Strength statistics of adhesive contact between a fibrillar structure and a rough substrate

Abstract

Equal distribution of load among fibrils in contact with a substrate is an important characteristic of fibrillar structures used by many small animals and insects for contact and adhesion. This is in contrast with continuum systems where stress concentration dominates interfacial failure. In this work, we study how adhesion strength of a fibrillar system depends on substrate roughness and variability of the fibril structure, which are modelled using probability distributions for fibril length and fibril attachment strength. Monte Carlo simulations are carried out to determine the adhesion strength statistics where fibril length follows normal or uniform distribution and attachment strength has a power-law form. Our results indicate that the strength distribution is Gaussian (normal) for both the uniform and the normal distributions for length. However, the fibrillar structure having normally distributed lengths has higher strength and lower toughness than one having uniformly distributed lengths. Our simulations also show that an increase in the compliance of the fibrils can compensate for both the substrate roughness and the attachment strength variation. We also show that, as the number of fibrils n increases, the load-carrying efficiency of each fibril goes down. For large n, this effect is found to be small. Furthermore, this effect is compensated by the fact that the standard deviation of the adhesive strength decreases as 1= ffiffiffi n p .

Gecko‐Inspired Surfaces: A Path to Strong and Reversible Dry Adhesives

“…[81] These results are surprising, as theoretical studies have predicted a beneficial effect of hierarchy in adhesion. [45,111,[113][114][115][116][117] This can be tentatively attributed to the imperfection of the fibrils of the second level as a consequence of misalignment during mask superposition and lithographic exposure [41] or to the lower density of contact elements on hierarchical structures. [81] To date, only hierarchical structures containing macroscopic first-level fibrils (1.2/0.1 mm in height, 300/50 mm in diameter for first/second level) succeeded in increasing adhesion, although with only marginal improvements over single-level ones.…”

Functional Adhesive Surfaces with “Gecko” Effect: The Concept of Contact Splitting

“…[9] (iv) Hierarchy effect: theoretical studies have predicted a beneficial effect of hierarchy in adhesion. [112][113][114][115][116] However, two-level structures produced so far showed a drop in adhesion as compared to single-level structures. [117] Shear adhesion strength was also reduced for hierarchical structures.…”

Adhesive contact of rough brushes

“…For example, the adhesion can be optimized by controlling the size and shape of the fiber cap [2–3]; this mushroom-shaped microstructure can provide a stronger adhesive performance than the flat punch [4–5]. The compliant fiber is known to increase the strength of adhesion [6–7]. Almost all works in this field are based on the idea that contact splitting is the sole reason for the enhanced adhesion [8–9].…”