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Nonsmooth Contact Dynamics for the large-scale simulation of granular material.pdf

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Nonsmooth Contact Dynamics for the large-scale simulation of granular material.pdf

Journal of Computational and Applied Mathematics 316 (2017) 345–357 Contents lists available at ScienceDirect Journal of Computational and Applied Mathematics journal homepage: /locate/cam Nonsmooth Contact Dynamics for the large-scale simulation of granular material Jan Kleinert a,b, Bernd Simeon c,?, Klaus Dre?ler a a Fraunhofer ITWM, Fraunhofer Platz 1, 67663 Kaiserslautern, Germany b Fraunhofer SCAI, Schloss Birlinghofen, 53754 Sankt Augustin, Germany c FB Mathematik, TU Kaiserslautern, 67663 Kaiserslautern, Germany article info Article history: Received 22 December 2015 Received in revised form 29 August 2016 Keywords: Granular material Nonsmooth Contact Dynamics Friction Interior point methods Conical optimization Timestepping scheme abstract For the large-scale simulation of granular material, the Nonsmooth Contact Dynamics Method (NSCD) is examined. First, the equations of motion of nonsmooth mechanical systems are introduced and classified as a Differential Variational Inequality (DVI) that has a structure similar to Differential–Algebraic Equations (DAEs). Using a Galerkin projection in time, we derive nonsmooth extensions of the SHAKE and RATTLE schemes. A matrixfree Interior Point Method (IPM) is used for the complementarity problems that need to be solved in each time step. We demonstrate that in this way, the NSCD approach yields highly accurate results and is competitive compared to the Discrete Element Method (DEM). ? 2016 Elsevier B.V. All rights reserved. 1. Introduction Granular material such as powders, pellets, sand and gravel are present in numerous engineering applications. The main loads acting on an excavator or wheel loader, for instance, result from the interaction of the shovel with the ground. A simulation framework to predict these loads is a desirable tool but still represents a great challenge today. Currently, two methods are mainly used: the classical Discrete Element Method (DEM) [1] and Non-Smooth Contact Dynamics (NSCD) [2,3]. Th