A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation

Tengattini, Alessandro; Das, Arghya; Einav, Itai

doi:10.1680/jgeot.14.p.164

Cited by 83 publications

(37 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Porosity ϕ is employed as a dissipative variable to describe plastic volumetric changes following the ideas of Rubin and Einav and Tengattini et al The plastic volumetric strain rate

{\dot{ε}}_{normalv}^{p}

is given by:

{\overset{ε}{true}}_{v}^{normalp} = - \frac{\overset{ϕ}{true}}{1 - ϕ},

where

\overset{ϕ}{true}

is the rate of porosity change. The dependency of the minimum and maximum porosity values, ϕ min and ϕ max , on particle gradation is captured using the following relations:…”

Section: A Rate‐dependent Breakage Model For Brittle Granular Materialsmentioning

confidence: 99%

“…Linear elasticity is employed here, and the following Helmholtz strain energy function Ψ is adopted:

Ψ = \frac{1}{2} false(1 - ϑ B false) false(K ε_{normalv}^{normale 2} + 3 G ε_{normals}^{normale 2} false),

where

ϑ

is the grading index, measuring the relative distance between the initial g 0 ( x ) and ultimate g u ( x ) PSDs based on the second order moments of these gradings (see Equation (), and K and G are the bulk and shear moduli, respectively. The triaxial stresses ( p , q ) and the breakage energy E B , which are obtained from the Helmholtz free energy potential given in Equation (), and the porosity energy E ϕ are given by:…”

Section: A Rate‐dependent Breakage Model For Brittle Granular Materialsmentioning

confidence: 99%

“…The constitutive modeling framework presented by Tengattini et al considers three main dissipative mechanisms in the mathematical derivation based on the work of Einav and Nguyen and Einav: (a) breakage dissipation due to crushing of particles, (b) volumetric dissipation associated with the reorganization of particles, and (c) frictional shear dissipation. Three dissipation functions for these irreversible processes along with the free energy function Ψ of Equation () are employed to derive the evolution laws for breakage and plastic strains, which is described in detail in Tengattini et al The flow rules and yield function derived by Tengattini et al are enriched in the work of Cil et al to simulate the concurrent evolution of breakage and dilation, and strain softening in dilatant specimens. The strain rate dependency is incorporated into the model in this study using the overstress concept of viscoplasticity introduced by Perzyna .…”

Section: A Rate‐dependent Breakage Model For Brittle Granular Materialsmentioning

confidence: 99%

“…The main objective of this study is to present a novel rate‐dependent constitutive model for brittle granular materials based on a recent extension of breakage mechanics framework . The model is enhanced by incorporating rate dependency using the overstress concept of viscoplasticity introduced by Perzyna .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A rate‐dependent constitutive model for brittle granular materials based on breakage mechanics

2019

View full text Add to dashboard Cite

Modeling the rate‐dependent mechanical behavior of brittle granular materials is of interest to defense applications, civil and mining engineering, geology, and geophysics. In particular, granulated ceramics in armor systems play a significant role in the overall dynamic material response of ceramics, particularly in their penetration resistance. This paper presents a rate‐dependent constitutive model for brittle granular materials based on a recent reformulation of breakage mechanics theory. The rate‐dependency is introduced via the overstress theory of viscoplasticity. The proposed formulation incorporates the effects of relative density and particle grading on strength and porous compaction/dilation, and is capable of tracking their evolution. The model is devised with internal variables linked to underlying dissipative micromechanisms including configurational reorganization, particle breakage and frictional dissipation. A strategy for calibrating model parameters and required experiments are described. The impact of loading rate on shear strength and grading evolution are explored through a sensitivity analysis. The presented model is capable of capturing several key features of the experimentally observed behavior of brittle granular materials including stress‐, rate‐ and density‐dependent stress‐strain and volume change responses, the competition between dilation and breakage‐induced compaction, the evolving particle grading due to particle breakage, and the evolution toward a critical (steady) state under shearing. A possible application of this micromechanics‐inspired modeling framework involves integrating it into rate‐dependent models for ceramics to assist in improving the impact performance of next‐generation ceramics.

show abstract

“…Porosity ϕ is employed as a dissipative variable to describe plastic volumetric changes following the ideas of Rubin and Einav and Tengattini et al The plastic volumetric strain rate

{\dot{ε}}_{normalv}^{p}

is given by:

{\overset{ε}{true}}_{v}^{normalp} = - \frac{\overset{ϕ}{true}}{1 - ϕ},

where

\overset{ϕ}{true}

is the rate of porosity change. The dependency of the minimum and maximum porosity values, ϕ min and ϕ max , on particle gradation is captured using the following relations:…”

Section: A Rate‐dependent Breakage Model For Brittle Granular Materialsmentioning

confidence: 99%

“…Linear elasticity is employed here, and the following Helmholtz strain energy function Ψ is adopted:

Ψ = \frac{1}{2} false(1 - ϑ B false) false(K ε_{normalv}^{normale 2} + 3 G ε_{normals}^{normale 2} false),

where

ϑ

Section: A Rate‐dependent Breakage Model For Brittle Granular Materialsmentioning

confidence: 99%

Section: A Rate‐dependent Breakage Model For Brittle Granular Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A rate‐dependent constitutive model for brittle granular materials based on breakage mechanics

2019

View full text Add to dashboard Cite

show abstract

“…Kikumoto et al (2010) explained how the broadening of the grading will shift the critical state line and compression line downwards in the compression plane, and have developed a constitutive model that incorporates the changes due to particle crushing. Tengattini et al (2016) explained why the critical state of sand is non-unique, when expressed in terms of stress and void ratio. They used a thermodynamically consistent framework to predict the critical state and its dependence on breakage, rather than fitting experimental data, and introduced a new breakage mechanics model.…”

Section: Introductionmentioning

confidence: 99%

Evolution of deformation and breakage in sand studied using X-ray tomography

et al. 2018

View full text Add to dashboard Cite

Particle breakage of a granular material can cause significant changes in its microstructure, which will govern its macroscopic behaviour; this explains why the mechanisms leading to particle breakage have been a common subject within several fields, including geomechanics. In this paper, X-ray computed micro-tomography is used, to obtain three-dimensional images of entire specimens of sand, during high-confinement triaxial compression tests. The acquired images are processed and measurements are made on breakage, local variations of porosity, volumetric strain, maximum shear strain and grading. The evolution and spatial distribution of quantified breakage and the resulting particle size distribution for the whole specimen and for specific areas are presented here for the first time and are further related to the localised shear and volumetric strains. Before peak stress is reached, compaction is the governing mechanism leading to breakage; neither compressive strains nor breakage are significantly localised and the total amount of breakage is rather low. Post peak, in areas where strains localise and breakage is present, a dilative volumetric behaviour is observed locally, as opposed to the overall compaction of the specimen. Some specimens exhibited a compaction around the shear band at the end of the test, but there was no additional breakage at that point. From the grading analysis, it is found that mainly the grains with diameter close to the mean diameter of the specimen are the ones that break, whereas the biggest grains that are present in the specimen remain intact.

show abstract

Relationships between gradation and deformation behavior of dense granular materials: Role of high‐order gradation characteristics

Liu

Deng

et al. 2021

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

This paper numerically investigates deformation behavior of coarse‐grained granular materials with emphasis on the effect of grain size distribution (GSD). Biaxial compression tests are simulated in two dimensions using distinct element method (DEM) on a set of samples composed of uncrushable spheres following a wide variety of GSDs. The results prove that high‐order characteristics of gradation, such as the shape of the GSD curve, significantly affect deformation behavior of widely‐graded materials. Two grading indices are proposed to consider the combined effects of the spread and the shape of the GSD curve, and they are highly correlated with the parameters of the materials’ internal fabric. Strong correlations are found between the proposed grading indices and deformation parameters, such as those of the normal compression line and the critical state line (CSL) in the e‐p space, and the deformation modulus. In contrast, using the more conventional coefficient of uniformity cannot reach effective gradation‐dependent relations for those deformation parameters due to the deficiency in characterizing high‐order features of gradation. This study suggests the need for incorporating high‐order characteristics of gradation into a refined measure of size polydispersity in order to establish gradation‐dependent relations of deformation parameters widely effective for polydisperse granular materials.

show abstract

A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation

Cited by 83 publications

References 33 publications

A rate‐dependent constitutive model for brittle granular materials based on breakage mechanics

A rate‐dependent constitutive model for brittle granular materials based on breakage mechanics

Evolution of deformation and breakage in sand studied using X-ray tomography

Relationships between gradation and deformation behavior of dense granular materials: Role of high‐order gradation characteristics

Contact Info

Product

Resources

About