The strength of an adhesive contact between two bodies can strongly depend on the macroscopic and microscopic shape of the surfaces. In the past, the influence of roughness has been investigated thoroughly. However, even in the presence of perfectly smooth surfaces, geometry can come into play in form of the macroscopic shape of the contacting region. Here we present numerical and experimental results for contacts of rigid punches with flat but oddly shaped face contacting a soft, adhesive counterpart. When it is carefully pulled off, we find that in contrast to circular shapes, detachment occurs not instantaneously but detachment fronts start at pointed corners and travel inwards, until the final configuration is reached which for macroscopically isotropic shapes is almost circular. For elongated indenters, the final shape resembles the original one with rounded corners. We describe the influence of the shape of the stamp both experimentally and numerically. Numerical simulations are performed using a new formulation of the boundary element method for simulation of adhesive contacts suggested by Pohrt and Popov. It is based on a local, mesh dependent detachment criterion which is derived from the Griffith principle of balance of released elastic energy and the work of adhesion. The validation of the suggested method is made both by comparison with known analytical solutions and with experiments. The method is applied for simulating the detachment of flat-ended indenters with square, triangle or rectangular shape of cross-section as well as shapes with various kinds of faults and to "brushes". The method is extended for describing power-law gradient media.
Using the boundary element method, we calculate the normal interfacial stiffness and constriction resistance of two elastic bodies with randomly rough surfaces and varying fractal dimensions. The contact stiffness as a function of the applied normal force can be approximated by a power law, with an exponent varying from 0.51 to 0.77 for fractal dimensions varying from 2 to 3.
The boundary element method as a numerical tool in contact mechanics is widely used and allows for surface roughness to be investigated with very fine grids. However, for every two grid points, influence coefficients have to be employed for every forcedisplacement combination. In this paper, we derive the matrixes of influence coefficients for the deformation of an elastic half space, starting from the classical solutions of Boussinesq and Cerruti. We show how to overcome complexity problems by using ..T-based fast convolution. A comprehensive algorithm is given for solving the case of dry Coulomb friction with partial slip. The resulting computer program can be used effectively in iterative schemes also in similar problems, such as mixed lubrication and notably improves the applicability of the boundary element method in contact mechanics.
It was shown earlier that some classes of three-dimensional contact problems can be mapped onto one-dimensional systems without loss of essential macroscopic information, thus allowing for immense acceleration of numerical simulations. The validity of this method of reduction of dimensionality has been strictly proven for contact of any axisymmetric bodies, both with and without adhesion. In [T. Geike and V. L. Popov, Phys. Rev. E 76, 036710 (2007)], it was shown that this method is valid "with empirical accuracy" for the simulation of contacts between randomly rough surfaces. In the present paper, we compare exact calculations of contact stiffness between elastic bodies with fractal rough surfaces (carried out by means of the boundary element method) with results of the corresponding one-dimensional model. Both calculations independently predict the contact stiffness as a function of the applied normal force to be a power law, with the exponent varying from 0.50 to 0.85, depending on the fractal dimension. The results strongly support the application of the method of reduction of dimensionality to a general class of randomly rough surfaces. The mapping onto a one-dimensional system drastically decreases the computation time.
The adhesive contact between a parabolic indenter with superimposed roughness and an elastic half space is studied in the JKR-limit (infinitely small range of action of adhesive forces) using the boundary element method with mesh-dependent detachment criterion suggested in 2015. Three types of superimposed roughness are considered: one-and two-dimensional waviness and randomly rough roughness. It is shown that in the case of regular waviness, the character of adhesion is governed by the Johnson adhesion parameter. For our randomly rough surfaces a new adhesion parameter has been identified numerically, which uniquely determines the adhesive strength of the contact.
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