Size effects in the mixed mode crack propagation: Softening and snap-back analysis

Bocca, Pietro Giovanni; Carpinteri, Alberto; Valente, Silvio

doi:10.1016/0013-7944(90)90193-k

Cited by 111 publications

(53 citation statements)

References 7 publications

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“…The test results, obtained under careful laboratory control, were quite systematic, with only a small scatter of the measured failure loads (which was not larger than in compression tests of concrete cylinders). Further extensive studies of the size effect for concretes with normal aggregate size have later also been performed (Iguro et al 1985;Eligehausen et al 1988;Eligehausen and Sawade 1989;Walraven 1990;Marti 1989;Wittman, et al 1990;Bocca et at. 1990;.…”

Section: Nature Of Problemmentioning

confidence: 99%

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: Nature Of Problemmentioning

confidence: 99%

Fracture Size Effect: Review of Evidence for Concrete Structures

Bažant

Ožbolt²,

Eligehausen³

1994

J. Struct. Eng.

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“…[52], where it has been very roughly presented. The plot denoted MS corresponds to the numerical multi-scale solution (BC's case I).…”

Section: A) Morphology Of the Crack Patternsmentioning

confidence: 99%

“…The stiffness matrix of elements with DDM, in state 2, is derived from the equilibrium equations (51) and (52), and can be written as follows:…”

Section: Stiffness Matrix Of Finite Elements With Ddmmentioning

confidence: 99%

“…These data have been taken from Unger and Eckardt [51] with all the elastic moduli increased 10%. The parameters defined in [51], such as peak stresses and fracture energies of constituents, are considered a very rough estimation for simulating the concrete beam test in sub-Section 4.3 Note that the experimental work (Bocca et al [52]) taken for validating the numerical results in sub-Section 4.3, reports an overall Young's modulus: E = 27. [GP a] and an overall fracture energy G f = 100.[N/m].…”

Section: Materials Parameters Of the Meso-scale Modelmentioning

confidence: 99%

“…The experimental report ( [52]) shows one of the broken specimen, with the ratio: c/b = 0.4. From there, it can be observed a curved crack developing from the notch root to the load application point.…”

Section: A) Morphology Of the Crack Patternsmentioning

confidence: 99%

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Cohesive surface model for fracture based on a two-scale formulation: computational implementation aspects

et al. 2016

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Keywords: multi-scale cohesive models, computational homogenization, heterogeneous material failure, Embedded Finite Elements (EFEM). AbstractThe paper describes the computational aspects and numerical implementation of a two-scale cohesive surface methodology developed for analyzing fracture in heterogeneous materials with complex microstructures. This approach can be categorized as a semi-concurrent model using the Representative Volume Element (RVE) concept.A variational multi-scale formulation of the methodology has been previously presented by the authors. Subsequently, the formulation has been generalized and improved in two aspects: i) cohesive surfaces have been introduced at both scales of analysis, they are modeled with a strong discontinuity kinematics (new equations describing the insertion of the macro-scale strains, into the micro-scale and the posterior homogenization procedure have been considered); ii) the computational procedure and numerical implementation have been adapted for this formulation. The first point has been presented elsewhere, and it is summarized here. Instead, the main objective of this paper is to address a rather detailed presentation of the second point.Finite element techniques for modeling cohesive surfaces at both scales of analysis (FE 2 approach) are described: i) finite elements with embedded strong discontinuities (EFEM) are used for the macroscale simulation, and ii) continuum-type finite elements with high aspect ratios, mimicking cohesive surfaces, are adopted for simulating the failure mechanisms at the micro-scale.The methodology is validated through numerical simulation of a quasi-brittle concrete fracture problem. The proposed multi-scale model is capable of unveiling the mechanisms that lead from the material degradation phenomenon at the meso-structural level to the activation and propagation of cohesive surfaces at the structural scale.

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Continuum approach to the numerical simulation of material failure in concrete

Oliver

Huespe

Samaniego

et al. 2004

Num Anal Meth Geomechanics

142

117

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Some new aspects of the continuum strong discontinuity approach (CSDA) to model material failure in geomaterials are addressed. A new global algorithm, for tracking multiple crack lines/surfaces in 2D/3D cases is proposed. It is based on solving a simple heat conduction‐like problem accompanying the standard mechanical algorithm. A viscous perturbation method on the crack surface is also proposed to remedy the instabilities caused by mutual interactions of multiple developing cracks. A simple procedure to compute the critical time step that ensures algorithmic uniqueness is then provided. Numerical simulations of two‐ and three‐dimensional problems displaying a multi‐crack pattern are finally presented. Copyright © 2004 John Wiley & Sons, Ltd.

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Size effects in the mixed mode crack propagation: Softening and snap-back analysis

Cited by 111 publications

References 7 publications

Fracture Size Effect: Review of Evidence for Concrete Structures

Fracture Size Effect: Review of Evidence for Concrete Structures

Cohesive surface model for fracture based on a two-scale formulation: computational implementation aspects

Continuum approach to the numerical simulation of material failure in concrete

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