Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape

TL;DR

This paper revises the equations governing adhesive tape peeling by including tape kinetic energy, enabling the natural occurrence of stick-slip jumps and revealing the significant influence of tape mass on the dynamics.

Contribution

It introduces a new model incorporating tape kinetic energy, resolving previous singularities and supporting realistic stick-slip behavior in peeling dynamics.

Findings

Inclusion of tape kinetic energy allows for natural stick-slip jumps.

Tape mass significantly affects the dynamics of peeling.

The new equations reproduce previous solutions in the low mass limit.

Abstract

It is now known that the equations of motion for the contact point during peeling of an adhesive tape mounted on a roll introduced earlier are singular and do not support dynamical jumps across the two stable branches of the peel force function. By including the kinetic energy of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier equations. Our analysis also shows that mass of the ribbon has a strong influence on the nature of the dynamics.