On comminution and yield in brittle granular mixtures

Einav, Itai; Valdès, Julio R.

doi:10.1016/j.jmps.2008.02.002

Cited by 17 publications

(4 citation statements)

References 14 publications

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“…The evolution law of B is derived from the postulation that the dissipation due to grain crushing is equal to the loss in the residual breakage energy [Einav, 2007a]. The details on the fundamentals of breakage mechanics theory, along with a series of model developments and various applications in geotechnical engineering and geophysics, can be found in earlier works [Buscarnera and Einav, 2012;Einav and Valdes, 2008;Nguyen and Einav, 2009;Zhang et al, 2012].…”

Section: Breakage Mechanics Theorymentioning

confidence: 99%

The propagation of compaction bands in porous rocks based on breakage mechanics

2013

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[1] We analyze the propagation of compaction bands in high porosity sandstones using a constitutive model based on breakage mechanics theory. This analysis follows the work by Das et al. [2011] on the initiation of compaction bands employing the same theory. In both studies, the theory exploits the links between the stresses and strains, and the micromechanics of grain crushing and pore collapse, giving the derived constitutive models advantages over previous models. In the current post localization analysis, the bifurcation instability of the continuum model is suppressed by the use of a rate-dependent regularization. This allows us to perform a series of finite element analyses of drained triaxial tests on porous sandstone specimens. The obtained numerical results compare well with experimental counterparts, in terms of both the initiation and propagation of compaction bands, besides the macroscopic stress-strain responses. On this basis, a parametric study is carried out to explore the effects of loading rate, degree of structural imperfections, and confining pressure on the propagation of compaction bands.

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Section: Breakage Mechanics Theorymentioning

confidence: 99%

The propagation of compaction bands in porous rocks based on breakage mechanics

2013

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“…A power-law distribution, which is well supported experimentally and in field observations (Sammis, King and Biegel, 1987;Turcotte, 1986) is typically chosen. Using the thermodynamic principles of constitutive modelling, Breakage Mechanics models can be defined which range from simple models drawing analogies with fracture mechanics (Einav, 2007c,d) to models that describe granular mixtures (Einav and Valdes, 2008), large flow problems (Zhang, 2012;Zhang, Einav and Nguyen, 2012), the energetics of cataclasis (Einav and Nguyen, 2008;Nguyen and Einav, 2009), the formation of compaction bands (Das, 2013;Das, Nguyen andEinav, 2011, 2013), partial saturation effects (Buscarnera and Einav, 2012), inter-particle cementation effects (Das et al, 2014;Tengattini, 2015;Tengattini, Das and Einav, 2014;Tengattini et al, 2014), coupling with fracture mechanics (Zhang andBuscarnera, 2014, 2015;Zhang, Buscarnera and Einav, 2016), shock loading conditions (Herbold, Homel and Rubin, 2020), and the non-unique dependence of critical state on porosity (Tengattini, Das and Einav, 2016). Of particular note is a formulation of Breakage mechanics in a non-local continuum (Nguyen and Einav, 2010).…”

Section: Introductionmentioning

confidence: 99%

A Cosserat Breakage Mechanics model for brittle granular media

Collins-Craft

Stefanou

Sulem

et al. 2020

Journal of the Mechanics and Physics of Solids

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This paper introduces a Breakage Mechanics model formulated in the framework of Cosserat continuum theory. This formulation allows us to account for the interaction of grain size evolution with shear band formation in a physically motivated and thermodynamically consistent way. We provide an upscaling procedure that introduces material parameters accounting for the contribution of the Cosserat rotations, as well as the micro-inertia of the entire grain size distribution. A particular highlight of the new formulation is the capacity to describe an evolving internal Cosserat length that takes account of the complete grain size distribution and its evolution. In addition, we specify a particular model that requires no additional calibration relative to the same model in the classical continuum. We apply this model to the study of a layer sheared under constant volume which simulates the fast undrained deformation observed in seismogenic faults. Through linear stability analysis we use the model to examine the effect of grain size polydispersity on the thickness of shear bands. By implementing the model using the finite element method we provide an explanation for the geological formation of double cataclastic shear bands.

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“…. Of particular interest in the current article are the formulae of a breakage mechanics theory , which is capable of describing the grain crushing behavior by taking into account the evolution of the GSD.…”

Section: Introductionmentioning

confidence: 99%

“…Grain crushability has been studied theoretically by several researchers, for example, by Indraratna and Salim [5] and Einav [10,11] using a continuum approach and by Astrom and Herrmann [12], Tsoungui et al [13], Cheng et al [14], Marketos and Bolton [15], Muir Wood and Maeda [16], Vallejo and Lobo-Guerrero [17] and Ben-Nun and Einav [18] using a discrete element model (DEM), or through the theoretical investigations of crushability at the particle level, for example, McDowell et al [19] and Russel et al [20]. Of particular interest in the current article are the formulae of a breakage mechanics theory [10,11,21], which is capable of describing the grain crushing behavior by taking into account the evolution of the GSD.…”

Section: Introductionmentioning

confidence: 99%

Effect of grain crushing on shear localization in granular bodies during plane strain compression

Tejchman

Górski

Einav

2011

Num Anal Meth Geomechanics

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SUMMARYThis article deals with the effect of grain crushing on shear localization in granular materials during plane strain monotonic compression tests under constant lateral pressure. The grain diameter and the initial void ratio were stochastically distributed using a spatial correlation. To describe the mechanical behavior of cohesionless granular materials during a monotonic deformation path in plane strain compression, we used a micropolar hypoplastic constitutive model that is able to describe the salient properties of granular bodies including shear localization. The model was extended by introducing changes to the grain diameter with varying pressure using formulae from breakage mechanics proposed for crushable granulates. The initial void ratios and grain diameters took the form of correlated random spatial fields described by both symmetric and nonsymmetric random distributions using a homogeneous correlation function. The field realizations were generated with the help of an original conditional rejection method. A few representative samples of the random fields selected from the generated set were taken into account in numerical calculations.

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On comminution and yield in brittle granular mixtures

Cited by 17 publications

References 14 publications

The propagation of compaction bands in porous rocks based on breakage mechanics

The propagation of compaction bands in porous rocks based on breakage mechanics

A Cosserat Breakage Mechanics model for brittle granular media

Effect of grain crushing on shear localization in granular bodies during plane strain compression

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