Static adhesion hysteresis in elastic structures

Abstract

Adhesive interactions between elastic structures such as graphene sheets, carbon nanotubes, and microtubule axonemes exhibit hysteresis due to irrecoverable energy loss associated with bond breakage, even in static (rate-independent) experiments. Here we provide a simple theory that explains how bond breaking and elastic relaxation can drive static adhesion hysteresis over a debonding/rebonding cycle. We show that energy loss emerges from the coupling of a local event (bond breaking) to a nonlocal event (overall elastic relaxation), in a manner similar to the Lake-Thomas effect in polymers. Experiments with adherent microtubules allow us to quantify the hysteresis as a function of adhesion and elasticity parameters. Our model also helps guide the derivation of a self-consistent continuum boundary condition at the interface of adherent mechanical systems.

Stick-slip phenomena and Schallamach waves captured using reversible cohesive elements

“…Mathematical proof of this was provided by Mishra et al (2015b). Moreover, the analytical studies by Brochard-Wyart and de Gennes (2007) and Memet et al (2020) provide analytical evidence of the link between oscillations in the force-displacement curve and the stick-slip events on the surface. Recently, finite element formulations have been developed to deal with the friction-adhesion contact coupling present on the contact surface (Cocou et al, 2010;Mergel et al, 2020Mergel et al, , 2019Raous, 2011;Khajeh Salehani et al, 2019;Sauer, 2016).…”