Microplane Model M5f for Multiaxial Behavior and Fracture of Fiber-Reinforced Concrete
Publication: Journal of Engineering Mechanics
Volume 133, Issue 1
Abstract
Despite impressive advances, the existing constitutive and fracture models for fiber-reinforced concrete (FRC) are essentially limited to uniaxial loading. The microplane modeling approach, which has already been successful for concrete, rock, clay, sand, and foam, is shown capable of describing the nonlinear hardening–softening behavior and fracturing of FRC under not only uniaxial but also general multiaxial loading. The present work generalizes model M5 for concrete without fibers, the distinguishing feature of which is a series coupling of kinematically and statically constrained microplane systems. This feature allows simulating the evolution of dense narrow cracks of many orientations into wide cracks of one distinct orientation. The crack opening on a statically constrained microplane is used to determine the resistance of fibers normal to the microplane. An effective iterative algorithm suitable for each loading step of finite element analysis is developed, and a simple sequential procedure for identifying the model parameters from test data is formulated. The model allows a close match of published test data on uniaxial and multiaxial stress–strain curves, and on multiaxial failure envelopes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Partial financial support under U.S. National Science Foundation Grants NSFCMS-0301145 and NSFCMS-0556323 to Northwestern University is gratefully acknowledged.
References
Batdorf, S. B., and Budianski, B. (1949). “A mathematical theory of plasticity based on the concept of slip.” Technical Note No. 1871, National Advisory Committee for Aeronautics, Washington, D.C.
Bažant, Z. P. (1985). “Mechanics of fracture and progressive cracking in concrete structures.” Fracture mechanics of concrete: Structural application and numerical calculation, G. C. Sih and A. DiTommaso, eds., Martinus Nijhoff, Dordrecht, The Netherlands, pp. 1–94.
Bažant, Z. P. (2002). Scaling of structural strength, Hermes Penton Science, London (and French translation with updates, Hermes, Paris, 2004).
Bažant, Z. P. (2004). “Scaling theory for quasibrittle structural failure.” Proc. Natl. Acad. Sci. U.S.A., 101(37), 13400–13407.
Bažant, Z. P., et al. (2000b). “Large-strain generalization of microplane model for concrete and application.” J. Eng. Mech., 126(9), 971–980.
Bažant, Z. P., Caner, F. C., Carol, I., Adley, M. D., and Akers, S. A. (2000a). “Microplane model M4 for concrete: I. Formulation with work-conjugate deviatoric stress.” J. Eng. Mech., 126(9), 944–953.
Bažant, Z. P., and Caner, F. C. (2005a). “Microplane model M5 with kinematic and static constraints for concrete fracture and anelasticity. I. Theory.” J. Eng. Mech., 131(1), 31–40.
Bažant, Z. P., and Caner, F. C. (2005b). “Microplane model M5 with kinematic and static constraints for concrete fracture and anelasticity. II. Computation.” J. Eng. Mech., 131(1), 41–47.
Bažant, Z. P., and Chen, E.-P. (1997). “Scaling of structural failure.” Appl. Mech. Rev., 50(10), 593–627.
Bažant, Z. P., and Desmorat, R. (1994). “Size effect in fiber or bar pullout with interface softening slip.” J. Eng. Mech., 120(9), 1945–1962.
Bažant, Z. P., and Jirásek, M. (2002). “Nonlocal integral formulations of plasticity and damage: Survey of progress.” J. Eng. Mech., 128(11), 1119–1149.
Bažant, Z. P., Li, Z., and Thoma, M. (1995). “Identification of stress-slip law for bar or fiber pullout by size effect tests.” J. Eng. Mech., 121(5), 620–625.
Bažant, Z. P., and Oh, B.-H. (1983a). “Microplane model for fracture analysis of concrete structures.” Proc., Symp. on the Interaction of Non-Nuclear Munitions with Structures, U.S. Air Force Academy, Colorado Springs, Colo., 49–53.
Bažant, Z. P., and Oh, B.-H. (1983b). “Crack band theory for fracture of concrete.” Mater. Constr. (Paris), 16, 155–177.
Bažant, Z. P., and Oh, B.-H. (1985). “Microplane model for progressive fracture of concrete and rock.” J. Eng. Mech., 111(4), 559–582.
Bažant, Z. P., and Oh, B.-H. (1986). “Efficient numerical integration on the surface of a sphere.” Z. Angew. Math. Mech., 66(1), 37–49.
Bažant, Z. P., and Pijaudier-Cabot, G. (1989). “Measurement of characteristic length of nonlocal continuum.” J. Eng. Mech., 115(4), 755–767.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC Press, Boca Raton, Fla.
Bažant, Z. P., and Prat, P. C. (1988). “Microplane model for brittle plastic material: I. Theory.” J. Eng. Mech., 114(10), 1672–1688.
Bažant, Z. P., and Şener, S. (1988). “Size effect in pullout tests.” ACI Mater. J., 85, 347–351.
Bažant, Z. P., Xiang, Y. and Prat, P. C. (1996). “Microplane model for concrete: I. Stress-strain boundaries and finite strain.” J. Eng. Mech., 1224(3), 245–254
Bažant, Z. P., and Zi, G. (2003). “Microplane constitutive model for porous isotropic rock.” Int. J. Numer. Analyt. Meth. Geomech., 27, 25–47.
Brocca, M., and Bažant, Z. P. (2001). “Microplane finite element analysis of tube-squash test of concrete with shear angle up to .” Int. J. Numer. Methods Eng., 52, 1165–1188.
Brocca, M., Bažant, Z. P., and Daniel, I. M. (2001). “Microplane model for stiff foams and finite element analysis of sandwich failure by core indentation.” Int. J. Solids Struct., 38, 8111–8132.
Caner, F. C., and Bažant, Z. P. (2000). “Microplane model M4 for concrete: II. Algorithm and calibration.” J. Eng. Mech., 126(9), 954–961.
Camacho, G. T., and Ortiz, M. (1996). “Computational modeling of impact damage in brittle materials.” Int. J. Solids Struct., 33(20–22), 2899–2938.
Carol, I., and Bažant, Z. P. (1997). “Damage and plasticity in microplane theory.” Int. J. Solids Struct., 34(29), 3807–3835.
Carol, I., Jirásek, M., and Bažant, Z. P. (2004). “A framework for microplane models at large strain, with application to hyperelasticity.” Int. J. Solids Struct., 41, 511–557.
Červenka, J., Bažant, Z. P., and Wierer, M. (2005). “Equivalent localization element for crack band approach to mesh-sensitivity in microplane model.” Int. J. Numer. Methods Eng., 62(5), 700–726.
Chern, J.-C., Yang, H.-J., and Chen, H.-W. (1992). “Behavior of steel fiber-reinforced concrete in multiaxial loading.” ACI Mater. J., 89(1), 32–40.
Cho, S. H., and Kim, Y. I. (2003). “Effects of steel fibers on short beams loaded in shear.” ACI Struct. J., 100(6), 765–774.
Grimaldi, A., and Luciano, R. (2000). “Tensile stiffness and strength of fiber-reinforced concrete.” J. Mech. Phys. Solids, 48(9), 1987–2008.
Kabele, P. (2004). “Linking scales in modeling of fracture in high performance fiber-reinforced cementitious composites.” Fracture Mechanics of Concrete Structures, Proc., FraMCoS-5, 5th Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures, Vail, Colo., Vol. 1, V. C. Li, K. Y. Leung, K. J. Willam, and S. L. Billington, eds., IA-FraMCoS, Evanston, Ill., pp. 71–80.
Kholmyansky, M. M. (2002). “Mechanical resistance of steel fiber-reinforced concrete to axial load.” J. Mater. Civ. Eng., 14(4), 311–319.
Kullaa, J. (1994). “Constitutive modeling of fiber-reinforced concrete under uniaxial tensile loading.” Composites, 25(10), 935–944.
Kupfer, H., Hilsdorf, H. K., and Rüsch, H. (1969). “Behavior of concrete under biaxial stresses.” ACI J. 66(8), 656–666.
Kwak, Y. K., Eberhard, M. O., Kim, W. S., and Kim, J. (2002). “Shear strength of fiber-reinforced concrete beams without stirrups.” ACI Struct. J., 99(4), 530–538.
Li, F., and Li, Z. (2001). “Continuum damage mechanics based modeling of fiber-reinforced concrete in tension.” Int. J. Solids Struct., 38, 777–793.
Li, Z., Li, F., Chang, T.-Y.-P, and Mai, Y.-W. (1998). “Uniaxial tensile behavior of concrete reinforced with randomly distributed short fibers.” ACI Mater. J., 95(5), 564–574.
Mirsayah, A. A., and Banthia, N. (2002). “Shear strength of steel fiber-reinforced concrete.” ACI Mater. J., 99(5), 473–479.
Nataraja, M. C., Dhang, N., and Gupta, A. P. (1999). “Stress–strain curves for steel-fiber reinforced concrete under compression.” Cem. Concr. Compos., 21(5–6), 383–390.
Nelissen, L. J. M. (1972). “Biaxial testing of normal concrete.” Heron, 18(1), 1–90.
Pantazopoulou, S. J., and Zanganeh, M. (2001). “Triaxial tests of fiber-reinforced concrete.” J. Mater. Civ. Eng., 13(5), 340–348.
Peng, X., and Meyer, C. (2000). “A continuum damage mechanics model for concrete reinforced with randomly distributed short fibers.” Comput. Struct., 78, 505–515.
Pizzari, G. A., Cangiano, S., and Cere, N. (2000). “Postpeak behavior of fiber-reinforced concrete under cyclic tensile loads.” ACI Mater. J., 97(2), 182–192.
Ramesh, K., Seshu, D. R., and Prabhakar, M. (2003). “Constitutive behavior of fibre reinforced concrete under axial compression.” Cem. Concr. Compos., 25(3), 343–350.
Reinhardt, H. W., and Cornelissen, H. A. W. (1984). “Post-peak cyclic behavior of concrete in uniaxial tensile and alternating tensile and compressive loading.” Cem. Concr. Res., 14(2), 263–270.
RILEM Committee QFS. (2004). “Quasibrittle fracture scaling and size effect.” Mater. Struct., 37(272), 547–586.
Soroushian, P., and Bayasi, Z. (1991). “Fiber-type effects on the performance of steel fiber-reinforced concrete.” ACI Mater. J., 88(2), 129–134.
Stroud, A. H. (1971). Approximate calculation of multiple integrals, Prentice-Hall, Englewood Cliffs, N.J.
Tasuji, M. E., Slate, F. O., and Nilson, A. H. (1978). “Stress–strain response and fracture of concrete in biaxial loading.” ACI J., 75(7), 306–312.
Taylor, G. I. (1938). “Plastic strain in metals.” J. Inst. Met., 62, 307–324.
Traina, L. A., and Mansour, S. A. (1991). “Biaxial strength and deformational behavior of plain and steel fibre concrete.” ACI Mater. J., 88(4), 354–362.
Yin, W. S., Su, E. C. M., Mansur, M. A., and Hsu, T. T. C. (1989). “Biaxial tests of plain and fiber concrete.” ACI Mater. J., 86(3), 236–243.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 1 • January 2007
Pages: 66 - 75
Copyright
© 2007 ASCE.
History
Received: Jul 21, 2005
Accepted: Mar 3, 2006
Published online: Jan 1, 2007
Published in print: Jan 2007
Notes
Note. Associate Editor: Yunping Xi
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.