Non-smooth numerical solution of frictional contact problems in multibody systems

JAVIER GALVEZ; FEDERICO J. CAVALIERI; ALEJANDRO COSIMO; OLIVIER BRÜLS; ALBERTO CARDONA

Duisburg

Congreso; ECCOMAS Thematic Conference on Multibody Dynamics; 2019

University of Duisburg-Essen

The simulation of mechanical systems subjected to impacts and friction present the difficulty to solve highly non-linear systems of equations coming from the Signorini's conditions and the Coulomb friction's law. New advances and numerical algorithms including friction, large deformations or rotations, between other effects, are constantly been introduced to solve different mechanical engineering applications. However, there is not yet a completely robust algorithm for a wide range of applications, and for this reason, the study of impact formulations is an active research area. In the non-smooth dynamics, the time integrators are usually classified in two main groups: event-driven and time-stepping integrators. The first schemes are based on the exact impact detection, instead, the second ones, the impact is solved in the same time step by using a constitutive impact law, for example, the Newton or Poisson impact's law [5]. These methods are provided to be robust, however, they leads to a first order approximation with high numerical dissipation when the vibration in flexible components are considered. In case to study the dynamics of structures with space discretization, the most classical time integrators schemes are the Newmark family methods, Hilbert-Hughes-Taylor or the generalized-alpha, see [1]. They are implicit integrators with a second order of precision. However, when abrupt changes of velocity occurs as consequence of impacts, the numerical solutions show a non physical behaviour. Other alternative to these integrators has been recently presented by Brüls et al [3], where the terms of the equation of motion are split a smooth contribution and other non-smooth contribution. This splitting makes possible to integrate the therms of the equation of motion using a time-stepping method with first order accuracy meanwhile, the smooth contributions are integrated using a second order scheme by using a generalized-α method. This work presents a new formulation to deal with the friction impact problem between a flexible body and a rigid foundation in the frame of non-smooth dynamic. The regularization of the variational frictional contact problem is solved with a mixed approach based on an augmented Lagrangian technique and the Coulomb friction's law. The method presented leads to an implicit formulation which can be solved at every time step using a Newton semi-smooth algorithm. The equation of motion are integrated with the non-smooth generalized−alpha time integration scheme [3], where the constraints are imposed both at position and velocity levels preventing any non-physical penetration. Additionally, the numerical results do not depend on the definition of any user-defined penalty parameter affecting the normal or tangential component of forces.