Numerical analysis of the contact problem considering inhomogeneous inclusions

Nonmetallic inclusions and cracks during the smelting generate stress concentration, which may be the fatigue source under an alternating load. The fatigue source may enable some materials to separate from the matrix material and the cracks occur. The cracks can greatly influence the fatigue life of material. Based on the semi-analytical method(SAM), the computational domain is divided into many infinitesimal cuboids, thus each inclusion can be represented by a number of infinitesimal cuboids. According to equivalent inclusion method(EIM), each cuboid has an unknown eigenstrains which are obtained by a set of simultaneous constitutive equations about stresses and strains relationship. The contact pressure is solved based on conjugate gradient method; furthermore, the subsurface stress distributions are obtained by the semi-analytical method. The two-dimensional and three-dimensional fast Fourier transform(DC-FFT) based approaches are used to speed up the computations related to deformation and eigenstress. The results show the excellent stability and convergence of the algorithm; the inclusions greatly affect the contact pressure and stress distribution; the inclusions with large size and small depth have significant effect on the contact performance. The inclusion with arbitrary shape can be modeled by this model.