Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts

Kachanov, Mark

doi:10.1115/1.3119761

Cited by 798 publications

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“…Furthermore, this normalization explicitly accounts for the observed scaling of the connectivity of networks near the percolation threshold ]. Significantly, unlike fracture frequencies, the fracture density defined in (6) can be related to the effective elastic properties of a fractured medium [Kachanov, 1992] Substituting the power law length distribution (equation (3)) into (6) and recognizing that a < 3, the fracture spatial density for a power law network within an L x L area is p = CL3-a/4(3 -a)…”

Section: Connectivity Of Power Law Networkmentioning

confidence: 99%

Connectivity of joint networks with power law length distributions

Renshaw¹

1999

Water Resources Research

101

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Abstract. Over the range of fracture spatial densities commonly observed in the field, existing effective medium models for network connectivity yield inconsistent results because the connectivity depends on both the density and length distribution of the joints. Field observations indicate that joint lengths often follow a power law length distribution. Requiring the frequency of joint lengths to decrease with increasing length and the total area of the joints to be finite suggests approximate upper and lower bounds on the power law exponent which are consistent with observed distributions. The appropriate relationship between connectivity and density is investigated numerically. Results motivate a new measure of fracture intensity, the effective fracture density, and the development of a new approach toward a closed-form prediction of connectivity using measurable parameters. Although limited, model predictions compare favorably to the conductivities of networks simulated using a geomechanical model and observed in the field. [1997, 1998] but extend this previous work in several respects. We redefine and analyze the connectivity of the network to reflect the conductive properties of the network rather than just the probability that it percolates. Furthermore, 2661

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Section: Connectivity Of Power Law Networkmentioning

confidence: 99%

Connectivity of joint networks with power law length distributions

Renshaw¹

1999

Water Resources Research

101

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“…4 shows that the self-consistent scheme predicts zero secant stiffness for a finite value of the crack density parameter, p = 9/16. This is contradicted by tests of concrete and other quasi-brittle materials which show that the post-peak softening diagram has a very long tail (Budiansky and O'Connell, 1976 ;Sayers and Kachanov, 1991 ;Kachanov, 1992;Kachanov, 1993).…”

Section: Equivalent Elastic Stiffness Predicted By the Self-consistenmentioning

confidence: 94%

“…Approximate estimation of this function has been extensively reviewed by Kachanov and co-workers (Kachanov, 1992;Kachanov, 1993;Sayers and Kachanov, 1991;Kachanov et al, 1994). The incremental constitutive relation can be obtained by differentiation of (14), which yields (16) where L\ denotes small increments over a loading step.…”

Section: Equivalent Elastic Modulus Of a Materials With Arbitraril Y Omentioning

confidence: 99%

“…Other methods, such as the differential scheme (Roscoe, 1952;Salganik, 1973;Zimmerman, 1985;Hashin, 1988), the Mori-Tanaka method (Mori and Tanaka, 1973), and Dvorak's recent method of uniform fields (Dvorak and Benveniste, 1992;Dvorak, 1992), have also been proven useful. Using these techniques, the effect of various types of microcrack systems on the overall elastic properties of a body has been studied extensively, and many important results have been achieved in fields ranging from composite manufacture to geophysical research, rock mechanics and high-performance concretes (Budiansky and O'Connell, 1976;Hoenig, 1978Hoenig, , 1979Kachanov, 1980;Horii and Nemat-Nasser, 1983;Fabrikant, 1987;Ju and Tseng, 1992;Kachanov, 1992;Mauge and Kachanov, 1992;Fares, 1993;Hu and Huang, 1993;NematNasser and Yu, 1993;Huang et al, 1994;Ju and Chen, 1994;Mauge and Kachanov, 1994;Sayers and Kachanov, 1995).…”

Section: Introductionmentioning

confidence: 99%

“…Crack arrays of various configurations have been analyzed. Variational bounds on the effective elastic moduli of crack materials have also been obtained (Kachanov, 1992(Kachanov, , 1993. Highly accurate numerical solutions for elastic bodies with various examples of specific crack configurations have been presented (Kachanov, 1992).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tangential stiffness of elastic materials with systems of growing or closing cracks

Prat

Bažant

1997

Journal of the Mechanics and Physics of Solids

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Although much has been learned about the elastic properties of solids with cracks, virtually all the work has been confined to the case when the cracks are stationary, that is, neither grow nor shorten during loading. In that case, the elastic moduli obtained are the secant moduli. The paper deals with the practically much more important but more difficult case of tangential moduli for incremental deformations of the material during which the cracks grow while remaining critical, or shorten. Several families of cracks of either uniform or random orientation, characterized by the crack density tensor, are considered. To simplify the solution, the condition of crack criticality, i.e. the equality of the energy release rate to the energy dissipation rate based on the fracture energy of the material, is imposed only globally for all the cracks in each family, rather than individually for each crack. Sayers and Kachanov's approximation of the elastic potential as a tensor polynomial that is quadratic in the macroscopic stress tensor and linear in the crack density tensor, with coefficients that are general nonlinear functions of the first invariant of the crack density tensor, is used. The values of these coefficients can be obtained by one of the well-known schemes for elastic moduli of composite materials, among which the differential scheme is found to give more realistic results for post-peak strain softening of the material than the self-consistent scheme. For a prescribed strain tensor increment, a system of N + 6 linear equations for the increments of the stress tensor and of the crack size for each of N crack families is derived. Iterations of each loading step are needed to determine whether the cracks in each family grow, shorten, or remain stationary. The computational results are qualitatively in good agreement with the stress-strain curves observed in the testing of concrete.

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Crush-crack': a non-local damage model for concrete

Prisco

Mazars

1996

Mech. Cohes.-Frict. Mater.

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A model is presented based on the non‐local damage theory. It sets out to describe the behavior of concrete under free‐variable loads, which are constant in sign. Its purpose is to analyze shear behavior and high strain‐gradient localized problems, and it takes Mazar's model as a starting point with reference to the basic idea of a scalar isotropic non‐local damage controlled by principal tensile strains. In addition, the other two main features are an internal variable denoted to the control or reversible volumetric expansion in compression, and irreversible strains aimed at modelling crushing in compression and cracks both in tension and compression. As a consequence, induced‐anisotropy, dilatancy and path‐dep endency can be reproduced. In particular, the modelling of micro‐ and macrocracks makes it possible to capture mixed‐mode cracking as well as aggregate interlock, which requires a residual stiffness to guarantee the transmission of transversal and normal stresses for assigned slips. The model requires the knowledge of the material response in uniaxial tension and compression, and biaxial compression tests which can be introduced directly by adopting experimental curves, or by means of a reduced number of parameters. The effectiveness of the model is shown through comparisons with several sets of experimental tests on both small specimens, assumed to be homogeneous, and boundary value problems.

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Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts

Cited by 798 publications

References 0 publications

Connectivity of joint networks with power law length distributions

Connectivity of joint networks with power law length distributions

Tangential stiffness of elastic materials with systems of growing or closing cracks

Crush-crack': a non-local damage model for concrete

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