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TECHNICAL PAPERS

Study of Frictional Impact Using a Nonsmooth Equations Solver

[+] Author and Article Information
L. Johansson, A. Klarbring

Division of Mechanics, Department of Mechanical Engineering, Linköping University, S581 83 Linköping, Sweden

J. Appl. Mech 67(2), 267-273 (Nov 01, 1999) (7 pages) doi:10.1115/1.1304825 History: Received May 13, 1999; Revised November 01, 1999
Copyright © 2000 by ASME
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References

Newton, I., 1687, Philosophiae Naturalis Principia Mathematica, Swedish translation by C. V. L. Charlier, Gleerups, Lund, 1927–1931 and Liber, Malmö, 1986.
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Brach,  R. M., 1989, “Rigid Body Collisions,” ASME J. Appl. Mech., 56, pp. 133–138.
Stronge,  W. J., 1990, “Rigid Body Collisions With Friction,” Proc. R. Soc. London, Ser. A, 431, pp. 169–181.
Walton, O. R., 1993, “Numerical Simulation of Inelastic, Frictional Particle-Particle Interactions,” Particulate Two-Phase Flow, M. C. Roco, ed., Butterworth-Heinemann, Stoneham, pp. 884–911.
Stoianovici,  D., and Hurmuzlu,  Y., 1996, “A Critical Study of the Applicability of Rigid-Body Collision Theory,” ASME J. Appl. Mech., 63, pp. 307–316.
Calsamiglia,  J., Kennedy,  S. W., Chatterjee,  A., Ruina,  A., and Jenkins,  J. T., 1999, “Anomalous Frictional Behavior in Collisions of Thin Disks,” ASME J. Appl. Mech., 66, pp. 146–152.
Moreau, J. J., 1988, “Unilateral Contact and Dry Friction,” Nonsmooth Mechanics and Applications (CISM Courses and Lectures No. 302), J. J. Moreau and P. D. Panagiotopoulos, eds., Springer, Wien, pp. 1–82.
Moreau,  J. J., 1994, “Some Numerical Methods in Multibody Dynamics: Application to Granular Materials,” Eur. J. Mech. A/Solids, 13, pp. 93–114.
Johansson,  L., 1999, “A Linear Complementarity Algorithm for Rigid Body Impact With Friction,” Eur. J. Mech. A/Solids, 18, pp. 703–717.
Christensen,  P. W., Klarbring,  A., Pang,  J. S., and Strömberg,  N., 1998, “Formulation and Comparison of Algorithms for Frictional Contact Problems,” Int. J. Numer. Methods Eng., 42, pp. 145–173.
Alart,  P., and Curnier,  A., 1991, “A Mixed Formulation for Frictional Contact Problems Prone to Newton Like Solution Methods,” Comput. Methods Appl. Mech. Eng., 92, pp. 353–375.
Stevens, B. L., and Lewis, F. L., 1992, Aircraft Control and Simulation, John Wiley and Sons, New York.
Brogliato, B., 1996, Nonsmooth Impact Mechanics: Models, Dynamics and Control, Springer, Berlin.
Pang,  J. S., 1990, “Newton’s Method for B-Differentiable Equations,” Math. Op. Res., 15, pp. 311–341.
Klarbring, A., 1992, “Mathematical Programming and Augmented Lagrangian Methods for Frictional Contact Problems,” Proceedings Contact Mechanics International Symposium, A. Curnier, ed., Presses Polytechniques et Universitaires Romandes, Lausanne, pp. 409–422.

Figures

Grahic Jump Location
Geometry of the contact
Grahic Jump Location
Photograph from the experiments
Grahic Jump Location
Comparison with experiment and computations for single ball case
Grahic Jump Location
Comparison between experiments and computations using et=0.68 as obtained from single ball experiment
Grahic Jump Location
Comparison between experiments and computations using et=en=0.91
Grahic Jump Location
Energy balance corresponding to Fig. 4
Grahic Jump Location
Motion in the three dimensional example

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