The Exponentially Faster Stick-Slip Dynamics of the Peeling of an Adhesive Tape

The stick-slip dynamics is considered from the nonlinear differential-algebraic equation (DAE) point of view and the peeling dynamics is shown to be a switching differential index DAE model. In the stick-slip regime with bifurcations, the differential index can be arbitrarily high. The time scale of the peeling velocity, the algebraic variable, in this regime is shown to be exponentially faster compared to the angular velocity of the spool and/or the stretch rate of the tape. A homogenization scheme for the peeling velocity which is characterized by the bifurcations is discussed and is illustrated with numerical examples.