Simple models of viscoelastic fibrillar adhesion between rigid rough surfaces

Adhesive interactions between rigid rough surfaces commonly occur in biological attachment systems and bioinspired adhesives, often facilitated by fibrillar contact structures composed of soft, viscoelastic materials. In this study, we analytically investigate the behavior of such systems using two distinct models for detachment criteria: the Schapery model, which assumes a rate-independent bond energy and failure initiated by defects; and the Shrimali–Lopez-Pamies (SLP) model, which assumes failure occurs at a critical fibril elongation. The model gives reduction of pull-off pressure with increasing amplitude of roughness, although not as strongly as in the elastic case and further depending on the loading protocols: starting from a fully relaxed state leads to the highest enhancements of pull-off pressure. These findings provide insights into biological adhesion mechanisms and offer design principles for engineered adhesive systems capable of functioning on rough, rigid substrates.