# Analyse numérique: exercises et problèmes corrigés by Héron Bernard, Issard-Roch Françoise, Picard Colette

By Héron Bernard, Issard-Roch Françoise, Picard Colette

Heron, Issard-Roch, Picard. examine numerique (fr)(Dunod, 1999)(ISBN 2100043722)(C)(302s)

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6). ref Two peaks appear in the temporal evolution of d(z h , z h ) (dotted line in Fig. 6). 5 crack propagation starts in data without the effect. Those peaks show the time when the difference in crack path starts. t = 10 t = 20 ref t = 30 t = 40 ref Fig. 5 u h − u h (upper) shows the difference of displacement u, and z h − z h the difference of phase field (crack shape) z (bottom) shows Phase Field Crack Growth Model with Hydrogen Embrittlement Fig. 2 0 0 10 20 time 30 40 50 5 Concluding Remarks A complex model of the crack growth is proposed, and shows some numerical results with some simple assumptions of the hydrogen embrittlement and faster diffusivity on crack surface.

Metall. Trans. 3, 437–451 (1972) 8. : The phenomenon of rupture and flow in solids. Philos. Trans. Roy. Soc. Lond. A221, 163–198 (1921) 9. : Numerical implementation of the variational formulation of brittle fracture. Interfaces Free Bound. 9, 411–430 (2007) 10. : Energy minimizing brittle crack propagation. J. Elast. 52, 201–238 (1998/99) 11. : Modeling and numerical simulations of dendritic crystal growth. Physica D 63, 410–423 (1993) 12. : New development in FreeFem++. J. Numer. Math. 20, 251–265 (2012) On Singularities in 2D Linearized Elasticity Hiromichi Itou Abstract The aim of this paper is to introduce some convergent expansion formulae of solutions of two-dimensional linearized elasticity equation so-called as Navier’s equation around a crack tip and a tip of thin rigid inclusion, explicitly.

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