Numerical method for quasi-static adhesive elastic contact subjected to tangential loading

•A three-dimensional numerical model of adhesive elastic contact based on the Boussinesq-Cerruti integral equations for elasticity and the Maugis-Dugdale model for adhesion, considering the coupled effects of adhesive energy, normal indentation, and tangential frictional shear, capable of analyzing rough-surface problems.•Numerical solution for details of the adhesion zone and the stick–slip state of the contact area.•In-depth understanding of the attenuation mechanism of adhesion energy with the increase in tangential load and/or the normal force if the ratio of tangential load to normal load remains constant.•Details of stick-zone variation on a concentric wavy surface with the increase in tangential loading.•Impact of amplitude and wavelength of a concentric wavy surface on the magnitude, direction, and distribution of shear tractions. This paper presents a three-dimensional (3D) numerical model for simulating the adhesive contact with linear isotropic elasticity considering the interaction between normal and tangential loads. The model is based on the Boussinesq-Cerruti integral equations for elasticity, the Maugis-Dugdale (MD) model for adhesion, and the friction/adhesion interaction theory in the McMeeking model; it uses the Coulomb's law of friction to identify the occurrence of local microslip. Efficient and accurate determination of the contact behavior, together with adhesive and stick/slip regions, uses the iterative conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) algorithm. The model analyzes adhesive-contact pressure, shear traction, and subsurface stress fields. It is used to study the effects of increasing tangential loading on the variations of stick/slip zones and adhesive-energy dissipation, as well as the influence of sinusoidal roughness on surface adhesion behavior. Compared with most theoretical models, the proposed numerical model has no restrictions on surface geometry and roughness of contact bodies, and it should have a wider range of applications.