Nonlocal Microplane Model for Fracture, Damage, and Size Effect in Structures

Bažant, Zdeněk P.; Ožbolt, Joško

doi:10.1061/(asce)0733-9399(1990)116:11(2485)

Cited by 200 publications

(76 citation statements)

References 29 publications

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“…Shear, v" = UN = fj2hd, Where f~, = Peak Load; d = Beam Depth; and h = Beam Width c. Numerical microstructural simulations on a supercomputer, in which the concrete is modeled as a random array of particles (hard aggregate pieces), with a softening interparticle force-displacement relation (Bazant et al 1990; van Mier 1992). d. Nonlinear fracture mechanics solutions based on the fictitious crack model with a gradually softening law for the crack bridging stresses (Hillerborg 1985 Fig.…”

Section: Fig 4 Laboratory and Numerical Size Effect Tests Of Geometmentioning

confidence: 99%

“…In the microplane model, the strain calculated for each integration point of each finite element, and each loading stage of each iteration, is first decomposed into components on a discrete set of microplanes [typically 21 of them, see Bazant and Ozbolt (1990)]. After calculating the stresses from the strains on all the microplanes, the macroscopic stress tensor is obtained by summation over these microplanes, which approximates an integral over -…”

Section: 0 ---------------- (H)brazilian Split-cylindermentioning

confidence: 99%

See 1 more Smart Citation

Fracture Size Effect: Review of Evidence for Concrete Structures

Bažant

Ožbolt²,

Eligehausen³

1994

J. Struct. Eng.

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The paper reviews experimental evidence on the size effect caused by energy release due to fracture growth during brittle failures of concrete structures. The experimental evidence has by now become quite extensive. The size effect is verified for diagonal shear failure and torsional failure of longitudinally reinforced beams without stirrups, punching shear failure of slabs, pull-out failures of deformed bars and of headed anchors, failure of short and slender tied columns, double-punch compression failure and for part of the range also the splitting failure of concrete cylinders in the Brazilian test. Although much of this experimental evidence has been obtained with smaller laboratory specimens and concrete of reduced aggregate size, some significant evidence now also exists for normal-size structures made with normal-size aggregate. There is also extensive and multifaceted theoretical support. A non local finite element code based on the microplane model is shown to be capable of correctly simulating the existing experimental data on the size effect. More experimental data for large structures with normal-size aggregate are needed to strengthen the existing verification and improve the calibration of the theory. NATURE OF PROBLEMAs a result of many important studies, including Humphreys (1957), Rusch et al. (1962), Leonhardt and Walter (1962), Kani (1967), Bhal (1968, Hsu (1968), McMullen and Daniel (1972), Taylor (1972), Hillerborg et al. (1976), Walsh (1976), Walraven (1978,1990), Chana (1981, Petersson (1981), Reinhardt (1981a,b), Hawkins (1985), Iguro et al. (1985), Hillerborg (1985), Ingraffea (1985, Rots (1988Rots ( , 1992 and others, it has been known that failure of concrete structures exhibits a size effect. For a long time the size effect has been explained statistically as a consequence of the randomness of material strength, particularly by the fact that in a larger structure it is more likely to encounter a material point of smaller strength. Various existing test data on the size effect were interpreted in terms of Weibull weakest-link theory [e.g. Mihashi and Zaitsev (1981) and Mihashi (1983)]. Later, however, it was proposed (Bazant 1984(Bazant , 1986) that whenever the failure does not occur at the initiation of cracking, which represents most situations, the size effect should properly be explained by energy release caused by macrocrack growth, and that the randomness of strength plays only a negligible role [in detail see Bazant and Xi (1991)].The size effect, however, does not follow the classical, linear form of fracture mechanics, in which all the fracture process is presumed to be happening at one point-the crack tip. Rather, the size effect in concrete structures must be explained by a nonlinear form of fracture mechanics that takes into account the localization of damage into a fracture process zone lWalter P. Murphy Prof. of Civ. Engrg. and Mat. Sci., Northwestern Univ., Evanston, IL 6020S.2Res. Engr., Institut fUr Werkstoffe im Bauwesen, Stuttgart Univ., Germany. 3Prof., ...

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Section: Fig 4 Laboratory and Numerical Size Effect Tests Of Geometmentioning

confidence: 99%

Section: 0 ---------------- (H)brazilian Split-cylindermentioning

confidence: 99%

Fracture Size Effect: Review of Evidence for Concrete Structures

Bažant

Ožbolt²,

Eligehausen³

1994

J. Struct. Eng.

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“…A substantial increase of computational efficiency was achieved by later improvements based on the idea that only the quantities directly associated with strainsoftening (such as the damage, the damage energy release rate, or the accumulated plastic strain) should be treated as nonlocal, while the elastic part of the behavior should remain local. Nonlocal versions of several constitutive models were successfully implemented into finite-element codes and applied to a variety of problems by Bazant and Pijaudier-Cabot (1988), Bazant and Lin (1988), and Bazant and Ozbolt (1990). The non local version (Bazant and Ozbolt 1990) of the microplane model (BaZant and Prat 1988) proved to be particularly efficient for the computer analysis of structures made of quasi-brittle materials such as concrete.…”

Section: New Approach To Nonlocal Averagingmentioning

confidence: 99%

“…Nonlocal versions of several constitutive models were successfully implemented into finite-element codes and applied to a variety of problems by Bazant and Pijaudier-Cabot (1988), Bazant and Lin (1988), and Bazant and Ozbolt (1990). The non local version (Bazant and Ozbolt 1990) of the microplane model (BaZant and Prat 1988) proved to be particularly efficient for the computer analysis of structures made of quasi-brittle materials such as concrete. However, it also became clear that the classical non local concept based on an isotropic weight function has its limitations and does not allow formulating a model universally applicable to the same material under different loading conditions.…”

Section: New Approach To Nonlocal Averagingmentioning

confidence: 99%

Localization Analysis of Nonlocal Model Based on Crack Interactions

Jirásek

Bažant²

1994

J. Eng. Mech.

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The conventional non local model, often used as a localization limiter for continuum-based constitutive laws with strain·softening, has been based on an isotropic averaging function. It has recently been shown that this type of nonlocal averaging leads to a model that cannot satisfactorily reproduce experimental results for very different test geometries without modifying the value of the characteristic length depending on geometry. A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one·dimensional description. Strain localization in an infinite layer under plane stress is studied using both the old and the new non local formulations. The importance of a renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out. In addition to the detection of bifurcations from an initially uniform state, the stable branch of the load·displacement diagram is followed using an incremental procedure.

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“…These difficulties can be addressed by supplementing the material model with some mathematical condition [16][17][18]. Other strategies are the non-local continuum models [19,20], the gradient models [21], and the micropolar continuum [22]. These procedures are suited to specific problems, but none gives a general solution to the problem.…”

Section: Introductionmentioning

confidence: 99%

An embedded cohesive crack model for finite element analysis of quasi-brittle materials

Gálvez

Planãs

Sancho

et al. 2013

Engineering Fracture Mechanics

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This paper presents a numerical implementation of the cohesive crack model for the anal-ysis of quasibrittle materials based on the strong discontinuity approach in the framework of the finite element method. A simple central force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need for performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent procedure for the selection of the separated nodes. Such a model is then implemented into a commercial program by means of a user subroutine, consequently being contrasted with the experimental results. The model takes into account the anisotropy of the material. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the fracture of quasibrittle materials such as mortar, con-crete and masonry.

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Nonlocal Microplane Model for Fracture, Damage, and Size Effect in Structures

Cited by 200 publications

References 29 publications

Fracture Size Effect: Review of Evidence for Concrete Structures

Fracture Size Effect: Review of Evidence for Concrete Structures

Localization Analysis of Nonlocal Model Based on Crack Interactions

An embedded cohesive crack model for finite element analysis of quasi-brittle materials

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