Measurement of Characteristic Length of Nonlocal Continuum
Publication: Journal of Engineering Mechanics
Volume 115, Issue 4
Abstract
The characteristic length of a heterogeneous brittle material such as concrete represents a material property that governs the minimum possible width of a zone of strain‐softening damage in nonlocal continuum formulations or the minimum possible spacing of cracks in discrete fracture models. This length is determined experimentally. The basic idea is to compare the response of two types of specimens, one in which the tensile softening damage remains distributed and one in which it localizes. The latter type of specimen is an edge‐notched tensile fracture specimen, and the former type of specimen is of the same shape but without notches. Localization of softening damage is prevented by gluing to the specimen surface a layer of parallel thin‐steel rods and using a cross section of a minimum possible thickness that can be cast with a given aggregate. The characteristic length l is the ratio of the fracture energy (i.e., the energy dissipated per unit area, dimension ) to the energy dissipated per unit volume (dimension ) Evaluation of these energies from the present tests of concrete yields times the maximum aggregate size.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bažant, Z. P. (1976). “Instability, ductility, and size effect in strain‐softening concrete.” J. Engrg. Mech. Div., ASCE, 102(2), 331–344;
closure 104, 501–502.
2.
Bažant, Z. P. (1982). “Crack band model for fracture of geomaterials.” Proc., 4th Int. Conf. on Numerical Methods in Geomechanics, Edmonton, Canada, Z. Eisenstein, ed., Vol. 3, 1137–1152.
3.
Bažant, Z. P. (1986). “Mechanics of distributed cracking.” Appl. Mech. Rev., ASME, 39(5), 675–705.
4.
Bažant, Z. P. (1987). “Stable states and paths of structures with plasticity or damage.” Structural Engineering Report No. 87‐10/606s, Dept. of Civil Engineering, Northwestern Univ., Evanston, Ill.
also (1988), J. Engrg. Mech., ASCE, 114(12), 2013–2034.
5.
Bažant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Mater. Struct., RILEM, Paris, France, 16, 155–177.
6.
Bažant, Z. P., and Pfeiffer, P. (1987). “Fracture energy of concrete: Its definition and determination from size effect tests.” Concrete durability, Proc. K. and B. Mather Int. Conf., J. Scanlon, ed., Vol. 3, 89–109.
7.
Bažant, Z. P., and Pijaudier‐Cabot, G. (1987a). “Modeling of distributed cracking by nonlocal continuum with local strain.” Proc., 4th. Int. Conf. on Numerical Methods in Fracture Mechanics, San Antonio, Texas, A. R. Luxmoore et al., eds., Pineridge Press, Swansea, U.K., 411–432.
8.
Bažant, Z. P., and Pijaudier‐Cabot, G. (1987b). “Measurement of characteristic length of nonlocal continuum.” Report No. 87‐12/498 m, Center for Concrete and Geomaterials, Northwestern University, Evanston, Ill.
9.
Bažant, Z. P., and Pijaudier‐Cabot, G. (1987c). “Nonlocal damage: Continuum model and localization instability.” Report No. 87‐2/428n‐I, Center for Concrete and Geomaterials, Northwestern University, Evanston, Ill;
also J. Appl. Mech., ASME, 55(1988), 287–293.
10.
Bažant, Z. P., and Pijaudier‐Cabot, J. (1988). “Nonlocal continuum damage and measurement of characteristic length.” Mech. of Composite Materials—1988, G. J. Dvorak and N. Laws, eds., AMD Vol. 92, ASME, 79–85 (presented at Joint ASME/SES Appl. Mech. and Eng. Sci. Conf., Berkeley, Calif., June, 1988).
11.
Hillerborg, A., Modéer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cement Concr. Res., 6(6), 773–782.
12.
Hordijk, D. A., Reinhardt, H. W., and Cornelissen, H. A. W. (1987). “Fracture mechanics parameters of concrete from uniaxial tensile tests as influenced by specimen length.” Preprints of the SEM/RILEM Int. Conf. on Fracture of Concrete and Rock, Houston, Tex. S. P. Shah and S. Swartz, eds., SES (Society of Experimental Mechanics), 138–149.
13.
Irwin, G. R. (1958). “Fracture.” Encyclopaedia of physics, Vol. VI, Springer, Berlin, Germany.
14.
L'Hermite, R. (1960). “Volume changes of concrete.” Proc., 4th Int. Symp. on the Chemistry of Cement, Washington, D.C., 659–702.
15.
Raiss, M. E. (1986). “Observation of the development of fracture process zone in concrete under tension,” thesis presented to Imperial College, London, U.K., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
16.
RILEM Committee 50‐FMC. (1985). “Determination of the fracture energy of mortar and concrete by means of three‐point‐bend tests on notched beams.” RILEM Draft Recommendation, Mater. Struct.(RILEM, Paris), 18(106), 285–290.
17.
Rots, J. G., Hordijk, D. A., and de Borst, R. (1987). “Numerical simulation of concrete fracture in direct tension.” Proc., 4th Int. Conf on Numerical Methods in Fracture Mechanics, San Antonio, Tex., A. R. Luxmoore et al., eds., Pineridge Press, Swansea, U.K., 457–471.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Apr 1, 1989
Published in print: Apr 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.