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

• Published in: Fatigue & fracture of engineering materials & structures 2022-05, Vol.45 (5), p.1448-1463
• Main Authors: Arhani, Afzal Akbari, Ayatollahi, Mojtaba
• Format: Article
• Language: English
• Subjects: Algorithms; Crack geometry; Cracks; Dislocation density; Dynamic response; dynamic stress intensity factor; Elastic layers; Exact solutions; functionally graded magneto‐electro‐elastic layer; Green's functions; Homogeneity; impact loads; Integral equations; Laplace transforms; Linear algebra; multiple cracks; orthotropic layer; Singular integral equations; Stress intensity factors; transient analysis; Transient response
• ISSN: 8756-758X; 1460-2695
• DOI: 10.1111/ffe.13673

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‐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. Highlights Cracked FGMEE layer sandwiched by two dissimilar orthotropic layers is investigated. Interaction of multiple cracks is studied for layered smart structure under sudden load. The analysis can be applied for any number of cracks with arbitrary arrangement. The effects of the non‐homogeneity parameter and crack location on DSIFs are discussed.