Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress
Publication: Journal of Engineering Mechanics
Volume 126, Issue 9
Abstract
The first part of this two-part study presents a new improved microplane constitutive model for concrete, representing the fourth version in the line of microplane models developed at Northwestern University. The constitutive law is characterized as a relation between the normal, volumetric, deviatoric, and shear stresses and strains on planes of various orientations, called the microplanes. The strain components on the microplanes are the projections of the continuum strain tensor, and the continuum stresses are obtained from the microplane stress components according to the principle of virtual work. The improvements include (1) a work-conjugate volumetric deviatoric split—the main improvement, facilitating physical interpretation of stress components; (2) additional horizontal boundaries (yield limits) for the normal and deviatoric microplane stress components, making it possible to control the curvature at the peaks of stress-strain curves; (3) an improved nonlinear frictional yield surface with plasticity asymptote; (4) a simpler and more effective fitting procedure with sequential identification of material parameters; (5) a method to control the steepness and tail length of postpeak softening; and (6) damage modeling with a reduction of unloading stiffness and crack-closing boundary. The second part of this study, by Caner and Bažant, will present an algorithm for implementing the model in structural analysis programs and provide experimental verification and calibration by test data.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Batdorf, S. B., and Budianski, B. (1949). “A mathematical theory of plasticity based on the concept of slip.” Tech. Note No. 1871, National Advisory Committee for Aeronautics, Washington, D.C.
2.
Bažant, Z. P. (1978). “Endochronic inelasticity and incremental plasticity.” Int. J. Solids and Struct., 14, 691–714.
3.
Bažant, Z. P. (1980). “Work inequalities for plastic-fracturing materials.” Int. J. Solids and Struct., 16, 870–901.
4.
Bažant, Z. P. (1984). “Chapter 3: Microplane model for strain controlled inelastic behavior.” Proc., Mech. of Engrg. Mat., C. S. Desai and R. H. Gallagher, eds., Wiley, London, 45–59.
5.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories, Oxford University Press, New York.
6.
Bažant, Z. P., and Gambarova, P. (1984). “Crack shear in concrete: Crack band microplane model.”J. Struct. Engrg., ASCE, 110(9), 2015–2035.
7.
Bažant, Z. P., and Kim, J.-K. (1986). “Creep of anisotropic clay: Microplane model.”J. Geotech. Engrg., ASCE, 112(4), 458–475.
8.
Bažant, Z. P., Kim, J.-H., and Brocca, M. (1999). “Finite strain tube-squash test for concrete at high pressure and shear angles up to 70°.” ACI Mat. J., 96(5), 580–592.
9.
Bažant, Z. P., and Oh, B.-H. (1983). “Microplane model for fracture analysis of concrete structures.” Proc., Symp. on Interaction of Non-Nuclear Munitions with Struct., U.S. Air Force Academy, Colorado Springs, Colo., 49–53.
10.
Bažant, Z. P., and Oh, B.-H. (1985). “Microplane model for progressive fracture of concrete and rock.”J. Engrg. Mech., ASCE, 111(4), 559–582.
11.
Bažant, Z. P., and Oh, B.-H. (1986). “Efficient numerical integration on the surface of a sphere.” Zeitschrift für angewandte Mathematik und Mechanik (ZAMM), Berlin, 66(1), 37–49.
12.
Bažant, Z. P., and Ožbolt, J. (1990). “Nonlocal microplane model for fracture, damage, and size effect in structures.”J. Engrg. Mech., ASCE, 116(11), 2485–2505.
13.
Bažant, Z. P., and Ožbolt, J. (1992). “Compression failure of quasi-brittle material: Nonlocal microplane model.”J. Engrg. Mech., ASCE, 118(3), 540–556.
14.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC Press, Boca Raton, Fla.
15.
Bažant, Z. P., and Prat, P. C. (1987). “Creep of anisotropic clay: New microplane model.”J. Engrg. Mech., ASCE, 113(7), 1050–1064.
16.
Bažant, Z. P., and Prat, P. C. (1988a). “Microplane model for brittle-plastic material. I: Theory.”J. Engrg. Mech., ASCE, 114(10), 1672–1688.
17.
Bažant, Z. P., and Prat, P. C. (1988b). “Microplane model for brittle-plastic material. II: Verification.”J. Engrg. Mech., ASCE, 114(10), 1689–1699.
18.
Bažant, Z. P., Xiang, Y., Adley, M. D., Prat, P. C., and Akers, S. A. (1996b). “Microplane model for concrete. II: Data delocalization and verification.”J. Engrg. Mech., ASCE, 122(3), 255–262.
19.
Bažant, Z. P., Xiang, Y., and Prat, P. C. (1996a). “Microplane model for concrete. I: Stress-strain boundaries and finite strain.”J. Engrg. Mech., ASCE, 122(3), 245–254.
20.
Budianski, B., and Wu, T. T. (1962). “Theoretical prediction of plastic strains of polycrystals.” Proc., 4th U.S. Nat. Congr. of Appl. Mech., ASME, New York, 1175–1185.
21.
Caner, F. C., and Bažant, Z. P. (2000). “Microplane model M4 for concrete. II: Algorithm and calibration.”J. Engrg. Mech., ASCE, 126(9), 954–961.
22.
Carol, I., and Bažant, Z. P. (1997). “Damage and plasticity in microplane theory.” Int. J. Solids and Struct., 34(29), 3807–3835.
23.
Carol, I., Bažant, Z. P., and Prat, P. C. (1991). “Geometric damage tensor based on microplane model.”J. Engrg. Mech., 117(10), 2429–2448.
24.
Carol, I., Jirásek, M., Bažant, Z. P., and Steinmann, P. (1998). “New thermodynamic approach to microplane model with application to finite deformations.” Tech. Rep. PI-145, International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain.
25.
Carol, I., Jirásek, M., and Bažant, Z. P. (2000). “New thermodynamic approach to microplane model. Part I: Free energy and consistent microplane stresses.” Rep., Northwestern University, Evanston, Ill.
26.
Carol, I., Prat, P. C., and Bažant, Z. P. (1992). “New explicit microplane model for concrete: Theoretical aspects and numerical implementation.” Int. J. Solids and Struct., 29(9), 1173–1191.
27.
Cofer, W. F., and Kohut, S. W. (1994). “A general nonlocal microplane concrete material model for dynamic finite element analysis.” Comp. and Struct., 53(1), 189–199.
28.
Hasegawa, T., and Bažant, Z. P. (1993). “Nonlocal microplane concrete model with rate effect and load cycles. I: General formulation.”J. Mat. in Civ. Engrg., ASCE, 5(3), 372–393.
29.
Hill, R. (1965). “Continuum micromechanics of elastoplastic polycrystals.” J. Mech. Phys. Solids, 13, 89–101.
30.
Hill, R. (1966). “Generalized constitutive relations for incremental deformations of metal crystals by multi-slip.” J. Mech. Phys. Solids, 14, 95–102.
31.
Jirásek, M. ( 1993). “Modeling of fracture and damage in quasibrittle materials.” PhD dissertation, Northwestern University, Evanston, Ill.
32.
Kröner, E. (1961). “Zur plastischen Verformung des Vielkristalls.” Acta Metallurgica, 9(Feb.), 155–161.
33.
Kuhl, E., and Carol, I. (2000). “New thermodynamic approach to microplane model. I: Dissipation and inelastic constitutive modeling.” Int. J. Solids and Struct., in press.
34.
Lin, T. H., and Ito, M. (1965). “Theoretical plastic distortion of a polycrystalline aggregate under combined and reversed stresses.” J. Mech. Phys. Solids, 13, 103–115.
35.
Lin, T. H., and Ito, M. (1966). “Theoretical plastic stress-strain relationship of a polycrystal.” Int. J. Engrg. Sci., 4, 543–561.
36.
Ožbolt, J., and Bažant, Z. P. (1992). “Microplane model for cyclic triaxial behavior of concrete and rock.”J. Engrg. Mech., ASCE, 118(7), 1365–1386.
37.
Ožbolt, J., and Bažant, Z. P. (1996). “Numerical smeared fracture analysis: Nonlocal microcrack interaction approach.” Int. J. Numer. Methods in Engrg., Chichester, U.K., 39, 635–661.
38.
Pande, G. N., and Sharma, K. G. (1981). “Time-dependent multi-laminate model for clay—a numerical study of the influence of rotation of principal stress axes.” Proc., Implementation of Comp. Procedures and Strain-Stress Laws in Geotech. Engrg., Vol. II, Acorn Press, Durham, N.C., 575–590.
39.
Pande, G. N., and Sharma, K. G. (1982). “Multi-laminate model of clays—A numerical evaluation of the influence of rotation of the principal stress axis.” Rep., Dept. of Civ. Engrg., University College of Swansea, U.K.
40.
Pande, G. N., and Xiong, W. (1982). “An improved multi-laminate model of jointed rock masses.” Proc., Int. Symp. on Numer. Models in Geomech., R. Dungar, G. N. Pande, and G. A. Studder, eds., Balkema, Rotterdam, The Netherlands, 218–226.
41.
Prat, P. C., and Bažant, Z. P. (1991). “Microplane model for triaxial deformation of saturated cohesive soils.”J. Geotech. Engrg., ASCE, 117(6), 891–912.
42.
Prat, P. C., Sánchez, F., and Gens, A. (1997). “Equivalent continuum anisotropic model for rocks: Theory and application to finite-element analysis.” Proc., 6th Int. Symp. on Numer. Methods in Geomech., Balkema, Rotterdam, The Netherlands, 159–166.
43.
Rice, J. R. (1970). “On the structure of stress-strain relations for time-dependent plastic deformation of metals.” J. Appl. Mech., 37(Sept.), 728–737.
44.
Stroud, A. H. (1971). Approximate calculation of multiple integrals, Prentice-Hall, Englewood Cliffs, N.J.
45.
Taylor, G. I. (1938). “Plastic strain in metals.” J. Inst. of Metals, London, 62, 307–324.
46.
Zienkiewicz, O. C., and Pande, G. N. (1977). “Time-dependent multi-laminate model of rocks—A numerical study of deformation and failure of rock masses.” Int. J. Numer. and Analytical Methods in Geomech., 1, 219–247.
Information & Authors
Information
Published In
History
Received: Mar 2, 1999
Published online: Sep 1, 2000
Published in print: Sep 2000
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.