Numerical EIM with 3D FFT for the contact with a smooth or rough surface involving complicated and distributed inhomogeneities

•An efficient method to model materials with complicated inhomogeneities in contact.•An approach capable of dealing with rough-surface contact of heterogeneous materials.•Full 3D FFTs and a new mesh scheme enhance computation efficiency and flexibility.

This paper presents a numerical solution approach of solving smooth- and rough-surface contact problems involving distributed inhomogeneities with arbitrary shapes and different material properties, based on the numerical equivalent inclusion method (EIM). Full 3D FFT techniques and a mesh differential refinement scheme are incorporated into the proposed solution method to enhance the efficiency and flexibility. Comparative studies referencing the FEM and a simplified method demonstrate the efficiency and accuracy of the present method. Computations of several heterogeneous contact cases verify the capability of the method in solving complicated and rough-surface contact problems involving materials with distributed inhomogeneities.