Collisions and Fracture: a 1-D Theory. How to Tear off a Chandelier from the Ceiling |
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Authors: | Elena Bonetti Michel Frémond |
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Affiliation: | (1) Dipartimento di Matematica F.Casorati, Università di Pavia, Via Ferrata, 1, I-27100 Pavia, Italy;(2) Laboratoire Lagrange – LCPC, 58 boulevard Lefebvre, 75732 Paris, France |
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Abstract: | When a plate falls on the ground, it breaks. We study this phenomenon at the macroscopic level. We restrict ourselves to 1-D problems and illustrate the theory with a chandelier to which a falling stone is tied. The collisions are assumed instantaneous. Percussions are introduced at the unknown fracture points. Equations of motion and constitutive laws give a set of differential equations, whose corresponding variational problem may be solved in SBV (special functions of bounded variation). The example shows how the theory applies and gives realistic results. |
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Keywords: | collisions fractures velocities of bounded variation |
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