Adhesive contact of rough brushes

Abstract

The adhesive contact between a rough brush-like structure and an elastic half-space is numerically simulated using the fast Fourier transform (FFT)-based boundary element method and the mesh-dependent detachment criterion of Pohrt and Popov. The problem is of interest in light of the discussion of the role of contact splitting in the adhesion strength of gecko feet and structured biomimetic materials. For rigid brushes, the contact splitting does not enhance adhesion even if all pillars of the brush are positioned at the same height. Introducing statistical scatter of height leads to a further decrease of the maximum adhesive strength. At the same time, the pull-off force becomes dependent on the previously applied compression force and disappears completely at some critical roughness. For roughness with a subcritical value, the pressure dependence of the pull-off force qualitatively follows the known theory of Fuller and Tabor with moderate modification due to finite size effect of the brush.

Simulation of Adhesive Contact of Soft Microfibrils

“…In the case of rough brushes where the height of pillars has an exponential probability density, similar qualitative results to Fuller and Tabor's prediction [16] were obtained, which states that the adhesive force is reduced with roughness [15]. However, in these studies [13][14][15], the pillars are rigid, which is not the case for insect or gecko feet. The flexibility may play an important role in adhesion and contact splitting.…”

“…For a flat brush structure, it is found that the adhesive force is roughly proportional to the square root of the real contact area, meaning that adhesion is not enhanced [14]. In the case of rough brushes where the height of pillars has an exponential probability density, similar qualitative results to Fuller and Tabor's prediction [16] were obtained, which states that the adhesive force is reduced with roughness [15]. However, in these studies [13][14][15], the pillars are rigid, which is not the case for insect or gecko feet.…”

“…It is noted that we replace the sum operation by matrix convolution, since σ is a matrix in discrete form. Thus, the deflection of the n-th spring ∆l n corresponds to elements of the matrix on the right side of Equation (15). Let us discuss the size and element arrangement of squared matrix Π.…”

“…Brush structures have also been modeled by rigid micro-cylinders, based on Kendall's theory of cylindrical contacts [13]. Recently, adhesive contacts Lubricants 2020, 8, 94 2 of 11 between a rigid brush structure and an elastic half space have been numerically simulated using the boundary element method (BEM) [14,15]. For a flat brush structure, it is found that the adhesive force is roughly proportional to the square root of the real contact area, meaning that adhesion is not enhanced [14].…”

“…corresponds to elements of the matrix on the right side of Equation(15). Let us discuss the size and element arrangement of squared matrix П.…”