Numerical method for the adhesive normal contact analysis based on a Dugdale approximation

Modeling adhesion between two contacting surfaces plays a vital role in nano-tribology. However, providing analytical models, although desirable, is mostly impossible, in particular for complex geometries. Therefore, much attention has to be paid to numerical modeling of this phenomenon. Based on the adhesive stress description of the Maugis-Dugdale model of adhesion, which is credible over a broad range of engineering applications, an extended Conjugate Gradient Method (CGM) has been developed for adhesive contact problems. To examine the accuracy of the proposed method, the common case of the adhesive contact of a rigid sphere on an elastic half-space is investigated. To further evaluate the accuracy of this method, the adhesive contact of a rigid sphere over a wavy elastic half-space is also studied for different combinations of the amplitude and wavelength. There is good agreement between the analytical solution and the values predicted by the proposed method in the force-approach curves. Moreover, the calculation of pull-off force at a bisinusoidal interface between two surfaces is carried out for various cases to study the effects of different influential parameters including work of adhesion, elastic modulus, radius curvature at a crest, and the wavelength ratio. A curve is fitted on the calculated pull-off force in order to express it as an analytical relation. Similar to the JKR and DMT expressions for the pull-off force of a rigid ball on an elastic half-plane, the fitted curve is not affected by the elastic modulus and is linearly dependent on the radius of curvature and the work of adhesion. In addition, a power law governs the relation between pull-off force and the wavelength ratio. In the end, it is shown that roughness can either increase or decrease the adhesive force at a rough interface depending on the degree of the roughness.