The cyclically symmetric cracks on the arc-shaped interface between a functionally graded magneto-electro-elastic layer and an orthotropic elastic substrate under static anti-plane shear load

•The problem of cyclically symmetric cracks in a composite cylinder is studied.•Methods of variable separation and Cauchy SIE are employed.•The interaction of multiple cracks is revealed.•As an example, the solution is used to analyze the single crack problem.

The present work investigates the problem of cyclically symmetric cracks on the arc-shaped interface of a functionally graded magneto-electro-elastic layer bonded onto an orthotropic elastic substrate under anti-plane shear load. Based on the method of variable separation, this mixed boundary value problem is reduced to a Cauchy singular integral equation, which is solved numerically by the Lobatto–Chebyshev quadrature technique. Special cases of the model are used to verify the correctness of theoretical derivation and numerical computation in this work. Numerical results are presented to show the effects of geometrical and physical quantities on the stress intensity factors.