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Engineering technologies frequently draw inspiration from nature, as exemplified in bio-inspired adhesive surfaces. These surfaces present textures adorned by pillars, mimicking the topography found on the pads of certain animals renowned for their exceptional adhesive capabilities. The adhesive response is strongly influenced by the morphology of these pillars. In typical existing models, perfect bonding conditions are assumed between the pillar and the countersurface, and solely the detachment process of the pillar from the countersurface is investigated. The proposed model, based on the assumption that interactions at the interface are governed by van der Waals forces modeled by the Lennard-Jones potential law, enables the examination of the entire approach and retraction cycle, tracking the movement of the pillar towards and away from the countersurface. Our findings reveal that adhesive contact mechanics is primarily influenced by the geometry of the pillar and the potential presence of interfacial 'defects', which in turn affect the distribution of contact pressure. Furthermore, we show that the detachment process may simultaneously involve various modes of separation, such as crack propagation from outer edge, crack propagation from inner defects, and uniform decohesion. This suggests that existing theoretical models alone cannot fully elucidate the complexity of detachment phenomena. Additionally, we anticipate the occurrence of hysteretic losses during the approach-retraction cycle, attributed to pull-in and pull-off contact jumps. Adhesive hysteresis is a phenomenon consistently observed in experiments but frequently overlooked in existing models. [ABSTRACT FROM AUTHOR]