A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined and used to derive conditions for when and where to apply reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5–50 times for model reduction level between 70–95 %.
Discrete elements Nonsmooth contact dynamics Adaptive model reduction Merge and split
This is a preview of subscription content, log in to check access.
This project was supported by Algoryx Simulations, LKAB (dnr 223-2442-09), UMIT Research Lab and VINNOVA (2014-01901).
Pöschel T, Schwager T (2005) Computational granular dynamics, models and algorithms. Springer, NewYorkGoogle Scholar
Radjai F, Richefeu V (2009) Contact dynamics as a nonsmooth discrete element method. Mech Mater 41(6):715–728CrossRefGoogle Scholar
Antoulas A (2005) Approximation of Large-Scale Dynamical Systems, Society for Industrial and Applied MathematicsGoogle Scholar
Kerschen G, Golinval J-C, Vakakis A, Bergman L (2005) The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlinear Dyn 41:147–169CrossRefMathSciNetzbMATHGoogle Scholar
Nowakowski C, Fehr J, Fischer M, Eberhard P (2012) Model order reduction in elastic multibody systems using the floating frame of reference formulation, In Proceedings MATHMOD 2012–7th vienna international conference on mathematical modelling, Vienna, AustriaGoogle Scholar
Lacoursière C (2007) Regularized, stabilized, variational methods for multibodies. In: Peter Bunus DF., Führer C (eds) The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007), Linköping University Electronic Press, pp 40–48Google Scholar
Servin M, Wang D, Lacoursière C, Bodin K (2014) Examining the smooth and nonsmooth discrete element approach to granular matter. Int. J Numer Meth Eng 97:878–902CrossRefGoogle Scholar
Renouf M, Bonamy D, Dubois F, Alart P (2005) Numerical simulation of two-dimensional steady granular flows in rotating drum: On surface flow rheology, Phys Fluids 17Google Scholar
Algoryx Simulations, AgX Dynamics User Guide Version 126.96.36.199, December 2014Google Scholar
Renouf M, Dubois F, Alart P (2004) A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media. J Comput Appl Math 168(1–2):375–382CrossRefMathSciNetzbMATHGoogle Scholar
Murty KG (1988) Linear complementarity, linear and nonlinear programming. Helderman, HeidelbergzbMATHGoogle Scholar