Survey and Performance Assessment of Solution Methods for Elastic Rough Contact Problems

[+] Author and Article Information
Julian Allwood

Institute for Manufacturing, Department of Engineering, University of Cambridge, Mill Lane, Cambridge CB2 1RX, United Kingdom

J. Tribol 127(1), 10-23 (Feb 07, 2005) (14 pages) doi:10.1115/1.1828073 History: Received December 19, 2003; Revised September 03, 2004; Online February 07, 2005
Copyright © 2005 by ASME
Your Session has timed out. Please sign back in to continue.


Polonsky,  I. A., and Keer,  L. M., 2000, “Fast Methods for Solving Rough Contact Problems: A Comparative Study,” ASME J. Tribol., 122, pp. 36–41.
Love,  A. E. H., 1929, “The Stress Produced in a Semi-infinite Solid by Pressure on Part of the Boundary,” Philos. Trans. R. Soc. London, Ser. A, 228, pp. 377–420.
Ferris,  M. C., and Pang,  J. S., 1997, “Engineering and Economic Applications of Complementarity Problems,” SIAM Rev., 39, pp. 669–713.
Greenwood,  J. A., and Williamson,  J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. London, Ser. A, 295, pp. 300–319.
Conry,  T. F., and Seireg,  A., 1971, “A Mathematical Programming Method for Design of Elastic Bodies in Contact,” J. Appl. Mech., 38, pp. 387–392.
Kalker,  J. J., and van Randen,  Y., 1972, “A Minimum Principle for Frictionless Elastic Contact with Application to Non-Hertzian Half-space Contact Problems,” J. Eng. Math., 6(2), pp. 193–206.
Kalker,  J. J., Dekking,  F. M., and Vollebregt,  E. A. H., 1997, “Simulation of Rough, Elastic Contacts,” J. Appl. Mech., 64, pp. 361–368.
Ahmadi,  N., Keer,  L. M., and Mura,  T., 1983, “Non-Hertzian Contact Stress Analysis for an Elastic Half Space-normal and Sliding Contact,” Int. J. Solids Struct., 19(4), pp. 357–373.
Liu,  Z., Neville,  A., and Reuben,  R. L., 2001, “A Numerical Calculation of the Contact Area and Pressure of Real Surfaces in Sliding Wear,” ASME J. Tribol., 123, pp. 27–35.
Webster,  M. N., and Sayles,  R. S., 1986, “A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces,” ASME J. Tribol., 108, pp. 314–320.
Björklund,  S., and Andersson,  S., 1994, “A Numerical Model for Real Elastic Contacts Subjected to Normal and Tangential Loading,” Wear, 179, pp. 117–122.
Allwood,  J. M., Bryant,  G. F., and Stubbs,  R. E., 1997, “An Efficient Treatment of Binary Nonlinearities Applied to Elastic Contact Problems Without Friction,” J. Eng. Math., 31, pp. 81–98.
Francis,  H. A., 1982, “A Finite Surface Element Model for Plane-strain Elastic Contact,” Wear, 76, pp. 221–245.
Chiu,  Y. P., and Hartnett,  M. J., 1983, “A Numerical Solution for Layered Solid Contact Problems with Applications to Bearings,” J. Lubr. Technol., 105, pp. 585–590.
Vollebregt,  E. A. H., 1995, “A Gauss-Seidel Type Solver for Special Convex Programs, with Applications to Frictional Contact Mechanics,” J. Optim. Theory Appl., 87(1), pp. 47–67.
Ren,  N., and Lee,  S. C., 1993, “Contact Simulation of Three-dimensional Rough Surfaces using Moving Grid Method,” ASME J. Tribol., 115, pp. 597.
Sui,  P. C., 1997, “An Efficient Computation Model for Calculating Surface Contact Pressures Using Measured Surface Roughness,” Tribol. Trans., 40, pp. 243–250.
Newland, D. E., 1993, An Introduction to Random Vibrations, Spectral and Wavelet Analysis, Longman Scientific and Technical.
Ju,  Y., and Farris,  T. N., 1996, “Spectral Analysis of Two-dimensional Contact problems,” ASME J. Tribol., 118, pp. 320–328.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge.
Ai,  X., and Sawamiphakdi,  K., 1999, “Solving Elastic Contact Between Rough Surfaces as an Unconstrained Strain Energy Minimization by Using CGM and FFT Techniques,” ASME J. Tribol., 121, pp. 639–647.
Hu,  Y-Z., Barber,  G. C., and Zhu,  D., 1999, “Numerical Analysis for the Elastic Contact of Real Rough Surfaces,” Tribol. Trans., 42(3), pp. 443–452.
Stanley,  H. M., and Kato,  T., 1997, “An FFT-based Method for Rough Surface Contact,” ASME J. Tribol., 119, pp. 481–485.
Brandt,  A., and Lubrecht,  A. A., 1990, “Multilevel Matrix Multiplication and Fast Solution of Integral Equations,” J. Comput. Phys., 90, pp. 348–370.
Lubrecht,  A. A., and Ioannides,  E., 1991, “A Fast Solution of the Dry Contact Problem and the Associated Sub-surface Stress Field, Using Multilevel Techniques,” ASME J. Tribol., 113, pp. 128–133.
Venner, C. H., and Lubrecht, A. A., 1994, “Multilevel Solution of Integral and Integro-differential Equations in Contact Mechanics and Lubrication,” Proc. EMG 93, UK, pp. 111–127.
Polonsky,  I. A., and Keer,  L. M., 1999, “A Numerical Method for Solving Rough Contact Problems Based on the Multilevel Multisummation and Conjugate Gradient Techniques,” Wear, 231, pp. 206–219.
Yongqing,  J., and Linqing,  Z., 1992, “A Full Numerical Solution for the Elastic Contact of Three-dimensional Real Rough Surfaces,” Wear, 157, pp. 151–161.
Snidle,  R. W., and Evans,  H. P., 1994, “A Simple Method of Elastic Contact Simulation,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 208, pp. 291–293.
Chang,  L., and Gao,  Y., 1999, “A Simple Numerical Method for Contact Analysis of Rough Surfaces,” ASME J. Tribol., 121, pp. 425–432.
Golub, G. H., and van Loan, C. F., 1989, Matrix Computations, 2nd ed., John Hopkins University Press, Baltimore and London.
Duncan,  W. J., 1944, “Some Devices for the Solution of Large Sets of Simultaneous Linear Equations,” London, Edinburgh Dublin Philos. Mag. J. Sci., 35, pp. 660–670.
Dongarra, J. J., Bunch, J. R., Moler, C. B., and Stewart, G. W., 1979, Linpack: User’s Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Shewchuk, J. R., 1994, “An Introduction to the Conjugate Gradient Method Without the Agonizing Pain,” http://www.cs.cmu.edu/∼quake-papers/painless-conjugate-gradient.ps
Bakolas,  V., 2003, “Numerical Generation of Arbitrarily Oriented Non-Gaussian Three Dimensional Rough Surfaces,” Wear, 254, pp. 546–554.


Grahic Jump Location
Percentage error in predicting (a) contact area and (b) peak pressure
Grahic Jump Location
Memory requirements against (a) problem size and (b) contact area size
Grahic Jump Location
Flop-rates for Matlab implementations of algorithms compared to an ideal
Grahic Jump Location
Execution time against contact area size
Grahic Jump Location
Definition of notation used in describing the model of rough contact
Grahic Jump Location
Flow chart for Kalker’s CONTACT algorithm
Grahic Jump Location
Performance of iterative schemes in solving Eq. (1b)
Grahic Jump Location
Flow chart for the method of Sec. 3.1—active set with Cholesky factorization
Grahic Jump Location
Flow chart for the method of Sec. 3.2—active set with conjugate gradient solver
Grahic Jump Location
Flow chart for the method of Sec. 3.3—multigrid integration with conjugate gradient solver
Grahic Jump Location
Relative error in displacement prediction by MLMS multiplication for a 51×51 grid



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In