In this work, we present the combination of two efficient algorithms to solve non linear elastodynamic problems with a large number of degrees of freedom. The non linearities come from hyperelastic constitutive law but also from frictional contact conditions. These large non linear problems are generally charaterized by large computational times. So initialy, we focus our attention on the development of a time-stepping scheme which makes it possible to have energy conservation properties and also to reduce the time integration cost; we present then an energy-conserving algorithm for hyperelastodynamic contact problems which differs from the usual approaches. The second improvment deals with the solution of the linearized problems; in order to reduce the cost of this stage, we present a scalable domain decomposition method well adapted to solve the corresponding linearized systems.

Key Words: Non linear dynamics, Large deformations, Frictional contact, Energy conserving algorithm, Domain decomposition method, Balancing method, Numerical scalability.

2000 Mathematics Subject Classification: Primary: 65K05, 74H15, 74B20, 74M20, 65Y05, 65N99,
Secondary: 74M15, 74M10, 49M15, 68W10, 65N22.