Optimal load sharing in bioinspired fibrillar adhesives: Asymptotic solution

TL;DR

This paper derives an asymptotic solution for optimal compliance distribution in fibrillar adhesives, revealing conditions for maximum strength and improved robustness against misalignment, with validation against discrete models.

Contribution

It introduces a closed-form asymptotic model for optimal load sharing in fibrillar adhesives, enhancing understanding of their strength and robustness.

Findings

Asymptotic model matches discrete data better with more fibrils.

Optimal compliance distribution achieves equal load sharing among fibrils.

Model shows reduced sensitivity to misalignment, increasing adhesive robustness.

Abstract

We propose here an asymptotic solution defining the optimal compliance distribution for a fibrillar adhesive to obtain maximum theoretical strength. This condition corresponds to that of equal load sharing (ELS) among fibrils, i.e. all the fibrils are carrying the same load at detachment, hence they all detach simultaneously. We model the array of fibrils as a continuum of linear elastic material that cannot laterally transmit load (analogous to a Winkler soil). Ultimately, we obtain the continuum distribution of fibril's compliance in closed-form solution and compare it with previously obtained data for a discrete model for fibrillar adhesives. The results show improving accuracy for an incremental number of fibrils and smaller center-to-center spacing. Surprisingly, the approximation introduced by the asymptotic model show reduced sensitivity of the adhesive strength with respect to misalignment and improved adhesive strength for large misalignment angles.