Stress field solution to anisotropic plate with mode II crack based on pan-complex function

Abstract

The crack-tip stress problem to the anisotropic materials was mainly discussed under the shear loading model. For the sake of solving the stress boundary problem, the pan-complex function method was achieved in the first place. The elastic theory of composite materials has been clearly reviewed in order to determine the material physical parameters. Equilibrium equations and deformable compatibility condition were introduced on the basis of plane elastic mechanics. The key to the settlement of the boundary question must lie in solving the partial derivative equation and the axial transformation of the pan-complex variables. The reasonable stress functions were chosen in order to meet the needs of shear loading states. The pan-complex function and the polar coordinate replace approach are utilized with the aim of solving the stress boundary problems for the anisotropic plate. The formulas of the stress components near the crack-tip region were finally determined by the real functions. The method in this article may be much important to the fracture analysis of composite materials.