A mathematical solution of a special mixed-boundary-value problem of anisotropic elasticity

The mixed-boundary-value problem of an anisotropic bimaterial interface containing a finite cut with displacements prescribed on one side and tractions on the other is solved using the Stroh formulation for anisotropic elastic materials. For the case of anisotropic materials and bimaterials under unidirectional loading, a rotation along the cut can occur depending on the nature of anisotropy. A relation between the applied loading and the rotation of the cut is obtained as a function of material orientation. In addition, stress singularities at the tips of the cut are obtained along with crack-opening displacements and stresses along the cut. Results are presented for a single anisotropic material and a bimaterial composed of two anisotropic materials. The present formulation reduces to the well-known results in the special cases of an isotropic bimaterial interface for the mixed problem, and of a crack and an anti-crack along a bimaterial interface.