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

Abstract

This 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-electroelastic 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.

Transient analysis of a cracked functionally graded magneto‐electro‐elastic rectangular finite plane under anti‐plane mechanical and in‐plane electric and magnetic impacts

“…In Equation ( 3), the field of mechanical displacement is coupled with the field of electric and magnetic potentials. In order to decouple the governing equations, we now define the following auxiliary functions 15 :…”

“…14 In another work, the transient response of an FGMEE layer bonded to two different layers composed of orthotropic materials containing multiple interacting parallel cracks has been solved by Arhani and Ayatollahi. 15 The paper, among other results, analyzed the effects of crack geometry, loadings coupling factors, and the properties of the materials on the DSIF. Generally, obtaining analytical closed-form solutions for the transient crack problem in FGMEEMs with finite geometry is complicated and only those with infinite or semi-infinite geometries may be found in the previous studies.…”

Thermal Contact Response of a Transversely Isotropic Magneto-Electro-Elastic Coating

“…Wan et al studied the periodic interface damage problem of multilayer piezoelectric/piezomagnetic composites subjected to electric and magnetic loads, and they analyzed the effect of the material parameters on the stress intensity factor [ 21 ]. Arhani and Ayatollahi [ 22 ] derived an analytical solution for MEE dislocation in a cracked, functionally graded MEE material and investigated the dynamic stress intensity factor.…”

Modeling of crack path in layered architectures composed of dissimilar materials

“…For instance, different structures at different length scales are organized hierarchically to provide stiffness as well as fracture resistance in some biological systems 1 . Multi‐layered components comprising three main functional layers are applied in some moving mechanical systems within the internal combustion engine, which provide the combined properties of high mechanical strength, conformability, good wear resistance, and fatigue performance 3–5 . Multilayer metal films are used to endure large stretching, compressing, or twisting deformations to resist the occurrence of cracking and buckling in stretchable electronics, especially paper‐like electronic displays, wearable electronics, and prosthetic skin 6–8 .…”

“…1 Multi-layered components comprising three main functional layers are applied in some moving mechanical systems within the internal combustion engine, which provide the combined properties of high mechanical strength, conformability, good wear resistance, and fatigue performance. [3][4][5] Multilayer metal films are used to endure large stretching, compressing, or twisting deformations to resist the occurrence of cracking and buckling in stretchable electronics, especially paper-like electronic displays, wearable electronics, and prosthetic skin. [6][7][8] However, these varied advantages offered by layered architectures in the optimization of performance may be limited due to a lack of understanding of the failure mechanisms.A series of studies have been carried out on the mechanisms of fatigue of layered architectures, but most just focus on the effect of multiple layers on the crack growth behavior and note this extends the crack growth life in…”