Multiple crack problem in nonhomogeneous composite materials subjected to dynamic anti-plane shearing

A recently developed method for the dynamic response of nonhomogeneous composite material subjected to in plane loading is further extended to accommodate the case of anti-plane loading. It is assumed that the composite material is orthotropic and all the material properties vary arbitrarily along the thickness direction. In the analysis, the elastic region is modeled using a series of layers of infinite length, with each layer having slightly different properties. By utilizing the Laplace transform and Fourier transform technique, the general solution for each layer is derived. The singular integral equations of the entire elastic region are then obtained through introducing the mechanical boundary and layer interface conditions via the flexibility/stiffness matrix approach. The integral equations are solved by weighted residual value method. As the numerical illustrations, the dynamic stress intensity factors for a cracked metal-ceramic joint with a functionally graded interlayer under sudden applied stress on the joint surface are presented. The results demonstrate that there existing optimal nonhomogeneity parameter at which the stress intensity factor is minimized.