Rate-dependent adhesion in dynamic contact of spherical-tip fibrillar structures

Fibrillar adhesives that rely on the Van der Waals interactions exhibit fascinating prospects in dynamic attachment applications like perching of aerial robots and capture of orbital debris. Understanding the dynamic attachment/detachment behaviors of fibrillar adhesive structures plays a crucial role in realizing reliable attachment to target surfaces. In this paper, we investigate the dynamic contact of a single spherical-tip fibrillar structure model and emphasize the significance of rate-dependent adhesion. A theoretical model considering both crack-tip and bulk viscoelasticity is presented. The proposed model is verified by comparing with elaborate collision tests under different dynamic contact conditions. The dynamic evolution of contact radius, displacement and force are investigated in detail. The energy dissipation mechanism is discussed by analyzing the variation of coefficient of restitution vs. initial contact velocity. Under the combined effect of rate-dependent adhesion and inertia force, the radius-displacement curve in sticking mode appears peculiar superposition loops, and a new critical sticking mode is found which can broaden the initial velocity range that ensures successful attachment. It is demonstrated that rate-dependent adhesion and bulk dissipation are coupled closely while the former is dominant near the critical sticking velocity. Moreover, the decrease of the reference speed, pillar size, and modulus of materials are favorable for increasing the critical sticking velocity, thereby enhancing the capacity to resist dynamic detachment. This work provides an underlying theoretical support on the dynamic contact of fibrillar adhesives and offers a clear insight on the role of the rate-dependent adhesion during the process.