Contact of transversely isotropic materials containing inhomogeneities

This paper presents a model for the contact involving inhomogeneities with a transversely isotropic matrix and a detailed investigation of the contact behavior of this type of material loaded by a rigid spherical indenter. The model is built on the core influence coefficients (ICs) for solving the inclusion problem of transversely isotropic half-space material and the numerical equivalent inclusion method (EIM). The frictionless contact responses of the transversely isotropic materials containing stiff or compliant, rigid or void, one-type or two-types, and single or double inhomogeneities are reported, and the effect of inhomogeneity anisotropy orientation on the stress field is also shown. The analysis results reveal that the von Mises stress produced by a set of adjacent cuboidal void and rigid inhomogeneity could be more than three times that in the corresponding homogeneous half space. In addition, the maximum value of the von Mises stress in the cross-section varies with the anisotropy orientation of inhomogeneities, and the symmetry of the disturbed stress field reflects the pattern of anisotropy of the inhomogeneous material, further proving the correctness of the proposed method in solving contact problems with various symmetries.