Adhesive strength of bio-inspired fibrillar arrays in the presence of contact defects

Abstract

The performance of bio-inspired fibrillar adhesives can be compromised by surface roughness, manufacturing imperfections or impurities. Previous studies investigated the cases of distributed defects on the array, and defects at the level of single fibrils. However, the influence of localized, macroscopic defects remains largely unexplored. Using numerical simulations of a discrete mechanical model for a fibrillar adhesive with a thick backing layer, we investigate how the size and location of a single circular defect affect the established scaling law between the adhesion force ($F$) and the effective compliance of the system ($β$), \ie, $F \propto β^{-1/2}$. We find that edge defects are generally more detrimental than central ones, as they act as pre-cracks that amplify stress concentrations at the adhesive's edge, accelerating a crack-like failure. Consequently, the established adhesion scaling law is preserved, with the defect only reducing the effective contact area. In contrast, a central defect fundamentally alters the mechanics of detachment. By transforming the contact geometry into an annulus, it promotes more uniform load sharing across the remaining fibrils and mitigates the edge-dominated failure mechanism. This change makes the adhesive strength less sensitive to the compliance of the system, as reflected by a less negative scaling exponent. The transition between these two regimes appears to occur for defects whose boundary merges with the one of the adhesive. These results provide practical guidance for the design, engineering and quality control of bio-inspired fibrillar adhesives.