Numerical Model for Time-Dependent Fracturing of Concrete
Publication: Journal of Engineering Mechanics
Volume 135, Issue 7
Abstract
A finite-element formulation for the analysis of time-dependent failure of concrete is presented. The proposed formulation incorporates: (1) the viscoelastic behavior of uncracked concrete through a Maxwell chain model; and (2) the inelastic behavior of damaged concrete, characterized by a modified version of the microplane Model M4 which includes the rate dependence of fracturing. The proposed formulation is applied to the simulation of quasi-static concrete failure in the time domain. The different effects of creep and rate dependence of crack growth and their role in the lifetime of concrete structures are studied. The influence of different loading rates on the size effect is also analyzed with reference to single notched specimens, revealing the link between the size of the fracture process zone and the loading rate. The capability of the proposed numerical formulation is also verified for the case of sustained uniaxial compressive loads.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writer gratefully acknowledges financial support from the Italian Department of Education, University and Scientific Research (MIUR)MIUR.
References
Barpi, F., and Valente, S. (2003). “Creep and fracture in concrete: A fractional order rate approach.” Eng. Fract. Mech., 70(5), 611–623.
Baxevanis, T., Dufour, F., Pijaudier-Cabot, G., and Desiassyifayanty, R. (2006). “Bifurcation and size effect in a viscoelastic nonlocal damageable continuum.” Proc., Computational Modelling of Concrete Structures—EURO-C 2006, G. Meschke, R. de Borst, H. A. Mang, and N. Bicanic, eds., Mayrhofen, Tirol, Austria, 283–290.
Bažant, Z. P. (1992). “Rate effects, size effects and nonlocal concept for fracture of concrete and other quasi-brittle material.” Mechanisms of quasibrittle material, S. Shah, ed., Kluwer, Dordrecht, The Netherlands, 131–153.
Bažant, Z. P. (1995). “Creep and damage in concrete.” Proc., 4th Materials Science of Concrete, J. Skalny and S. Mindess, eds., American Ceramic Society, Westerville, Ohio, 355–389.
Bažant, Z. P., Caner, F., Adley, M., and Akers, S. A. (2000a). “Fracturing rate effect and creep in microplane model for dynamics.” J. Eng. Mech., 126(9), 962–970.
Bažant, Z. P., Caner, F., Carol, I., Adley, M., and Akers, S. A. (2000b). “Microplane model M4 for concrete. I: Formulation with work-conjugate deviatoric stress.” J. Eng. Mech., 126(9), 944–953.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories, Oxford University Press, New York.
Bažant, Z. P., and Gettu, R. (1992). “Rate effect and load relaxation in static fracture of concrete.” ACI Mater. J., 89(5), 456–468.
Bažant, Z. P., and Jiràsek, M. (1993). “R-curve modeling of rate and size effects in quasibrittle material.” Int. J. Fract., 62, 355–373.
Bažant, Z. P., and Oh, B.-H. (1983). “Crack band theory for fracture of concrete.” Mater. Constr. (Paris), 16(93), 155–177.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC, Boca Raton, Fla.
Benboudjema, F., Meftah, F., and Torrenti, J. M. (2005). “Interaction between drying, shrinkage, creep and cracking phenomena in concrete.” Eng. Struct., 27, 239–250.
Carol, I., and Bažant, Z. P. (1993). “Viscoelasticity with aging caused by solidification of nonaging constituent.” J. Eng. Mech., 119(11), 2252–2269.
Challamel, N., Lanos, C., and Casandjian, C. (2005). “Creep damage modelling for quasibrittle materials.” Eur. J. Mech. A/Solids, 24, 593–613.
Crisfield, M. A. (1991). Nonlinear finite-element analysis of solids and structures, Vol. 1, Wiley, New York.
De Borst, R. (1987). “Smeared cracking, plasticity, creep, and thermal loading: A unified approach.” Comput. Methods Appl. Mech. Eng., 62(1), 89–110.
Di Luzio, G. (2007). “A symmetric over-nonlocal microplane model M4 for fracture in concrete.” Int. J. Solids Struct., 44, 4418–4441.
Di Luzio, G., and Cedolin, L. (2007). “Numerical model for time-dependent fracturing of concrete structures and its applications.” Proc., Fracture Mechanics of Concrete and Concrete Structures—FraMCoS-6, A. Carpinteri et al., eds., Taylor & Francis Group, Catania, Italy, 175–180.
Hansen, E. (1992). “A viscoelastic fictitious crack model.” Proc., Micromechanics of Quasibrittle Materials, S. P. Shah, S. E. Swartz, and M. L. Wang, eds., Elsevier, London, 156–165.
Loukili, A., Omar, M., and Pijaudier-Cabot, G. (2001). “Basic creep of ultra high strength concrete experiments and modeling.” Proc., Concreep 6, Z. P. Bazant, F.-J. Ulm, and F. H. Whitmann, eds., Elsevier, Amsterdam, The Netherlands, 545–550.
Mazzotti, C., and Savoia, M. (2003). “Nonlinear creep damage model for concrete under uniaxial compression.” J. Eng. Mech., 129(9), 1065–1075.
Press, W. H., Teukolsky, W. A., Vetterling, W. T., and Flennery, B. P. (1996). Numerical recipes in Fortran 90: The art of parallel scientific computing, Cambridge University Press, Cambridge, U.K.
Rüsch, H. (1960). “Researches towards a general flexural theory for structures concrete.” ACI J., 57(1), 1–28.
Santhikumar, S., Karihaloo, B., and Reid, G. (1998). “A model for ageing viscoelastic tension softening material.” Mech. Cohesive-Frict. Mater., 3, 27–39.
van Zijl, G., de Borst, R., and Rots, J. (2001). “A numerical model for the time-dependent cracking of cementitious materials.” Int. J. Numer. Methods Eng., 38, 5063–5092.
Wu, Z. S., and Bažant, Z. P. (1993). “Finite element modeling of rate effect in concrete fracture with influence of creep.” Proc., 5th Int. RILEM Symp. on Creep and Shrinkage of Concrete, Z. P. Bažant, and I. Carol, eds., London, E & FN Spon, London, 427–432.
Zhang, C., and Karihaloo, B. (1992). “Stability of crack in linear visco-elastic tension softening material.” Proc., Fracture Mechanics of Concrete Structures, Z. P. Bažant, ed., Elsevier Applied Science, Amsterdam, The Netherlands, 75–81.
Zhou, F. P. (1992). “Time-dependent crack growth and fracture in concrete.” Ph.D. thesis, Lund Univ. of Technology, Lund, Sweden.
Zhou, F. P., and Hillerborg, A. (1992). “Time-dependent fracture of concrete: Testing and modelling.” Proc., Fracture Mechanics of Concrete Structures, Z. P. Bažant, ed., Elsevier Applied Science, Amsterdam, The Netherlands, 75–81.
Zi, G., and Bažant, Z. (2002). “Continuous relaxation spectrum for concrete creep and its incorporation into microplane model M4.” J. Eng. Mech., 128(12), 1331–1336.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 7 • July 2009
Pages: 632 - 640
Copyright
© 2009 ASCE.
History
Received: Jun 30, 2006
Accepted: Nov 25, 2008
Published online: Jun 15, 2009
Published in print: Jul 2009
Notes
Note. Associate Editor: Christian Hellmich
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.