On quantitative characterization of microstructures and effective properties

Kachanov, Mark; Sevostianov, Igor

doi:10.1016/j.ijsolstr.2004.06.016

Cited by 250 publications

(125 citation statements)

References 50 publications

(66 reference statements)

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“…Cracked material is just one case in the widely dealt with topic of physical properties of heterogeneous media. [1][2][3][4] The different physical properties to be described encompass conductive, transport, and also elastic quantities. [5][6][7] Often, one starts from a coarse-grained picture and aims to find an effective description for the heterogeneous mixture.…”

Section: Introductionmentioning

confidence: 99%

Effective elastic moduli in solids with high density of cracks

2009

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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.

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Section: Introductionmentioning

confidence: 99%

Effective elastic moduli in solids with high density of cracks

2009

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“…(Note that the significance of crack-influence parameters η 4 , η 6 , and η 7 have been changed from the definitions made by Kachanov [27], Kachanov and Sevostianov [28], and Sayers and Kachanov [5], so that here η 4 is the coefficient of a contribution second order in α, η 6 third order in α, and η 7 fourth order in α.) The coefficients pertinent to the isotropic background elastic medium are given by Φ (0)…”

Section: Appendix B: Crack-influence Decomposition Methodsmentioning

confidence: 99%

Random polycrystals of grains containing cracks: Model of quasistatic elastic behavior for fractured systems

Berryman

Grechka

2006

Journal of Applied Physics

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A model study on fractured systems was performed using a concept that treats isotropic cracked systems as ensembles of cracked grains by analogy to isotropic polycrystalline elastic media. The approach has two advantages: (a) Averaging performed is ensemble averaging, thus avoiding the criticism legitimately leveled at most effective medium theories of quasistatic elastic behavior for cracked media based on volume concentrations of inclusions. Since crack effects are largely independent of the volume they occupy in the composite, such a non-volume-based method offers an appealingly simple modeling alternative. (b) The second advantage is that both polycrystals and fractured media are stiffer than might otherwise be expected, due to natural bridging effects of the strong components. These same effects have also often been interpreted as crack-crack screening in high-crack-density fractured media, but there is no inherent conflict between these two interpretations of this phenomenon. Results of the study are somewhat mixed. The spread in elastic constants observed in a set of numerical experiments is found to be very comparable to the spread in values contained between the Reuss and Voigt bounds for the polycrystal model. However, computed Hashin-Shtrikman bounds are much too tight to be in agreement with the numerical data, showing that polycrystals of cracked grains tend to violate some implicit assumptions of the Hashin-Shtrikman bounding approach. However, the self-consistent estimates obtained for the random polycrystal model are nevertheless very good estimators of the observed average behavior.

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“…Further, we will deal with "quantitatively characterized" materials [3], those whose macroscopic or effective physical properties can be expressed as functions of identified microstructural parameters: e.g., fiber orientation in fiber-reinforced polymers [4], density and irregularity factors in materials with isolated inhomogeneities [3,5], size of particles or beads in coating of dental implants [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…The dependence of effective properties on microstructural parameters can be determined experimentally -the most expensive option-, analytically -for simple microstructures- [3,5], by using simplified homogenization techniques like SIMP (solid isotropic material with penalization) [4,8], or numerically using Computational Multiscale Modeling (CMM) [6,7]. The latter is the most general approach, the one preferred in this work.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity of the thermomechanical response of elastic structures to microstructural changes

Fachinotti

Toro

Sánchez

et al. 2015

International Journal of Solids and Structures

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The paper presents a useful technique for analyzing the sensitivity of the thermomechanical response of a body with variable microstructure. The technique can be applied to attain a desired macroscopic response by altering the body microstructure. This problem is a key issue in material design.The sensitivity analysis relies on an accurate determination of the effective properties of the heterogeneous material. These effective properties are determined by computational homogenization. And their sensitivities, with respect to the parameters defining the microstructure, are then computed.For an efficient evaluation of the thermomechanical response, we propose to build response surfaces for the effective material properties. The surfaces are generated in an offline stage, by solving a series of homogenization problems at the microscale. In such a way, the fully online multiscale response analysis reduces to a standard monoscale problem at the macroscale. Thus, an important reduction in computational time is achieved, which is a crucial * Corresponding author advantage for material design.The capability of the proposed methodology is shown in light of its application to the design of a thermally-loaded structure with variable microstructure. Perceptible improvements in the structural response are achieved.

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On quantitative characterization of microstructures and effective properties

Cited by 250 publications

References 50 publications

Effective elastic moduli in solids with high density of cracks

Effective elastic moduli in solids with high density of cracks

Random polycrystals of grains containing cracks: Model of quasistatic elastic behavior for fractured systems

Sensitivity of the thermomechanical response of elastic structures to microstructural changes

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