The emergence of complexity in a common scotch roller

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The fracture is a very complicated phenomenon and its dynamics is not well described, until today, by a consistent physical and/or mathematical model. In this paper we synthetically present the main experimental and theoretical results for the peeling of an adhesive tape, i.e. a viscoelastic dissipative system, viewed as a two dimensional fracture propagation. Varying the control parameter the crack dynamics appears stable in a first branch of the state curve, unstable in a second branch with stick-slip propagation, and finally again stable, but very rapid, in a third region. The unstable stick-slip dynamics becomes more and more irregular increasing the control parameter and exhibits different behaviors with transitions between periodic, aperiodic and disordered regimes. In an experiment recently performed at ESPCI-PMMH (Paris, France), the emergence of hierarchical structures in a broad range of time scales was observed in a definite region of the stick-slip regime, and this is one the indicators commonly used speaking of complex systems. At last, we underline that we do not still have a complete mathematical description of empirical data and that we lack a physical model able to explain the observed complex dynamics.

Ciccotti M. and Giorgini B. The emergence of complexity in a common scotch roller. In: Symétries, brisures de symétries et complexité. Edited by L. Boi (Peter Lang, Bern, 2006) pp. 187-216.

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