Overall moduli of solids with microcracks: Load-induced anisotropy

Horii, Hideyuki; Nemat‐Nasser, Sia

doi:10.1016/0022-5096(83)90048-0

Cited by 540 publications

(167 citation statements)

References 20 publications

Supporting

Mentioning

161

Contrasting

Unclassified

Order By: Relevance

“…Even different loading paths can lead to a different elastic response of the material under investigation. 12 Therefore, special attention has to be paid to the underlying assumptions of the cavity distribution. It has been shown that the Hashin-Shtrikman-type bounds obtained for the bulk modulus of two-phase materials set important restrictions in terms of phase moduli and volume fractions, 7,10 and improvement to these bounds have to involve considerations of statistical details of phase distributions.…”

Section: Introductionmentioning

confidence: 99%

Effective elastic moduli in solids with high density of cracks

2009

View full text Add to dashboard Cite

We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented cracks of equal length in an isotropic plane-strain medium for lower crack densities; for higher densities the material is weaker than predicted due to precursors of percolation. For a parallel alignment of cracks, where percolation does not occur, we analytically predict a power-law decay of the effective elastic constants for high crack densities, and confirm this result numerically.

show abstract

Section: Introductionmentioning

confidence: 99%

Effective elastic moduli in solids with high density of cracks

2009

View full text Add to dashboard Cite

show abstract

“…in which S r is the Eshelby tensor whose expression for penny-shaped cracks can be found in [11] or in [20]. Following a dilute scheme-based approach of penny-shaped cracks (considered as spheroid with very low aspect ratio) (see for instance [11] or [7]), it can be shown that:…”

Section: Overall Potential Of the Microcracked Medium In The Presencementioning

confidence: 99%

“…Following a dilute scheme-based approach of penny-shaped cracks (considered as spheroid with very low aspect ratio) (see for instance [11] or [7]), it can be shown that:…”

Section: Overall Potential Of the Microcracked Medium In The Presencementioning

confidence: 99%

A two scale anisotropic damage model accounting for initial stresses in microcracked materials

Levasseur

Collin

Charlier

et al. 2011

Engineering Fracture Mechanics

View full text Add to dashboard Cite

a b s t r a c tIn a recent study [15], we proposed a class of isotropic damage models which account for initial stresses. The present paper extends this approach to anisotropic damage due to growth of an arbitrarily penny-shaped microcracks system. The basic principle of the upscaling technique in the presence of initial stress is first recalled. Then, we derive a closed-form expression of the elastic energy potential corresponding to a system of arbitrarily oriented microcracks. It is shown that the coupling between initial stresses and damage is strongly dependent of the microcracks density and orientation. Predictions of the proposed model are illustrated through the investigation of the influence of initial stresses on the material response under non monotonous loading paths. Finally, by considering a particular distribution of microcracks orientation, described by a second order damage tensor, it is shown that the model is a generalization of the macroscopic damage model of Halm and Dragon [9], for which a physically-based interpretation is then proposed.

show abstract

“…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%

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

Prat

Bažant

1997

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

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.

show abstract

Overall moduli of solids with microcracks: Load-induced anisotropy

Cited by 540 publications

References 20 publications

Effective elastic moduli in solids with high density of cracks

Effective elastic moduli in solids with high density of cracks

A two scale anisotropic damage model accounting for initial stresses in microcracked materials

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

Contact Info

Product

Resources

About