Contact analysis in presence of spherical inhomogeneities within a half-space

Abstract

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

Thermoelastic strain and stress fields due to a spherical inclusion in an elastic half-space

“…Zhou et al (2009) introduced a fast method for solving the problem of three-dimensional arbitrarily shaped inclusions in an isotropic half-space using a combination of 2D and 3D fast Fourier transform. A fast method for solving contact problems for a half-space containing multiple inhomogeneities such as voids, cavities, inclusions and fibers was presented by Leroux et al (2010). The displacement and stress fields due to eigenstrains of all spherical inclusion were obtained using Eshelby's equivalent inclusion method along with 2D and 3D fast Fourier transforms.…”

A Stress-Criterion-Based Model for the Prediction of the Size of Wear Particles in Boundary Lubricated Contacts

“…This approach is also applicable to the calculation of the subsurface stresses [29][30][31] and temperatures in the contact [32]. Boundary element methods (BEM) are widely spread in this group.…”

Multigrid numerical simulation of contact mechanics of elastic materials with 3D heterogeneous subsurface topology

“…Since the pioneering modeling work of Eshelby [28,29], the effects of single or multiple inclusions on the stress field have been studied by many authors. Recently, Nelias et al [30,31] and Zhou et al [32,33] developed numerical approaches to perform parametric studies of the influence of inclusions on the contact parameters. Nelias et al use the Eshelby model and a 3D-FFT approach to solve the displacement and stress fields on the surface and in the subsurface.…”