A New Model for Predicting Fiber Clumping Phenomenon in Bio-Inspired Dry Adhesives

Abstract

Self-adhesion, or clumping, primarily occurs in bio-inspired dryadhesives when two or more adjacent fibers become in contact and adhere to each other due to large van der Waals (vdW) intermolecular forces. Studying self-adhesion is of primary interest as dry-adhesives drastically lose their adhesion strength after few load cycles if clumping occurs. An optimization procedure to select material properties, shape, and geometry of the fibers is therefore highly desirable for both improving the adhesion and reducing the probability of clumping. Few numerical models have been utilized to attain optimal geometry and material parameters. These models are developed based on the small-deflection beam theory and use an over-simplified elastic-contact model to determine adhesion forces. In this work, a model suitable to simulate large deformations with distributed intermolecular forces is proposed. The model is based on the finite element method (FEM) and uses an adaptive meshing procedure to accurately calculate adhesion forces. By using this model, clumping is studied and predictions are compared against experimental results obtained from the literature. In addition to the FEM model, an analytical model that considers large-deflection reactions of fibers is proposed to corroborate finite element results. Results from analytical and finite element models show precise clumping predictions.

Bioinspired fibrillar adhesives: a review of analytical models and experimental evidence for adhesion enhancement by surface patterns

“…Dense arrays of high aspect ratio, small radius pillars are prone to condensation, where neighbouring pillars collapse into one another. A useful model of pillar condensation was developed by Ahmadi et al [1].…”

“…Comparison with Equation 8shows that pillars reduce the peeling strength dramatically for thin backing layers, whilst the peeling strength converges with Equation 8 for thick backing layers [80]. However, there has been no experimental verification of Zhou's model, and high aspect-ratio pillars are prone to collapsing into clumps of pillars, which is detrimental to adhesion [1].…”

A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces

“…Notable previous approaches to similar problems have made simplifying assumptions. Ahmadi and Menon [29] study the clumping of fibers due to vdW adhesion by means of an analytical 2D beam method, yet only include vdW interaction between the hemispherical tips based on an analytical expression for the interaction of two spheres. A numerical study of the influence of inter-fiber adhesion on the mechanical behavior of 2D fiber networks assumes an effective adhesion energy per unit length of perfectly parallel fiber segments and solves for the unknown contact length in a second, nested minimization algorithm [30].…”

Investigation of the peeling and pull-off behavior of adhesive elastic fibers via a novel computational beam interaction model

“…It will thus be interesting to see how these differences carry over to the resulting force responses. Two approaches to investigate the undesirable effect of clumping in fibrillar arrays used for bio-inspired dry adhesives are presented in [14]. The analytical approach aims to predict the critical fiber length leading to tip-tip contact by calculating the vdW force between assumed spherical tips of the fibers and applying it as a tip load in Euler-Bernoulli beam theory for a 2D cantilever.…”