TECHNICAL PAPERS
Mar 1, 1986

Finite‐Strain, Elasto‐Plastic Solution for Contact Problems

Publication: Journal of Engineering Mechanics
Volume 112, Issue 3

Abstract

The finite element method is used to solve contact problems. The approach is general and is used to solve contact problems between flexible bodies. A system of constitutive relations which are applicable to elasto‐plastic materials subjected to finite strains is used to obtain the deformations and stresses for the contact problems. The materials exhibit both kinematic and isotropic strain‐hardening. An incremental iterative procedure is used to solve this problem. The solution to the Hertz contact problem is presented to demonstrate the applicability of the proposed method.

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References

1.
Aleksandrova, G. P., “A Contact Problem, Solved in Closed Form, of the Theory of Elasticity for a Cylindrical Body,” Inzhenernyi Zhurnal Mekhanika Tverdogo Tela, Vol. 2, 1968, pp. 143–153.
2.
Bathe, K. J., and Chaudhary, A., “A Solution Method for Planar and Axisymmetric Contact Problems,” International Journal for Numerical Methods in Engineering, Vol. 21, 1985, pp. 65–88.
3.
Campos, L. T., Oden, J. T., and Kikuchi, N., “A Numerical Analysis of a Class of Contact Problems with Friction in Elastostatics,” Computer Methods in Applied Mechanics Engineering, Vol. 34, 1982, pp. 821–845.
4.
Chan, S. K., and Tuba, I. S., “A Finite Element Method for Contact Problems of Solid Bodies—Part I. Theory and Validation,” International Journal of Mechanics and Science, Vol. 13, 1971, pp. 615–625.
5.
Cheng, H. S., and Keer, L. M., (Eds.), Solid Contact and Lubrication, Applied Mechanics Division, Vol. 39, American Society of Mechanics Engineers, 1980.
6.
Desai, C. S., Zaman, M. M., Lightner, J. G., and Siriwardane, H. J., “Thin Element for Interfaces and Joints,” International Journal of Analytical and Numerical Methods in Geomechanics (in press).
7.
Eringen, A. C., Mechanics of Continua, John Wiley and Sons, Inc., New York, NY, 1967.
8.
Francavilla, A., and Zienkiewicz, O. C., “A Note on Numerical Computation of Elastic Contact Problems,” International Journal for Numerical Methods in Engineering, Vol. 9, 1975, pp. 913–924.
9.
Hardy, C., Baronet, C. N., and Tordion, G. V., “The Elasto‐Plastic Indentation of a Half‐Space by a Rigid Sphere,” International Journal for Numerical Methods in Engineering, Vol. 3, 1971, pp. 451–462.
10.
Herrmann, L. R., “Finite Element Analysis of Contact Problems,” Journal of the Engineering Mechanics Division, ASCE, Vol. 104, No. EM5, 1978, pp. 1043–1057.
11.
Hertz, H., Journal of Mathematics (Crelle's Journal), 92, 1881.
12.
Hughes, T. J. R., Raylor, R. L., and Kanoknukulchai, W., “A Finite Element Method for Large Displacement Contact and Impact Problems,” Formulations and Computational Algorithms in Finite Element Analysis (K. J. Bathe, et al., Eds.), Massachusetts Institute of Technology Press, Cambridge, MA, 1977.
13.
Ishlinsky, A. J., The Axial‐Symmetrical Problem in Plasticity and the Brinell Test, Theoretical Research Translation No. 2/47, British Ministry of Supply Armament Research Department, 1947.
14.
Kalker, J. J., “The Computation of Three‐Dimensiohal Rolling Contact with Dry Friction,” International Journal of Numerical Methods in Engineering, Vol. 14, 1979, pp. 1293–1307.
15.
Kalker, J. J., Allaert, J. C., and de Mul, J., “The Numerical Calculation of Contact Problem in the Theory of Elasticity,” Nonlinear Finite Element Analysis in Structural Mechanics, W. Wunderlich, et al., Eds., Springer‐Verlag, Inc., New York, NY, 1981.
16.
Kikuchi, N., and Oden, J. T., “Contact Problems in Elasticity—A Study of Variational Inequalities and Finite Element Methods for a Class of Contact Problems in Elasticity,” TICOM Report 79‐8, 1979.
17.
Kiousis, P. D., Voyiadjis, G. Z., and Tumay, M. T., “A Large Strain Theory for Two Dimensional Problems in Geomechanics,” International Journal of Analytical and Numerical Methods in Geomechanics (in press).
18.
Oden, J. T., and Pires, E. B., “Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity,” Journal of Applied Mechanics, ASME, Vol. 50, 1983, pp. 67–76.
19.
Oden, J. T., and Martins, J. A. C., “Models and Computational Methods for Dynamic Friction Phenomena,” to appear in Computer Methods in Applied Mechanics and Engineering, North Holland, Amsterdam.
20.
Ohte, S., “Finite Element Analysis of Elastic Contact Problems,” Bulletin of the Japanese Society of Mechanical Engineers, Vol. 16, No. 95, 1973, pp. 797–804.
21.
Okamoto, N., and Nakazawa, M., “Finite Element Incremental Contact Analysis with Various Frictional Conditions,” International Journal for Numerical Methods in Engineering, Vol. 14, 1979, pp. 337–359.
22.
Pian, T. H. H., and Kubomura, K., “Formulation of Contact Problems by Assumed Stress Hybrid Elements,” Nonlinear Finite Element Analysis in Structural Mechanics, W. Wunderlich, et al., Eds., Springer‐Verlag, Inc., New York, NY, 1981.
23.
Shield, R. T., and Ziegler, H., “On Prager's Hardening Rule,” Zeitschrift fuer Angewandte Mathematik und Mechanik, Vol. 9, pp. 260–276, 1958.
24.
Sneddon, I. H., The Use of Integral Transforms, McGraw Hill Book Co., Inc., New York, NY, 1972.
25.
Timoshenko, S., and Goodier, J. N., Theory of Elasticity, McGraw Hill Book Co., Inc., New York, NY, 1970.
26.
Truesdell, C., and Toupin, R., “The Classical Field Theories,” Handbuch der Physik, S. Flugge, Ed., Vol. III/1, Springer‐Verlag, Inc., Berlin, Germany, 1960.
27.
Tseng, J., and Olson, M. D., “The Mixed Finite Element Method Applied to Two‐Dimensional Elastic Contact Problems,” International Journal for Numerical Methods in Engineering, Vol. 17, 1981, pp. 991–1014.
28.
Urzua, J. L., and Pecknold, O. A., “Analysis of Frictional Contact Problems using an Interface Element,” Proceedings, Symposium on Applications of Computer Methods in Engineering, August 23–26, Los Angeles, CA, 1977.
29.
Voyiadjis, G. Z., and Buckner, N. E., “Indentation of a Half‐Space with a Rigid Indentor,” International Journal for Numerical Methods in Engineering, Vol. 19, 1983, pp. 1555–1578.
30.
Voyiadjis, G. Z., “Experimental Determination of the Material Parameters of Elasto‐Plastic, Work‐Hardening Metal Alloys,” Materials Science and Engineering Journal, Vol. 62, No. 1, 1984, pp. 99–107.
31.
Voyiadjis, G. Z., and Navaee, S., “Finite Strain Contact Problem of Cylinder Embedded in Body,” Journal of the Engineering Mechanics Division, ASCE, Vol. 110, No. 11, 1984, pp. 1597–1609.
32.
Wilson, E. A., and Parsons, B., “Finite Element Analysis of Elastic Contact Problems Using Differential Displacement,” International Journal for Numerical Methods in Engineering, Vol. 2, 1970, pp. 387–395.
33.
Ziegler, H., “A Modification of Prager's Hardening Rule,” Quarterly of Applied Mathematics, Vol. 17, 1959, pp. 55–65.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 112Issue 3March 1986
Pages: 273 - 292

History

Published online: Mar 1, 1986
Published in print: Mar 1986

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Authors

Affiliations

George Z. Voyiadjis
Assoc. Prof., Dept. of Civ. Engrg., Louisiana State Univ., Baton Rouge, LA 70802
Andrew A. Poe
Grad. Student, Dept. of Civ. Engrg., Louisiana State Univ., Baton Rouge, LA 70802
Panos D. Kiousis
Asst. Prof., Dept. of Civ. Engrg., Univ. of Arizona, Tuscon, AZ 85721; formerly Grad. Student, Dept. of Civ. Engrg., Louisiana State Univ., Baton Rouge, LA 70802

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