Numerical solution of dissimilar inclusion problem for square notch with small round corners in plane elasticity

Abstract

In this paper, the stress solution for a square notch with small round corners is studied. The square notch is composed of two portions, or the matrix and the inclusion. The elastic property of the inclusion portion is different to that of the matrix. Remote loading is applied. When the dissimilar inclusion is embedded in the matrix, the stress state in the inclusion will be changed significantly. The interface conditions along interface are formulated exactly. Complex variable function method is used to solve the problem. The complex potentials in the matrix and the inclusion are assumed in different structure. In the formulation, the number of the equations is larger than that of the unknowns. Therefore, the weight residue technique is used to solve the algebraic equation. The tangential, normal and shear stress components along the interface from the matrix and inclusion side are evaluated from the solution of the algebraic equation. In the computation, significant stress concentration has been found for the tangential stress component.