The goal of this project is to study so-called multiple-impact laws, with and without friction, in order on one hand to improve the capabilities of numerical methods, on the other hand to better understand the dynapics of nonsmooth multibody mechanical systems. The two aspects (theory and numerics) are closely linked oe to each other, since numerical simulations have become a mandatory path to better understand the dynamics of complex systems. Thisi is true in industry with virtual prototyping, and in the academic field (granualr media, robotic systems). Multiple impacts (several impacts at the same time in the system) are a crucial phenomenon and approximate modelling that does not correctly take into account 1) the local dissipation at the contact points, 2) the global effects of energy dispersion, which are mainly due to wave effects that travel through the system, are not acceptable. The goal of this project is to design multiple restitution laws which correctly model these two aspects, and which depends on identifiable parameters, and which can be reliably simulated (no stiff equations). Moreover such a restitution law should be generic enough to correctly predict the dynamics of significantly different sysems (for instance a chain of iron balls, or a chain of tennis balls). The preliminary results obtained in C. Liu, Z. Zhao, B. Brogliato, Theoretical analysis and numerical algorithm for frictionless multiple impacts in multibody systems, INRIA research Report, available at http://hal.inria.fr are quite promissing. A third aspect of the project is the design and construction of experimental setups, which will allow us to validate the theoretical and numerical results (and in turn which are indispensable to circumvent the main physical effects of a multiple impact). The targetted applications are granular media and kinematic chains. The theoretical works will be led by the two partners in close cooperation. The numerical aspects will be led by the French partner, which has a strong experience in software platform development (with the SICONOS platform). The experiments will be designed by the Chinese partner, which has a strong experience with the CAST. The three sides of the project (theory, numerics, experiments) will be led in parallel for obvious reasons.