A Contact Model of Heterogeneous Material by Method of Images

Contact analyses of heterogeneous materials may find crucial applications in many tribological studies. However, the simulations of such analyses may be difficult to be implemented since the nonlinear behaviors caused by the material heterogeneity and contact may be more complicated. Based on Eshelby's equivalent inclusion method (EIM), an arbitrarily shaped inhomogeneity interacting with a contact load may be evaluated by an equivalent inclusion model with a contact load, where the influences of the boundary surface are taken into account through the method of images. In order to improve the computational efficiency, a two-dimensional fast Fourier transform based algorithms (2D-FFT) with zero padding and wrap-around order are employed to solve the contact problem. To benchmark the present solutions, an elastic half-space containing inhomogeneities under Hertzian-type contact load is considered, and parametric studies are further performed to demonstrate the effects of elastic modulus and depth on the stress field.