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.
Similar content being viewed by others
References
D. Maugis, M. Barquins, Adhesion 12, edited by K.W. Allen (Elsevier, London, 1988), p. 205; D. Maugis, CRNS Report. (1991)
M. Ciccotti, B. Giorgini, M. Barquins, Int. J. Adhes. Adhes. 18, 35 (1998)
C. Gay, L. Leibler, Phys Today 52, 48 (1999)
M. Barquins, M. Ciccotti, Int. J. Adhes. Adhes. 17, 65 (1997)
M.C. Gandur, M.U. Kleinke, F.J. Galembeck, Adhes. Sci. Technol. 11, 11 (1997)
D. Maugis, C.R. Acad. Sci. Paris 304, 775 (1987)
D.C. Hong, S. Yue, Phys. Rev. Lett. 74, 254 (1995)
D.C. Hong, Private communication
R. De, A. Maybhate, G. Ananthakrishna, Phys. Rev. E 70, 46223 (2004)
E. Hairer, C. Lubich, M. Roche, Numerical Solutions of Differential-algebraic Systems by Runge-Kutta Methods (Springer-Verlag, Berlin, 1989)
R. De, G. Ananthakrishna, Phys. Rev. E 71, R55201 (2005)
Actually, the kinetic energy at the peel front should be \(\frac{m}{6} \dot u^2\). However, this does not alter the results
G. Ananthakrishna, R. De, Lecture Notes in Physics 705, 423 (Springer, 2006)
B.N.J. Persson, Sliding Friction: Physical Principles and Applications, 2nd edn. (Springer, Heidelberg, 2000)
A. Portevin, F. Le Chatelier, C.R. Acad. Sci. Paris 176, 507 (1923); F. Le Chatelier, Rev. de Métal. 6, 914 (1909)
L.P. Kubin, C. Fressengeas, G. Ananthakrishna, Collective Behaviour of Dislocations, in Dislocations in Solids, edited by F.R.N. Nabarro, M.S. Deusbery (North-Holland, Amsterdam, 2002), Vol. 11, p. 101
G. Ananthakrishna, Statistical and Dynamical Approaches to Collective Behaviour of Dislocations in Dislocations in Solids, edited by J. Hirth, F.R.N. Nabarro (North-Holland, 2007), Vol. 13, p. 81; Current Theoretical Approaches to Collective Behaviour of Dislocations, Phys. Rep. 440, 113 (2007)
L.P. Kubin, K. Chihab, Y. Estrin, Acta. Metall. 36, 2707 (1988)
P.G. de Gennes, Langmuir 12, 4497 (1996)
E.C.G. Sudarshan, N. Mukunda, Classical Dynamics: A Modern Perspective (John Wiley and Sons, New York, 1974)
M. Diener, The Mathematical Intelligence 6, 38 (1984)
N. Minirsky, Nonlinear Oscillations (Van Nostrand, Princeton, New Jersey, 1962)
S.H. Strogatz, Nonlinear Dynamics and Chaos (Westview Press, 2000)
G. Ananthakrishna, M.C. Valsakumar, Phys. Lett. A 95, 69 (1983)
G. Ananthakrishna et al., Phys. Rev. E 60, 5455 (1999)
M.S. Bharathi, et al., Phys. Rev. Lett. 87, 165508 (2001)
G. Ananthakrishna, M.S. Bharathi, Phys. Rev. E 70, 26111 (2004)
R. De, G. Ananthakrishna, Phys. Rev. Lett. 97, 165503 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
De, R., Ananthakrishna, G. Lifting the singular nature of a model for peeling of an adhesive tape. Eur. Phys. J. B 61, 475–483 (2008). https://doi.org/10.1140/epjb/e2008-00093-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2008-00093-1