The adhesive contact between bodies is a fundamental problem and is known to play a significant role in tribology, nanotechnology, colloidal science and many industrial processes. Adhesion arising from van der Waals (vdW) interactions strongly influences the mechanical behaviour of the interacting bodies. In this work, we study adhesive contact between an elastic hemispherical asperity and a rigid half-space using a self-consistent body-force (SCBF) formulation that incorporates vdW adhesion and steric repulsion as body forces. The body force formulation overcomes the restrictive assumptions of surface-force methods. A two-step quasi-static procedure (Appendix A) avoids the numerical ill-conditioning near jump-to and jump-off contact instabilities, enabling analysis of compliant systems. This study elucidates the effects of material and geometric parameters on adhesive contact behaviour. Results demonstrate that material compliance and geometry systematically influence elastic deformation, pull-off force, and instability separation. For stiff bodies ( \(\mu < 0.1\) ), geometric size has a significant impact on the pull-off. For the range \(0.1< \mu < 1\) , it is found that the pull-off force strongly depends on both the elastic modulus and the asperity size. However, for highly compliant bodies ( \(\mu > 1.5\) ), the pull-off force is weakly dependent on both the properties and may plateau before reaching the JKR value. The results also show that for all values of \(\mu\) , the instability is primarily controlled by elastic modulus, and that the asperity size only becomes a determining factor for \(\mu > 4\) . We further establish two geometry-based contact definitions: \(a_0\) and \(a_{\text {max}}\) , which qualitatively match the DMT-M and JKR theory descriptions, respectively and highlight the limitations of the classical models. The SCBF formulation eliminates the stress and displacement singularities of classical analytical models. The volumetric distribution of attractive force reveals a “sandwiching” effect, resulting in significantly high compressive stress magnitudes at the contact centre. The high subsurface stresses suggest that realistic adhesive contacts can potentially lead to material failure, accompanied by substantially increased energy dissipation, which fundamentally challenges purely elastic models. This framework advances our fundamental understanding of “soft adhesive contact” mechanics and adhesive wear mechanisms, enabling the predictive design of surfaces with controlled adhesion by better representing contact behaviour across a range of materials, from stiff to highly compliant.
