Return Mapping Procedure for Frictional Force Calculation: Some Insights
Publication: Journal of Engineering Mechanics
Volume 131, Issue 10
Abstract
The return mapping procedure is studied to gain insights for its numerical implementation to calculate the frictional force during contact analysis. A simple quasistatic truss–wall frictional contact analysis problem is used in the study. The problem has closed-form solutions which provide exact target solutions for a numerical algorithm. The penalty method and a true augmented Lagrangian method that automatically determines an accurate value of the penalty parameter are employed in the numerical study. It is determined that the return mapping procedure is not applicable unless the contacting node is constrained to stay at the initial contact point, and the total normal reaction force, the tangential reaction force and the friction limit have been determined. If these requirements are not met, inaccurate or even incorrect solutions are obtained. This characteristic of the procedure is studied by solving slip and stick cases with several different load increments. It is concluded that the return mapping procedure for friction force calculation should be implemented carefully to obtain accurate solutions for contact analysis problems.
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Acknowledgment
The writers would like to acknowledge support of Ford Motor Company for this research under URP, with Dr. C. C. Wu as the project monitor.
References
Agelet de Saracibar, C. (1998). “Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications.” Arch. Comput. Methods Eng., 5, 243–301.
Arora, J. S., Chahande, A. I., and Paeng, J. K. (1991). “Multiplier methods for engineering optimization.” Int. J. Numer. Methods Eng., 32, 1485–1525.
Curnier, A. (1984). “A theory of friction.” Int. J. Solids Struct., 20(7), 637–647.
Giannakopoulos, A. E. (1989). “The return mapping method for the integration of friction constitutive relations.” Comput. Struct., 32, 157–167.
Hallquist, J. O., Goudreau, G. L., and Benson, D. J. (1985). “Sliding interfaces with contact impact in large-scale Lagrangian computations.” Comput. Methods Appl. Mech. Eng., 51, 107–137.
Mijar, A. R., and Arora, J. S. (2000a). “Review of formulations for elastostatic frictional contact problems.” Struct. Multidiscip. Optim., 20(3), 167–189.
Mijar, A. R., and Arora, J. S. (2000b). “Study of variational inequality and equality formulations for elastostatic frictional contact problems.” Arch. Comput. Methods Eng., 7(4), 387–449.
Mijar, A. R., and Arora, J. S. (2004a). “An augmented Lagrangian optimization method for contact analysis problems, 1: Formulation and algorithm.” Struct. Multidiscip. Optim., 28, 99–112.
Mijar, A. R., and Arora, J. S. (2004b). “An augmented Lagrangian optimization method for contact analysis problems, 2: Numerical evaluation.” Struct. Multidiscip. Optim., 28, 113–126.
Powell, M. J. D. (1969). “A method for nonlinear constraints in minimization problems.” Optimization, R. Fletcher, ed., Academic, New York.
Shames, I. H., and Cozzarelli, F. A. (1992). Elastic and inelastic stress analysis, Prentice-Hall, Englewood Cliffs, N.J.
Simo, J. C., and Hughes, T. J. R. (1998). Computational inelasticity, Springer, New York.
Simo, J. C., and Laursen, T. A. (1992). “An augmented Lagrangian treatment of contact problems involving friction.” Comput. Struct., 42, 97–116.
Wriggers, P., Vu Van, T., and Stein, E. (1990). “Finite element formulation of large deformation impact-contact problems with friction.” Comput. Struct., 37, 319–331.
Zhong, Z.-H. (1993). Finite element procedures for contact-impact problems, Oxford University Press, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 131 • Issue 10 • October 2005
Pages: 1004 - 1012
Copyright
© 2005 ASCE.
History
Received: Oct 18, 2004
Accepted: Feb 1, 2005
Published online: Oct 1, 2005
Published in print: Oct 2005
Notes
Note. Associate Editor: Francisco Armero
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