Interface cracks in anisotropic elastic bimaterials—a decomposition principle

Abstract

For a mismatched bimaterial with a single interface crack subject to a constant traction along the crack surface, the solution can be written explicitly, separated into oscillatory part and non-oscillatory part. The separation is shown to be related to the decomposition of the surface traction tr into two components t0π and 7π t0π is in the direction of the right null vector of the Ŝ matrix defined in the paper and t7π lies on the right eigenplane of Ŝ. The solution associated with t0π is non-oscillatory. It has the property that the traction along the interface is in the direction of the right null vector of Ŝ while the crack opening displacement is in the direction of the left null vector of Ŝ. The solution associated with t7π. on the other hand, is oscillatory. It has the property that the traction along the interface lies on the right eigenplane of Ŝ while the crack opening displacement lies on the left eigenplane of Ŝ. The same decomposition and properties hold for multiple interface cracks with variable tractions prescribed on the crack surfaces.