# Force chain

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Force_chain
> Markdown URL: https://mediated.wiki/source/Force_chain.md
> Source: https://en.wikipedia.org/wiki/Force_chain
> Source revision: 1316809721
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

thumb|right|150px|Chain of transmission of stress forces in a granular media
In the study of the physics of [granular material](/source/granular_material)s, a '''force chain''' consists of a set of particles within a compressed granular material that are held together and [jammed into place](/source/jamming_(physics)) by a network of mutual compressive forces.<ref name=Peters2005>{{Cite journal 
| doi = 10.1103/PhysRevE.72.041307 
| last1 = Peters | first1 = J. F. 
| last2 = Muthuswamy | first2 = M. 
| last3 = Wibowo | first3 = J. 
| last4 = Tordesillas | first4 = A. 
| title = Characterization of force chains in granular material 
| journal = Physical Review E 
| volume = 72 
| issue = 4 Pt 1 
| article-number = 041307 
| year = 2005 
| pmid = 16383373
|bibcode = 2005PhRvE..72d1307P }}</ref>

Between these chains are regions of low stress whose grains are shielded for the effects of the grains above by [vaulting](/source/Vault_(architecture)) and [arch](/source/arch)ing.  A set of interconnected force chains is known as a '''force network'''.<ref name="Kondic2012">{{Cite journal | last1 = Kondic | first1 = L. | last2 = Goullet | first2 = A. | last3 = O'Hern | first3 = C. S. | last4 = Kramar | first4 = M. | last5 = Mischaikow | first5 = K. | last6 = Behringer | first6 = R. P. | doi = 10.1209/0295-5075/97/54001 | title = Topology of force networks in compressed granular media | journal = EPL | volume = 97 | issue = 5 | article-number = 54001 | year = 2012 |bibcode = 2012EL.....9754001K | s2cid = 14307013 }}</ref> Force networks visualise inter-particle forces, which is particularly informative for spherical particle systems. For non-spherical particle systems force chain networks benefit from being supplemented by '''traction chain networks'''. '''Traction chains''' visualise inter-particle tractions, which give additional insight in inter-particle contact not captured by force chains, in particular, the role of contact area over which inter-particle forces act.

Force networks are an [emergent phenomenon](/source/emergent_phenomenon) that are created by the complex interaction of the individual grains of material and the patterns of pressure applied within the material. Force chains can be shown to have [fractal](/source/fractal) properties.<ref name=Vallejo2005>{{Cite book | last1 = Vallejo | first1 = L. E. | last2 = Lobo-Guerrero | first2 = S. | last3 = Chik | first3 = Z. | doi = 10.1007/1-84628-048-6_5 | chapter = A Network of Fractal Force Chains and Their Effect in Granular Materials under Compression | title = Fractals in Engineering | page = 67 | year = 2005 | isbn = 1-84628-047-8 }}</ref>

Force chains have been investigated both experimentally, through the construction of specially instrumented physical models,<ref name=Vallejo2005/><ref name=Mueth1998>{{Cite journal | last1 = Mueth | first1 = D. | last2 = Jaeger | first2 = H. | last3 = Nagel | first3 = S. | doi = 10.1103/PhysRevE.57.3164 | title = Force distribution in a granular medium | journal = Physical Review E | volume = 57 | issue = 3 | page = 3164 | year = 1998 |arxiv = cond-mat/9902282 |bibcode = 1998PhRvE..57.3164M | s2cid = 119075098 }}</ref> and through computer simulation.<ref name=Vallejo2005/>

== References ==
{{reflist}}

== External links ==
* [https://web.archive.org/web/20100610053358/https://jfi.uchicago.edu/granular/force_chains.html Force Chains and Distributions in Bead Packs]

Category:Granularity of materials
Category:Emergence
Category:Fractals

{{material-stub}}
{{fractal-stub}}

---
Adapted from the Wikipedia article [Force chain](https://en.wikipedia.org/wiki/Force_chain) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Force_chain?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.