On probability distributions of contact force magnitudes in loaded dense granular media

Radeke, Charles; Bagi, Katalin; Paláncz, Béla; Stoyan, Dietrich

doi:10.1007/s10035-004-0154-1

Cited by 6 publications

(8 citation statements)

References 22 publications

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“…3 , see Section 4 of Radeke et al (2004). This model arose because many simulations showed that the force components F i in (1) and (2) are more or less correlated.…”

Section: Introductionmentioning

confidence: 96%

“…Until now, there have been various approaches: some of them purely empirical and others based on mathematical theory, (Sandstrom & Tucker 1993), Brockbank et al (1997), Radjai et al (1999), Schollmann (1999), Erikson et al (2002), Kruyt & Rothenburg (2002), Radeke et al (2002), Bagi (2003), Edwards et al (2003), Kruyt (2003), Vargas et al (2003), Goddard (2004), Metzger (2004), Radeke et al (2004), Chan & Ngan (2005), Nicot & Darve (2005), Tighe et al (2005), Youngquist et al (2005), Chan & Ngan (2006), Liu (2006), Ostojic et al (2006), andSnoeijer et al (2006). The theoretical approaches were pioneered by Kruyt & Rothenburg (2002) and Bagi (2003).…”

Section: Introductionmentioning

confidence: 98%

“…Theoretically, the exponential distribution in (3) is the distribution of maximum entropy in the set of all distributions of positive random variables with mean 1/λ i (Cover & Thomas 1991). The model given by (3) has been followed up by more recent papers, Goddard (2004), Metzger (2004) and Radeke et al (2004). The most generalized form of (3) suggested by Radeke et al (2004) has the joint post distribution force (pdf) given by…”

Section: Introductionmentioning

confidence: 98%

“…The model given by (3) has been followed up by more recent papers, Goddard (2004), Metzger (2004) and Radeke et al (2004). The most generalized form of (3) suggested by Radeke et al (2004) has the joint post distribution force (pdf) given by…”

Section: Introductionmentioning

confidence: 99%

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Some explicit expressions for the probability distribution of force magnitude

Nadarajah

2008

Sadhana

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Recently, empirical investigations have suggested that the components of contact forces follow the exponential distribution. However, explicit expressions for the probability distribution of the corresponding force magnitude have not been known and only approximations have been used in the literature. In this note, for the first time, I provide explicit expressions for the probability distribution of the force magnitude. Both two-dimensional and three-dimensional cases are considered.

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“…3 , see Section 4 of Radeke et al (2004). This model arose because many simulations showed that the force components F i in (1) and (2) are more or less correlated.…”

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some explicit expressions for the probability distribution of force magnitude

Nadarajah

2008

Sadhana

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“…Entropy-based theories have been formulated for the prediction of the probability density function of contact forces in hydrostatic stress states (Bagi, 1997(Bagi, , 2003Kruyt and Rothenburg, 2002a;Ngan, 2003, 2004a, 2005, Chan and Ngan, 2005Goddard, 2004;Radeke et al, 2004;Metzger, 2004b;Metzger and Donahue, 2005). These studies will be reviewed in Section 4.6, following the current formulation of an information-theoretical entropy.…”

mentioning

confidence: 99%

Micromechanical definition of an entropy for quasi-static deformation of granular materials

Rothenburg

Kruyt

2009

Journal of the Mechanics and Physics of Solids

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A micro‐macromechanical compression model of crushing in granular materials based on a probabilistic approach and energy aspects

Zheng

Song

2020

Num Anal Meth Geomechanics

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This paper presents a micro and macromechanical model to estimate the grading evolution and plastic strain caused by particle crushing in the isotropic compression of granular materials. A joint-probability particle crushing criterion of the maximum contact force and the particle strength is proposed to calculate the incremental particle crushing probability. The dependence of the contact force and particle strength during a multistage loading process is recognized. The distribution of the maximum contact force and the magnitude of the mean contact force are strictly derived from the stress-force relationship and maximizing the statistical entropy. The coordination number of polydisperse particles is derived from the geometric relationship and applies to any grading curve, which enables the consideration of the coupling effects of particle crushing and grading evolution during a multistage loading process. A multipoint load particle crushing criterion involving the particle strength size effect is adapted. To simulate the grading evolution, the fractal distribution assumption and Markov chain model are applied to describe the fragmentation mess after crushing. Finally, following the work equation by Mcdowell and Bolton, the energy consumption of particle crushing and the corresponding plastic strain are correlated with the increase in the particle surface area. The model is verified by published experimental data of silica sand with different initial grading curves and carbonate sand with different grain sizes.

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On probability distributions of contact force magnitudes in loaded dense granular media

Cited by 6 publications

References 22 publications

Some explicit expressions for the probability distribution of force magnitude

Some explicit expressions for the probability distribution of force magnitude

Micromechanical definition of an entropy for quasi-static deformation of granular materials

A micro‐macromechanical compression model of crushing in granular materials based on a probabilistic approach and energy aspects

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