Confinement-Shear Lattice Model for Concrete Damage in Tension and Compression: I. Theory
This article has a reply.
VIEW THE REPLYPublication: Journal of Engineering Mechanics
Volume 129, Issue 12
Abstract
The mechanical behavior of the mesostructure of concrete is simulated by a three-dimensional lattice connecting the centers of aggregate particles. The model can describe not only tensile cracking and continuous fracture but also the nonlinear uniaxial, biaxial, and triaxial response in compression, including the postpeak softening and strain localization. The particle centers representing the lattice nodes are generated randomly, according to the given grain size distribution, and Delaunay triangulation is used to determine the lattice connections and their effective cross-section areas. The deformations are characterized by the displacement and rotation vectors at the centers of the particles (lattice nodes). The lattice struts connecting the particles transmit not only axial forces but also shear forces, with the shear stiffness exhibiting friction and cohesion. The connection stiffness in tension and shear also depends on the transversal confining stress. The transmission of shear forces between particles is effected without postulating any flexural resistance of the struts. The shear transmission and the confinement sensitivity of lattice connections are the most distinctive features greatly enhancing the modeling capability. The interfacial transition zone of the matrix (cement mortar or paste) is assumed to act approximately in series coupling with the bulk of the matrix. The formulation of a numerical algorithm, verification by test data, and parameter calibration are postponed for the subsequent companion paper.
Get full access to this article
View all available purchase options and get full access to this article.
References
Arlsan, A., Ince, R., and Karihaloo, B. L.(2002). “Improved lattice model for concrete fracture.” J. Eng. Mech., 128(1), 57–65.
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., Caner, F. C., Adley, M. D., and Akers, S. A.(2000b). “Fracturing rate effect and creep in microplane model for dynamics.” J. Eng. Mech., 126(9), 962–970.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture, and damage theories, Oxford University Press, New York; also 2nd Ed., Dover, New York, 2003.
Bažant, Z. P., and Oh, B. H.(1983). “Crack band theory for fracture of concrete.” Mater. Struct. (Paris), 16, 155–177.
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., Tabarra, M. R., Kazemi, T., and Pijaudier-Cabot, G.(1990). “Random particle model for fracture of aggregate or fiber composites.” J. Eng. Mech., 116(8), 1686–1705.
Bažant, Z. P., Xiang, Y., and Prat, P. C.(1996). “Microplane model for concrete. I: Stress–strain boundaries and finite strain.” J. Eng. Mech., 122(3), 245–254.
Bolander, J. E., Hong, G. S., and Yoshitake, K.(2000). “Structural concrete analysis using rigid-body-spring networks.” J. Comput.-Aided Civil Infrastruct. Eng.,15, 120–133.
Bolander, J. E., and Saito, S.(1998). “Fracture analysis using spring network with random geometry.” Eng. Fract. Mech., 61(5-6), 569–591.
Bolander, J. E., Yoshitake, K., and Thomure, J.(1999). “Stress analysis using elastically uniform rigid-body-spring networks.” J. Struct. Mech. Earthquake Eng., JSCE, 633(I-49), 25–32.
Camacho, G. T., and Ortiz, M.(1996). “Computational modeling of impact damage in brittle materials.” Int. J. Solids Struct., 33(20-22), 2899–2938.
Caner, F. C., and Bažant, Z. P.(2000). “Microplane model M4 for concrete. II: Algorithm and calibration.” J. Eng. Mech., 126(9), 954–961.
Cundall, P. A. (1971). “A computer model for simulating progressive large scale movements in blocky rock systems.” Proc., Int. Symp. Rock Fracture, ISRM, Nancy, France, 2–8.
Cundall, P. A. (1978). “BALL—A program to model granular media using distinct element method.” Technical note, Advanced Tech. Group, Dames and Moore, London, U.K.
Cundall, P. A., and Strack, O. D. L.(1979). “A discrete numerical model for granular assemblies.” Geotechnique, 29, 47–65.
Cusatis, G., Bažant, Z. P., and Cedolin, L.(2003). “Confinement-shear lattice model for concrete damage in tension and compression: II. Computation and validation.” J. Eng. Mech., 129(12), 1449–1458.
Hrennikoff, A.(1941). “Solution of problems of elasticity by the framework method.” J. Appl. Mech. Tech. Phys., 12, 169–175.
Jirásek, M., and Bažant, Z. P.(1995a). “Macroscopic fracture characteristics of random particle systems.” Int. J. Fract., 69(3), 201–228.
Jirásek, M., and Bažant, Z. P.(1995b). “Particle model for quasibrittle fracture and application to sea ice.” J. Eng. Mech., 121(9), 1016–1025.
Kawai, T.(1978). “New discrete models and their application to seismic response analysis of structures.” Nucl. Eng. Des., 48, 207–229.
Lopez, C. M., Carol, I., and Aguado, A. (2000). “Microstructural analysis of concrete fracture using interface elements.” Proc., European Congress on Computational Methods in Applied Sciences and Eng., Barcelona, 1–18.
Pandolfi, A., Krysl, P., and Ortiz, M.(1999). “Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models.” Int. J. Fract., 95, 279–297.
Plesha, M. E., and Aifantis, E. C. (1983). “On the modeling of rocks with microstructure.” Proc., 24th U.S. Symp. Rock Mech., Texas A & M Univ., College Station, Tex., 27–39.
Rodriguez-Ortiz, J. M. (1974). “Study of behavior of granular heterogeneous media by means of analogical and mathematical discontinous models.” PhD thesis, Univ. Politécnica de Madrid, Spain (in Spanish).
Roelfstra, P. E. (1988). “Numerical concrete.” PhD thesis, Laboratoire de Matériaux de Construction, Ecole Polytéchnique Féderale de Lausanne, Lausanne, Switzerland.
Roelfstra, P. E., Sadouki, H., and Wittmann, F. H.(1985). “Le béton numérique.” Mater. Struct., 18, 327–335.
Schlangen, E. (1995). “Computational aspects of fracture simulations with lattice models.” Fracture mechanics of concrete structures (Proc., FraMCoS-2, Zürich), F. H. Wittmann, ed., Aedificatio, Freiburg, Germany, 913–928.
Schlangen, E. (1993). “Experimental and numerical analysis of fracture processes in concrete.” PhD thesis, Delft Univ. of Technology, Delft, The Netherlands.
Schlangen, E., and van Mier, J. G. M. (1992). “Shear fracture in cementitious composites, Part II: Numerical simulations.” Fracture mechanics of concrete structures (Proc., FraMCoS-1), Z. P. Bažant, ed., Elsevier, London, 671–676.
Serrano, A. A., and Rodriguez-Ortiz, J. M. (1973). “A contribution to the mechanics of heterogeneous granular media.” Proc., Symp. Plasticity and Soil Mech., Cambridge, U.K.
Ting, J. M., Meachum, L. R., and Rowell, J. D.(1995). “Effect of particle shape on the strength and deformation mechanics of ellipse-shaped granular assemblage.” Eng. Comput., 12, 99–108.
van Mier, J. G. M., van Vliet, M. R. A., and Wang, T. K.(2002). “Fracture mechanisms in particle composites: Statistical aspects in lattice type analysis.” Mech. Mater., 34(11), 705–724.
van Mier, J. G. M., Vervuurt, A., and Schlangen, E. (1994). “Boundary and size effects in uniaxial tensile tests: A numerical and experimental study.” Fracture and damage in quasibrittle structures (Proc., NSF Workshop, Prague), Z. P. Bažant, Z. Bittnar, M. Jirásek, and J. Mazars, eds., E & FN Spon, London, 289–302.
Wittmann, F. H., Roelfstra, P. E., and Kamp, C. L.(1988). “Drying of concrete: An application of the 3L approach.” Nucl. Eng. Des., 105, 185–198.
Zubelewicz, A. (1980). “Contact element method.” PhD thesis, Technical Univ. of Varsaw, Varsaw, Poland (in Polish).
Zubelewicz, A. (1983). “Proposal of a new structural model for concrete.” Arch. Inzyn. Ladow. 29, 417–429 (in Polish).
Zubelewicz, A., and Bažant, Z. P.(1987). “Interface element modeling of fracture in aggregate composites.” J. Eng. Mech., 113(11), 1619–1630.
Zubelewicz, A., and Mróz, Z.(1983). “Numerical simulation of rockburst processes treated as problems of dynamic instability.” Rock Mech. Rock Eng., 16, 253–274.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 129 • Issue 12 • December 2003
Pages: 1439 - 1448
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Aug 26, 2002
Accepted: Feb 21, 2003
Published online: Nov 14, 2003
Published in print: Dec 2003
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.