Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials

Abstract

Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single force acting on the surface of a half space with a power-law varying elastic modulus, the deformation produced by constant pressure acting on a rectangular element was calculated and the influence matrix was obtained for a rectangular grid. The inverse problem for the calculation of required stress in contact area from a known surface deformation was solved by use of conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used which drastically reduces the computation time. For the adhesive contact of graded material, the detachment criterion based on the method of Pohrt and Popov was proposed. A number of numerical test for the problem having exact analytical solution have been carried out confirming the correctness of underlying ideas and numerical implementation.

Boundary element method for nonadhesive and adhesive contacts of a coated elastic half-space

“…Recently it was also applied to contacts between flat-ended indenters of complicated shape and a flat soft body [12]. In [13], the BEM was developed for contacts with power-law graded materials.…”

Adhesive contact of rough brushes

“…Contrary to the above mentioned works, we consider the numerically exact solution of the adhesive contact problem using the boundary element method as described in [16] using the mesh-dependent detachment criterion [17], which later was extended to power-law-graded media [18] and extensively tested and validated experimentally in [19]. In this work, we find the dependence of the adhesive force on the size of the brush, the fill factor of pillars and the statistical distribution of the pillar heights (simulating the relative roughness of surfaces in contact).…”

Adhesive Force of Flat Indenters With Brush-Structure

“…This method can be applied to various adhesive contact problems, while some of them have been validated by existing theories or analytical solutions: the case of a spherical indenter validated by the classical JKR theory [16], the case of a cylindrical punch by Kendall's theory, tests with toroidal indenter, can be found in [17], and with elliptical one as well as two circular punches in [18]. Recently the BEM has been extended for contacts of power-law functionally graded materials [19] and has been validated by the theoretical solution and the method of the dimensionality reduction [20]. This effective numerical tool enables us to carry out simulation of various brush structures.…”