An Introduction to Impacts

Christopher Glocker (1)

1 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

Different methods to model and solve multi-contact collisions are presented in this report. The standard impact constitutive laws from non-smooth dynamics are reviewed for planar frictional collisions and formulated in terms of set-valued maps and linear complementarity. For the frictionless case, a geometric concept based on kinematic, kinetic and energetic compatibility is developed, which provides access to non-standard impact events as in Newton’s cradle. Within this context, Moreau’s impact law is reviewed and stated in various ways, providing even access to the collision problem at re-entrant corner points as an extension. Based on Moreau’s law, a geometric classification of impacts is proposed. Several examples are presented, such as the frictional reversible impact at a super ball, Newton’s cradle and the rocking rod.

Domaines: Mécanique des structures [physics.class-ph]

Christopher Glocker. An Introduction to Impacts. Haslinger J.; Stavroulakis G.E. Nonsmooth Mechanics of Solids , 485, Springer, 2006, CISM International Centre for Mechanical Sciences, 9783211482414. ⟨10.1007/978-3-211-48243-8_2⟩. ⟨hal-01716872⟩