dislocation are derived. The solutions are used to derive singular integral equations for the FGMEE layer containing multiple cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface by converting them to a system of linear algebraic equations. Finally, a numerical Laplace inversion algorithm is employed to determine the dynamic stress intensity factor. Numerical examples demonstrate the effects of the non‐homogeneity parameter of the FGMEE layer, applied electric and magnetic loads, and the crack geometry on the dynamic stress intensity. This solution can be used as a Green's function to solve transient problems involving multiple cracks in a functionally graded magneto‐electro‐elastic layer.