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Contact: collisions and fractures. A predictive theory Elena Bonetti, University of Pavia, Francesco Freddi, University of Parma, Michel Frémond, University of Roma Tor Vergata, Laboratorio Lagrange.

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obstacle Collision is instantaneous. There are velocities before collision and velocities after collision Fractures result from the collision. Thus velocity is a discontinuous function of x Positions of the fractures are unknown

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The velocities are discontinuous: with respect to time with respect to space right left

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There are closed form solutions for 1-D problems: A stone is tied to a chandelier.

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The impenetrability condition is taken into account by This is an old idea of Jean Jacques Moreau. CRAS, 259, 1965, p. 3948-3950, Sur la naissance de la cavitation dans une conduite. Journal de Mécanique, 5, 1966, p. 439-470, Principes extrémaux pour le problème de la naissance de la cavitation.

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The damage after collision DivU after collision

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Effect of the velocity

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Numerical Simulation rigid velocity undamaged material Two representative cases have been analyzed: all the parameters are fixed except the density of the material thus an heavy material and a light material, having the same resistance, have been considered (a ratio between the material densities equal to 10 has been adopted).

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Numerical Simulation: heavy material

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Numerical simulation: light material

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Numerical Simulation Rectangular slab M. Zineddin, T. Krauthammer, Int. J. Impact Eng. 34, 2007 Imposed percussion

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We have a schematic description of this phenomenon with 7 parameters

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