The behavior of two parallel interface cracks in magneto–electro–elastic materials under an anti-plane shear stress loading

An Interface Crack with Mixed Electro-Magnetic Conditions at it Faces in a Piezoelectric / Piezomagnetic Bimaterial under Anti-Plane Mechanical and In-Plane Electric Loadings

“…The presentations (32), (33) and (35), (36) were formulated for mechanical, electrical, and magnetic factors via a functions which are analytic in the whole plane except the crack region. With these representations the combined Dirichlet-Riemann boundary value problem (37), (38) and Hilbert problem (44) are formulated and solved in the form of relatively simple analytical formulas for any position of the point a.…”

“…Substituting (53) into (36), (39) and taking into account that ⟨ 2 ( 1 , 0)⟩ = 0, ⟨ 1 ( 1 , 0)⟩ = 0 at ( , ) we obtain the following expression for the displacement jump:…”

Interaction among interfacial offset cracks in composite materials under the anti‐plane shear loading

“…The results for the SIF at the tips of the cracks can be obtained as [37] $$$$\begin{equation} K_a=\lim _{x\rightarrow a+}\ \sqrt {2\ \pi \ (x-a)}\ \tau _{yz}^{(2)}(x,0) = -4\ \sqrt {\pi } \ \beta _4\ \sum _{n=1}^{\infty } c_n\ \frac{1}{\sqrt {2a}}\ \frac{\Gamma (2n-1/2)}{(2n-2)!} , \end{equation}$$$$ $$$$\begin{equation} K_b=\lim _{x\rightarrow b-}\ \sqrt {2\ \pi \ (b-x)}\ \tau _{yz}^{(3)}(x,h) =- 4\ \sqrt {\pi }\ \beta _1\ \sum _{n=1}^{\infty } \ b_n\ \frac{1}{\sqrt {c-b}}\ \frac{\Gamma (n+3/2)}{n!}$$…”

“…Under similar loading conditions, three cracks under static thermo-mechanical loadings were studied by Tanwar et al [36]. In [37], the authors have investigated the behaviour of two symmetric parallel interfacial cracks under anti-plane shear stress loading. Das and Patra [38] have studied dynamic SIFs in moving Griffith cracks present in dissimilar orthotropic materials.…”

2D fracture analysis of magnetoelectroelastic composites by the SBFEM

“…The magnetoelectroelastic fields for dissimilar semi-infinite magnetoelectroelastic bimaterial subjected to a general concentrated magnetoelectroelastic load were obtained analytically in Wan et al [6]. Zhou et al [7] presented the field intensity factors for the parallel interface cracks in magnetoelectroelastic multi-materials under an anti-plane shear load and Hu et al [8] investigated more complex dynamic problems involving the interface crack between magnetoelectroelastic and functionally graded elastic layers. 2D stress singularities in multi-magnetoelectroelastic material wedges were studied in Liu and Chue [9] and 3D stress singularities in the fracture magnetoelectroelastic body were reported in Huang and Hu [10].…”