Dynamics of stick-slip in peeling of an adhesive tape

TL;DR

This paper models the complex stick-slip dynamics in adhesive tape peeling using differential-algebraic equations, revealing how inertia and pull speed influence the emergence of rich, previously unreported behaviors.

Contribution

It introduces a novel dynamical model for tape peeling that incorporates inertia and pull speed effects, providing new insights into stick-slip phenomena.

Findings

Stick-slip jumps emerge purely from the dynamics.

Inertia significantly affects the nature of the dynamics.

A phenomenological peel force function reproduces experimental trends.

Abstract

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. We derive the equations of motion for the angular speed of the roller tape, the peel angle and the pull force used in earlier investigations using a Lagrangian. Due to the constraint between the pull force, peel angle and the peel force, it falls into the category of differential-algebraic equations requiring an appropriate algorithm for its numerical solution. Using such a scheme, we show that stick-slip jumps emerge in a purely dynamical manner. Our detailed numerical study shows that these set of equations exhibit rich dynamics hitherto not reported. In particular, our analysis shows that inertia has considerable influence on the nature of the dynamics. Following studies in the Portevin-Le Chatelier effect, we suggest a phenomenological peel force function which includes the influence of the pull speed. This reproduces the decreasing nature of the rupture force with the pull speed observed in experiments. This rich dynamics is made transparent by using a set of approximations valid in different regimes of the parameter space. The approximate solutions capture major features of the exact numerical solutions and also produce reasonably accurate values for the various quantities of interest.