Improved splitting methods for 3D frictional contact problems

Splitting methods have been developed in order to decompose the equations of motion of a nonsmooth mechanical system into a smooth subsystem and nonsmooth contributions. Then, a higher-order time-discretization method can be used for the smooth subsystem whereas the nonsmooth terms are solved using a first-order time-discretization. Compared to the Moreau-Jean scheme, this approach improves the quality of the numerical solution especially for the representation of the vibrating response of flexible bodies. Also, all the constraints can be exactly verified both at the velocity and position levels. However, the couplings between the equations of the different subsystems resulting from the splitting may penalize the numerical efficiency of the complete procedure.

This talk discusses a new splitting strategy which intends to minimize the coupling terms between the different subsystems. In this way, the different subsystems can be solved at each time step in a purely sequential manner. This strategy significantly accelerates the convergence of the nonlinear problem to be solved at each time step and it also simplifies the practical implementation in a simulation code. The proposed method is implemented in OOFELIE, a general-purpose finite element package, which allows the analysis of finite element models involving 3D frictional contact conditions.