Effects of the Presence of Multiple Spherical Inclusions Within an Elastic Half-Space in a Circular Point Contact

A fast method to solve contact problems when one of the mating bodies contains multiple heterogeneous inclusions is proposed, and numerical results are presented for soft or stiff inhomogeneities. The emphasis is put on the effects of spherical inclusions on the contact pressure distribution. The computing time and allocated memory are kept small, compared to the finite element method, by the use of analytical solution to account for the presence of inhomogeneities. The Eshelby’s equivalent inclusion method is considered in the contact solver. An iterative process is implemented to determine the displacements and stress fields caused by the eigenstrains of all spherical inclusions. The proposed method can be seen as an enrichment technique for which the effect of heterogeneous inclusions is superimposed to the homogeneous solution in the contact algorithm. 3D and 2D FFT are utilized to improve the computation efficiency. Configurations such as stringer and cluster of spherical inclusions are analyzed. The effects of the Young modulus, Poisson ratio, size and location of the inhomogeneities are also investigated.