Presentation on theme: "Contact: collisions and fractures. A predictive theory Elena Bonetti, University of Pavia, Francesco Freddi, University of Parma, Michel Frémond, University."— Presentation transcript:
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.
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
The velocities are discontinuous: with respect to time with respect to space right left
There are closed form solutions for 1-D problems: A stone is tied to a chandelier.
The impenetrability condition is taken into account by This is an old idea of Jean Jacques Moreau. CRAS, 259, 1965, p , Sur la naissance de la cavitation dans une conduite. Journal de Mécanique, 5, 1966, p , Principes extrémaux pour le problème de la naissance de la cavitation.
The damage after collision DivU after collision
Effect of the velocity
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).
Numerical Simulation: heavy material
Numerical simulation: light material
Numerical Simulation Rectangular slab M. Zineddin, T. Krauthammer, Int. J. Impact Eng. 34, 2007 Imposed percussion
We have a schematic description of this phenomenon with 7 parameters