We study the dynamic debonding of a onedimensional inextensible film, subject to a monotonic loading and under the hypothesis that the toughness of the glue can take only two values. We first consider the case of a single defect of small length in the glue where the toughness is lower than in the remaining part. The dynamic solution is obtained in a closed form and we prove that it does not converge to the expected quasistatic one when the loading speed tends to zero. The gap is due to a kinetic energy which appears when the debonding propagates across the defect at a velocity which is of the same order as the sound velocity. The kinetic energy becomes negligible again only when the debonding has reached a critical distance beyond the defect. The case of many defects is then considered and solved using an exact numerical solution of the wave equation and the Griffith law of propagation. The numerical results highlight the effects of the time evolution of the kinetic energy which induce alternate phases of rapid and slow debonding, these oscillations depending essentially on the volume fraction of the highest toughness.Keywords brittle fracture · crack propagation · Griffith's criterion · dynamic fracture · quasistatic evolution · shock waves · nonlinear stability PACS 62.20.mj · 62.50.Ef · 43.25.Cb · 68.35.Ja · 83.60.Uv
The aim of this Note is to investigate the discrete approach of anisotropic damage by microcracking by specifying the choice of the set of fixed directions that are to be effectively employed. Three conditions are presented, concerning the description of any damage configuration, and in particular isotropic and transversely isotropic ones. These conditions are given at two different orders in orientation (order 2 and order 4), as both tensorial terms intervene in the thermodynamic potential. The results show that the second order conditions are sufficient to represent a configuration of open microcracks, whereas fourth order conditions are necessary to represent a configuration of closed ones.
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