13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- 8. Conclusions and outlines. The complete dynamic crack kinematics is described from the Hamiltonian variational formulation associated to a modal decomposition. It is correctly described in a swift time, compared to the prediction of more heavy FE methods, even for a small number of modes (in many cases, three modes are sufficient, for a few seconds of computational time). The method has been also applied to a material, embedding some flaws with heterogeneous fracture properties. The crack kinematics, including the crack arrest, is very sensitive to the flaw position and toughness. The main drawback of our method is the non account of the crack growth irreversibility, which leads to small stages with negative crack velocities instead transient crack arrest, but without significant consequence on the results fairness. This disadvantage may be circumvented, adding the constraint inequality 0≥ l& in the motion equations, but with probably an increase in the computational cost. An extension of this method to a beam with variable section geometry (tapered DCB), a complex toughness distribution, is straightforward. On the other hand, some developments concerning the material behaviour such as the viscosity or plasticity, or the application to bidimensionnal geometries are possible but more ticklish. References 1. N.F. Mott, Brittle fracture in mild steel plates, Engineering 165, pp. 16-18, 1948. 2. L.B. Freund, A simple model of the double cantilever beam crack propagation specimen, J. Mech. Phys. Solids, Vol. 25, pp. 69-79, 1977. 3. K. Hellan, An alternative one-dimensional study of dynamic crack growth in DCB test specimens, Int. J. of Fracture, Vol.17, n°3, pp. 311-319, June 1981. 4. S.J. Burns, W.W. Webb, Fracture Surface Energies and Dislocation Processes during Dynamical Cleavage of LiF. I. Theory, J. of Applied Physics, Vol. 41, n° 5, pp. 2078-2085, April 1970. 5. L.B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, ISBN 0-521-30330-3, 1998 (first edition 1989). 6. V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer Verlag, 2nd edition, pp. 59-68, 1989. 7. G. Debruyne, P.E. Dumouchel, J. Laverne, Dynamic crack growth : Analytical and numerical Cohesive zone models approaches from basic tests to industrial structures , Eng. Fr. Mech., 2012. 8. A.A Willoughby, Significance of Pop-in fracture toughness testing, in Int. J. of Fract. 30, R3-R6, 1986
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