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Multilevel Numerical Algorithms and Experiments for Contact Dynamics

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Multifield Problems in Solid and Fluid Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 28))

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Summary

Nonlinear frictional contact problems are still a challenging task both from the mathematical and engineering point of view. These problems are of crucial importance in various applications. In this report we study dynamical contact problems on mathematical and experimental aspects. In the mathematical part we present a variationally consistent formulation based on mortar techniques with dual Lagrange multipliers for this type of problems. Furthermore, new optimal a priori and a posteriori error estimates were achieved, and numerical results for nearly incompressible materials are given. To solve the resulting nonlinear algebraic problem, we use a primal-dual active set strategy which can also be interpreted as semismooth Newton method. In combination with optimal multigrid methods, the inexact version of this approach can be regarded as a nonlinear multigrid method, and we end up with an efficient iterative solver. In the engineering part experiments to study the properties of the impact between a rotating disc and an elastic strip are presented. Experimental setup and methods are designed to release the disc with prescribed translational and rotational velocities. The impact event is captured by a high-speed digital camera system. Based on image processing, impact quantities, that is, coefficients of normal and tangential restitution, impulse ratio, rotational velocity change, incidence and rebound angles, are measured. A numerical model for interpreting the experimental data is developed, which can also give some insight into effects of strip flexibility. Results are also compared with those from finite element calculations.

Research Project B8 “Contact Dynamics with Multibody Systems and Multigrid Methods”

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Authors and Affiliations

  1. Institute of Engineering and Computational Mechanics (ITM), University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    Peter Eberhard & Yu Jiang

  2. Institute of Applied Analysis and Numerical Simulation (IANS), University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Stefan Hüeber & Barbara I. Wohlmuth

Authors
  1. Peter Eberhard
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  2. Stefan Hüeber
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  3. Yu Jiang
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  4. Barbara I. Wohlmuth
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Editors and Affiliations

  1. Institut für Wasserbau, Hydromechanik und Hydrosystemmodellierung, Universität Stuttgart, Pfaffenwaldring 61, 70569, Stuttgart, Germany

    Rainer Helmig

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  3. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Barbara I. Wohlmuth

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Eberhard, P., Hüeber, S., Jiang, Y., Wohlmuth, B.I. (2006). Multilevel Numerical Algorithms and Experiments for Contact Dynamics. In: Helmig, R., Mielke, A., Wohlmuth, B.I. (eds) Multifield Problems in Solid and Fluid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 28. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-34961-7_9

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  • DOI: https://doi.org/10.1007/978-3-540-34961-7_9

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