a b s t r a c tThis paper presents a fast method of solving contact problems when one of the mating bodies contains multiple heterogeneous inclusions, 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 and subsurface stress field in an elastic half-space. 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. 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 on the homogeneous solution in the contact algorithm. 3D and 2D Fast Fourier Transforms are utilized to improve the computational efficiency. Configurations such as stringer and cluster of spherical inclusions are analyzed. The effects of Young's modulus, Poisson's ratio, size and location of the inhomogeneities are also investigated. Numerical results show that the presence of inclusions in the vicinity of the contact surface could significantly changes the contact pressure distribution. From a numerical point of view the role of Poisson's ratio is found very important. One of the findings is that a relatively 'soft' and nearly incompressible inclusion -for example a cavity filled with a liquid -can be more detrimental for the stress state within the matrix than a very hard inclusion with a classical Poisson's ratio of 0.3. Ó
The elastic solution of a tangentially loaded contact is known as Cerruti’s solution. Since the contact surfaces could be easily discretized in small rectangles of uniform shear stress the elastic problem is usually numerically solved by summation of well known integral solution. For soft metallic materials, metals at high temperature, rough surfaces, or dry contacts with high friction coefficient, the yield stress within the material could be easily exceeded even at low normal load. This paper presents the effect of a cuboid of uniform plastic strain in a half-space on the tangential displacement of a surface point. The analytical solutions are first presented. All analytical expressions are then validated by comparison with the finite element method. It is found that the influence coefficients for tangential displacements are of the same order of magnitude as the ones describing the normal displacement (Jacq et al., 2002, “Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code,” ASME J. Tribol., 124(4), pp. 653–667). This result is of great importance for frictional contact problem when coupling the normal and tangential behaviors in the elastic-plastic regime, such as stick-slip problems, and also for metals and alloys with low or moderate yield stress.
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