Lifting the singular nature of a model for peeling of an adhesive tape |
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Authors: | R De G Ananthakrishna |
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Institution: | (1) Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, 76100, Israel;(2) Materials Research Centre and Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore, 560012, India |
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Abstract: | We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. Due to the constraint between
the pull force, peel angle and the peel force, the equations of motion derived earlier fall into the category of differential-algebraic
equations (DAE) requiring an appropriate algorithm for its numerical solution.
By including the kinetic energy arising from the stretched part of the tape in the Lagrangian, we derive equations of motion
that support stick-slip jumps as a natural consequence of the inherent dynamics itself, thus circumventing the need to use
any special algorithm. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic
algorithm introduced for the earlier singular equations. We find that mass has a strong influence on the dynamics of the model
rendering periodic solutions to chaotic and vice versa. Apart from the rich dynamics, the model reproduces several qualitative
features of the different waveforms of the peel force function as also the decreasing nature of force drop magnitudes. |
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Keywords: | 5 45 -a Nonlinear dynamics and chaos 68 35 Np Adhesion 02 90 +p Solution of differential-algebraic equation |
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