Constitutive Model and Finite Element Procedure for Dilatant Contact Problems
Publication: Journal of Engineering Mechanics
Volume 115, Issue 12
Abstract
A constitutive law for dilatant frictional behavior is reviewed. It is developed by distinguishing between the macrostructural and raicrostructural features of a material discontinuity. Macrostructural considerations provide the general form of the constitutive equations, while microstructural considerations ailow the inclusion of an appropriate surface idealization. The result is an incremental relation between contact stresses (traction) and relative surface deformation that accounts for phenomena such as surface damage due to wear and arbitrary cyclic sliding. A quadratic‐displacement‐isoparametric finite element is derived that permits modeling of curved‐contact surfaces and crack surfaces terminating at a tip with a surrounding medium that is modeled with quarter‐point quadratic elements. Emphasis is on the use of established finite‐element‐solution methodologies and program architecture for material‐nonlinear problems. Several examples are considered. The resulting methodology is useful for modeling geologic discontinuities, crack‐shear transfer in concrete, and dilatancy‐induced mixed‐mode fracture mechanics.s
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ballarini, R., and Plesha, M. E. (1987). “The effects of crack surface friction and roughness on crack tip stress fields.” Int. J. Fracture, 34(3), 195–207.
2.
Bandis, S., Lumsden, A. C., and Barton, N. R. (1981). “Experimental studies of scale effects on the shear behavior of rock joints,” Int. J. Rock Mech., Mineral Sci. and Geomech. Abstracts, 18(1), 1–21.
3.
Bathe, K. J. (1982). Finite element procedures in engineering analysis. Prentice‐Hall, Englewood Cliffs, N.J.
4.
Bažant, Z. P., and Gambarova, P. (1980). “Rough cracks in reinforced concrete.” J. Struct. Div., ASCE, 106(4), 819–842.
5.
Bažant, Z. P., and Gambarova, P. (1984). “Crack shear in concrete: Crack band microplane model.” J. Struct. Engrg., ASCE, 110(9), 2015–2035.
6.
Belytschko, T., Chiapetta, R. L., and Bartel, H. D. (1976). “Efficient large scale non‐linear transient analysis by finite elements.” Int. J. Numerical Methods in Engrg., 10(3), 579–596.
7.
Belytschko, T. (1983). “An overview of semidiscretization and time integration procedures.” Computational methods for transient analysis, T. Belytschko and T. J. R. Hughes, eds., North‐Holland Publishers, Amsterdam, The Netherlands, 1–65.
8.
Cheng, J. H., and Kikuchi, N. (1985). “An incremental constitutive relation of unilateral contact friction for large deformation analysis.” J. Appl. Mech., 52(3), 639–648.
9.
Curnier, A. (1984). “A theory of friction.” Int. J. Solids and Struct., 20(7), 637–647.
10.
Divakar, M. P., Fafitis, A., and Shah, S. P. (1987). “A constitutive model for shear transfer in cracked concrete.” J. Struct. Engrg., ASCE, 113(5), 1046–1062.
11.
Drucker, D. C. (1954). “Coulomb friction, plasticity and limit loads.” J. Appl. Mech., 21, 71–74.
12.
Fredriksson, B. (1976). “Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems.” Computers and Struct., 6(4/5), 281–290.
13.
Ghaboussi, J., Wilson, E. L., and Isenberg, J. (1973). “Finite element for rock joints and interfaces.” J. Soil Mech. and Found. Engrg. Div., ASCE, 99(10), 833–848.
14.
Goodman, R. E., Taylor, R. L., and Brekke, T. L. (1968). “A model for the mechanics of jointed rock.” J. Soil Mech. and Found. Engrg. Div., ASCE, 14(3), 637–659.
15.
Goodman, R. E. (1976). Methods of geological engineering in discontinuous rocks. West Publishing Co., St. Paul, Minn.
16.
Goodman, R. E. (1980). Introduction to rock mechanics. John Wiley and Sons, Inc., New York, N.Y.
17.
Kikuchi, N. (1982). “A smoothing technique forreduced integration penalty methods in contact problems.” Int. J. Numerical Methods in Engrg., 18(3), 343–350.
18.
Kikuchi, N., and Song, Y. J. (1981). “Penalty/finite element approximations of a class of unilateral problems in linear elasticity.” Quar. Appl. Math., 39(1), 1–22.
19.
Michalowski, R., and Mroz, Z. (1978). “Associated and non‐associated sliding rules in contact friction problems.” Archives of Mech., 30(3), 259–276.
20.
Oden, J. T., and Campos, L. (1981). “Some new results on finite element methods for contact problems with friction.” New concepts infinite element analysis, 44, T. J. R. Hughes et al., eds., Am. Soc. of Mech. Engrs., New York, N.Y., 1–9.
21.
Oden, J. T., and Kikuchi, N. (1982). “Finite element methods for constrained problems in elasticity.” Int. J. Numerical Methods in Engrg., 18(5), 701–725.
22.
Ortiz, M., and Popov, E. P. (1985). “Accuracy and stability of integration algorithms for elastoplastic constitutive relations.” Int. J. for Numerical Methods in Engrg., 21(9), 1561–1576.
23.
Pande, G. N., and Pietruszczak, S. (1986). “Symmetric tangential stiffness formulation for non‐associated plasticity.” Computers and Geotech., 2(2), 89–99.
24.
Plesha, M. E. (1987). “Constitutive models for rock discontinuities with dilatancy and surface degradation.” Int. J. Numerical and Analytical Methods in Geomech., 11(4), 345–362.
25.
Plesha, M. E., and Haimson, B. C. (1988). “An advanced model for rock joint behavior: Analytical, experimental and implementational considerations.” Proc., 29th U.S. Symp. on Rock Mechs., P. A. Cundall et al. eds., Univ. of Minnesota, 119–126.
26.
Riggs, H. R., and Powell, G. H. (1986). “Rough crack model for analysis of concrete.” J. Engrg. Mech., ASCE, 112(5), 448–464.
27.
Seguchi, Y., et al. (1974). “Sliding rule of friction in plastic forming of metal.” Computational Methods in Nonlinear Mech., Univ. of Texas‐Austin, Austin, Tex., 683–692.
28.
Shih, C. F., de Lorenzi, H. G., and German, M. D. (1976). “Crack extension modeling with singular quadratic isoparametric elements.” Int. J. of Fracture, 12(4), 647–651.
29.
Zubelewicz, A., et al. (1987). “A constitutive model for the cyclic behavior of dilatant rock joints.” Proc. 2nd Int. Conf. on Constitutive Laws for Engrg. Mater., C. S. Desai et al., eds., Univ. of Arizona, 1137–1144.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 115 • Issue 12 • December 1989
Pages: 2649 - 2668
Copyright
Copyright © 1989 ASCE.
History
Published online: Dec 1, 1989
Published in print: Dec 1989
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.