Standardized mean of a contrast variable: Difference between revisions

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The '''Inertial number''' <math>I</math> quantifies the significance of dynamic effects in a [[granular material]]. It measures the ratio of inertial forces of grains to imposed forces: a small value corresponds to the quasi-static state, while a high value corresponds to the inertial state or even the "dynamic" state. <ref>{{cite conference|title=Discrete numerical simulation, quasistatic deformation and the origins of strain in granular materials | last1=Combe | first1=G. | last2=Roux | first2=J.-N. |conference=3ème Symposium International sur le Comportement des sols et des roches tendres | location=Lyon | date=22–24 September 2003 |pages=1071–1078 (2003)|url=http://arxiv.org/abs/0901.3842v1}}</ref><ref>{{cite journal|title=On dense granular flows|first=G.D.R. |last=Midi|journal=[[European Physical Journal E|EPJ E]]|pages=341–365 (2004)|volume=14|doi=10.1140/epje/i2003-10153-0|url=http://epje.edpsciences.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/epje/abs/2004/08/epje03211/epje03211.html}}</ref><ref>{{cite journal|title=Discrete numerical simulation and the mechanical behavior of granular materials|author=Roux J.-N., Chevoir F.|journal=BULLETIN DES LABORATOIRES DES PONTS ET CHAUSSÉES - 254|year=2005|pages=109–138|url=http://navier.enpc.fr/rheophysique/pdf/Granulaires3.pdf}}{{dead link|date=March 2013}}</ref><ref>{{cite book|last1 = Radjaï | first1=F. | last2=Dubois | first2=F.| title = Discrete-Element Modeling of Granular Materials| publisher = ISTE Ltd and John Wiley & Sons Inc | date=8 March 2011 | chapter= Chapter 8 - Dimensional Analysis and Control Parameters | isbn = 1-84821-260-7}}</ref>
 
<center><math>I = \frac{\dot\gamma d}{\sqrt{P/\rho}},</math></center>
 
where <math>\dot\gamma</math> is the [[shear rate]], <math>d</math> the average particle diameter, <math>P</math> is the [[pressure]] and <math>\rho</math> is the density.
 
Generally three regimes are distinguished:
* <math>I<10^{-3}</math>: [[Quasistatic process|quasi static flow]]
* <math>10^{-3}<I<10^{-1}</math>: dense flow
* <math>I>10^{-1}</math>: collisional flow
 
==References==
{{Reflist}}
 
[[Category:Granular materials]]

Revision as of 04:34, 4 November 2013

The Inertial number quantifies the significance of dynamic effects in a granular material. It measures the ratio of inertial forces of grains to imposed forces: a small value corresponds to the quasi-static state, while a high value corresponds to the inertial state or even the "dynamic" state. [1][2][3][4]

where is the shear rate, the average particle diameter, is the pressure and is the density.

Generally three regimes are distinguished:

References

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