Poasonov odnos — разлика између измена
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== Puasonov odnos za različite materijale ==
[[Image:SpiderGraph PoissonRatio.gif|500px|thumb|Uticaj dodavanja pojedinih [[staklo|staklenih]] komponenti na Puasonov odnos specifičnog osnovnog stakla.<ref>{{cite web|url=http://www.glassproperties.com/poisson_ratio/|title=Poisson's Ratio Calculation for Glasses|first=Alexander|last=Fluegel|date=|website=www.glassproperties.com|accessdate=28 April 2018|deadurl=no|archiveurl=https://web.archive.org/web/20171023140523/http://glassproperties.com/poisson_ratio/|archivedate=23 October 2017|df=}}</ref>]]
{| class="wikitable sortable" cellpadding="4" cellspacing="0" border="1" style="border-collapse: collapse"
|- bgcolor="#cccccc"
! Materiјal
!
|
| [[guma]] ▼
|
| 0,4999<ref name="polymerphysics.net">{{cite web |url=http://polymerphysics.net/pdf/PhysRevB_80_132104_09.pdf |title=Archived copy |accessdate=2014-09-24 |deadurl=no |archiveurl=https://web.archive.org/web/20141031190845/http://polymerphysics.net/pdf/PhysRevB_80_132104_09.pdf |archivedate=2014-10-31 |df= }}</ref>
| - ▼
|-
| [[zlato]] | 0,
|
| zasićena [[glina]]
| 0,40–0,
|
| [[magnezijum]]
| 0,
|
| [[titanijum]]
| 0,265-0,34
|
| [[bakar]]
| 0,33
|
| [[
| 0,
|
| [[glina]]
| 0,30–0,45
|
| [[nerđajući čelik]]
| 0,30–0,31
|
| [[čelik]]
| 0,27–0,30
|
| [[liveno gvožđe]]
| 0,21–0,26
|
| [[pesak]]
| 0,20–0,
|
| [[beton]]
| 0,
|
| [[staklo]]
| 0,18–0,3
|
| [[Amorphous metal|metalično staklo]]
| 0,276–0,409<ref>Journal of Applied Physics 110, 053521 (2011)</ref>
|
| [[
|
|
| 0,0
|
{| class="wikitable sortable" cellpadding="4" cellspacing="0" border="1" style="border-collapse: collapse"
|- bgcolor="#cccccc"
!Materijal!!Ravan simetrije!!<math>\nu_{\rm xy}</math>!!<math>\nu_{\rm yx}</math>!!<math>\nu_{\rm yz}</math>!!<math>\nu_{\rm zy}</math>!!<math>\nu_{\rm zx}</math>!!<math>\nu_{\rm xz}</math>
| [[Nomex|Nomeks]] [[composite honeycomb|Struktura saća]]
| <math>x-y</math>, <math>x</math> = pravac trake
|0,49
|0,69
|0,01
|2,75
|3,88
|0,01
|-
| [[glass fiber|stakleno vlakno]]-[[epoxy resin|epoksidna smola]]
|<math>x-y</math>
|0,29
|0,32
|0,06
|0,06
|0,32
|}
=== Negativan Puasonov odnos materijala ===
Neki materijali poznati kao [[Auxetics|auksetični]] materijali pokazuju negativan Puasonov odnos. Kada se podvrgnu pozitivnom naprezanju u uzdužnoj osi, poprečna deformacija u materijalu će zapravo biti pozitivna (tj. dolazi do povećanja površine poprečnog preseka). Za ove materijale, to je obično usled jedinstveno orjentisanih, zglobnih molekularnih veza. Da bi se ove veze rastegnule u uzdužnom pravcu, zglobovi moraju da se „otvore” u poprečnom pravcu, efektivno ispoljavajući pozitivnu napetost.<ref>{{cite web|url=http://silver.neep.wisc.edu/~lakes/Poisson.html|title=Negative Poisson's ratio|first=Rod|last=Lakes|date=|website=silver.neep.wisc.edu|accessdate=28 April 2018|deadurl=no|archiveurl=https://web.archive.org/web/20180216025122/http://silver.neep.wisc.edu/~lakes/Poisson.html|archivedate=16 February 2018|df=}}</ref> Ovo se takođe može uraditi na strukturiran način i to može dovesti do novih aspekata u dizajnu materijala kao što su [[mehanički metamaterijali]].
== Puasonova funkcija ==
{{rut}}
At [[Finite_strain_theory|finite strains]], the relationship between the transverse and axial strains <math>\varepsilon_\mathrm{trans}</math> and <math>\varepsilon_\mathrm{axial}</math> is typically not well described by the Poisson's ratio. In fact, the Poisson's ratio is often considered a function of the applied strain in the large strain regime. In such instances, the Poisson's ratio is replaced by the Poisson function, for which there are several competing definitions<ref>{{Cite journal|last=Mihai|first=L. A.|last2=Goriely|first2=A.|date=2017-11-03|title=How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity|url=https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2017.0607 |journal=Proceedings of the Royal Society A|volume=473|pages=20170607|doi=10.1098/rspa.2017.0607}}</ref>. Defining the transverse stretch <math>\lambda_\mathrm{trans}=\varepsilon_\mathrm{trans}+1</math> and axial stretch <math>\lambda_\mathrm{axial}=\varepsilon_\mathrm{axial}+1</math>, where the transverse stretch is a function of the axial stretch (i.e., <math>\lambda_\mathrm{trans}=\lambda_\mathrm{trans}(\lambda_\mathrm{axial})</math>) the most common are the Hencky, Biot, Green, and Almansi functions
:<math> \nu^\mathrm{Hencky} = - \frac{\ln \lambda_\mathrm{trans}}{\ln \lambda_\mathrm{axial}} </math>
:<math> \nu^\mathrm{Biot} = \frac{1 - \lambda_\mathrm{trans}}{ \lambda_\mathrm{axial} - 1} </math>
:<math> \nu^\mathrm{Green} = \frac{1 - \lambda_\mathrm{trans}^2}{ \lambda_\mathrm{axial}^2 - 1} </math>
:<math> \nu^\mathrm{Almansi} = \frac{ \lambda_\mathrm{trans}^{-2} - 1}{ 1 - \lambda_\mathrm{axial}^{-2}} </math>
== Primena ==
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