Analysis of self-similar rate-dependent interfacial crack propagation in mode II

  • Milan JirásekEmail author
  • Olivier Allix
Original Paper


The present study analyzes the fundamental properties of a rate-dependent cohesive model applied to the description of dynamic mode-II crack propagation. To make a semi-analytical treatment possible, the idealised problem of a crack along the interface between a semi-infinite elastic layer and a rigid substrate is considered. Solutions corresponding to the propagation of the crack tip at a constant speed are constructed. Using asymptotic properties of the solution far from the crack tip allows obtaining the complete solution of the boundary value problem by direct integration without iterations, using a specific form of the shooting method. By conversion of the problem to dimensionless variables, the behavior of the system for all possible crack velocities and arbitrary combinations of material and geometric parameters can be characterized. The dependence of fracture energy and other important characteristics on model parameters and the crack speed can then be analyzed. Even if the approach is applied to a specific form of damage rate dependence and motivated by the analysis of delamination propagation, the same technique could be used for other classes of interfacial cohesive rate-dependent models.


Rate-dependent damage model Mode-II interfacial crack Dynamic self-similar propagation Semi-analytic solution Direct shooting method 



This research has been financially supported by the European Regional Development Fund through the Center of Advanced Applied Sciences at the Czech Technical University in Prague (Project No. CZ.02.1.01/0.0/0.0/16_019/0000778).


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Fac Civil Engn, Dept MechCzech Tech UnivPrague 6Czech Republic
  2. 2.LMT, ENS Paris-Saclay/CNRS/Université Paris-SaclayCachan CedexFrance

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