Modelling and simulation of coupled multibody systems and granular media using the non-smooth contact dynamics approach

Multibody models are often coupled with other domains in order to enlarge the scope of computer-based analysis. In particular, modeling multibody systems (MBSs) in interaction with granular media is of great interest for industrial process such as railway track maintenance, handling of aggregates, etc. This paper presents a strong coupling methodology for unifying a multibody formalism using relative coordinates and a discrete element method based on non-smooth contact dynamics (NSCD). Both tree-like and closed-loop MBSs are considered. For the latter, the coordinate partitioning techniques is applied in the NSCD framework. The proposed approach is applied on the slider–crank mechanism benchmark. Results are in very good agreement with results obtained with other techniques from the literature. Finally, a multibody model of a tamping machine is coupled to a discrete element model of railway ballast in order to analyse efficiency of track maintenance. This application demonstrates that the dynamics of the machine must be taken into account so as to estimate the performance of the maintenance process correctly.

[1]  V. Acary,et al.  On solving contact problems with Coulomb friction: formulations and numerical comparisons , 2018 .

[2]  V. Acary,et al.  A nonsmooth generalized‐ α scheme for flexible multibody systems with unilateral constraints , 2013 .

[3]  Jean-Claude Samin,et al.  Symbolic Modeling of Multibody Systems , 2003 .

[4]  B. Brogliato Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems , 2013 .

[5]  A. Cardona,et al.  Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-α scheme , 2014 .

[6]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[7]  J. Moreau,et al.  Unilateral Contact and Dry Friction in Finite Freedom Dynamics , 1988 .

[8]  Mihai Anitescu,et al.  An iterative approach for cone complementarity problems for nonsmooth dynamics , 2010, Comput. Optim. Appl..

[9]  V. Acary,et al.  Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb’s friction , 2013 .

[10]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[11]  E. Haug,et al.  Dynamic Analysis of Mechanical Systems With Intermittent Motion , 1982 .

[12]  Mihai Anitescu,et al.  GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview , 2011 .

[13]  F. Pfeiffer,et al.  Dynamical systems with unilateral contacts , 1992 .

[14]  Christian Duriez,et al.  Realistic haptic rendering of interacting deformable objects in virtual environments , 2008, IEEE Transactions on Visualization and Computer Graphics.

[15]  Vincent Acary,et al.  Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation , 2017, Multibody System Dynamics.

[16]  Christoph Glocker,et al.  Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach , 2010 .

[17]  R. Luciano,et al.  Stress-penalty method for unilateral contact problems: mathematical formulation and computational aspects , 1994 .

[18]  Paul Fisette,et al.  ROBOTRAN: a powerful symbolic gnerator of multibody models , 2013 .

[19]  J. Moreau Numerical aspects of the sweeping process , 1999 .

[20]  Hammad Mazhar,et al.  Chrono: An Open Source Multi-physics Dynamics Engine , 2015, HPCSE.

[21]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[22]  Frédéric Dubois,et al.  The Contact Dynamics method: A nonsmooth story , 2017 .

[23]  Peter Wriggers,et al.  Computational Contact Mechanics , 2002 .

[24]  P. A. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART I. A SCHEME TO DETECT AND REPRESENT CONTACTS IN A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .

[25]  Pierre-Etienne Gautier,et al.  Numerical modeling of the tamping operation by Discrete Element Approach , 2008 .

[26]  Antonio M. Recuero,et al.  An integrated framework for high-performance, high-fidelity simulation of ground vehicle-tyre-terrain interaction , 2019, International Journal of Vehicle Performance.

[27]  Werner Schiehlen,et al.  Modular Simulation in Multibody System Dynamics , 2000 .

[28]  B. Brogliato,et al.  Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics , 2008 .

[29]  Peter Eberhard,et al.  Dynamic simulation of sloshing fluid and granular cargo in transport vehicles , 2010 .

[30]  Pierre-Etienne Gautier,et al.  Modelling ballast behaviour under dynamic loading. Part 1: A 2D polygonal discrete element method approach , 2006 .