Editing Luffa (section)

==Mechanical properties==
The luffa sponge is a [[Biology|biological]] cellular material. These materials often exhibit exceptional [[List of materials properties|mechanical properties]] at low [[Density|densities]]. While their mechanical performance tends to fall behind manmade materials, such as [[alloy]]s, [[ceramic]]s, [[plastic]]s, and [[Composite material|composites]], as a [[structural material]], they have long term [[sustainability]] for the natural environment. When compressed longitudinally, a luffa sponge is able to absorb comparable energy per unit mass as [[Metal foam|aluminum foam]].<ref>{{Cite journal|date=2012-11-01|title=Mechanical properties of luffa sponge|url=https://www.sciencedirect.com/science/article/abs/pii/S1751616112001993|journal=Journal of the Mechanical Behavior of Biomedical Materials|language=en|volume=15|pages=141–152|doi=10.1016/j.jmbbm.2012.07.004|issn=1751-6161|last1=Shen |first1=Jianhu |last2=Min Xie |first2=Yi |last3=Huang |first3=Xiaodong |last4=Zhou |first4=Shiwei |last5=Ruan |first5=Dong |pmid=23032434 |url-access=subscription }}</ref> Luffa sponges are composed of a complex network of [[fiber]] bundles connected to form a 3-dimensional, highly-[[Porosity|porous]] network.<ref name=":0">{{Cite journal|date=2014-04-11|title=A multiscale study on the structural and mechanical properties of the luffa sponge from Luffa cylindrica plant|url=https://www.sciencedirect.com/science/article/abs/pii/S0021929014001031|journal=Journal of Biomechanics|language=en|volume=47|issue=6|pages=1332–1339|doi=10.1016/j.jbiomech.2014.02.010|issn=0021-9290|last1=Chen |first1=Qiang |last2=Shi |first2=Quan |last3=Gorb |first3=Stanislav N. |last4=Li |first4=Zhiyong |pmid=24636532 |url-access=subscription}}</ref>
[[File:Luffa sponge diagram.jpg|thumb|Definition of the parts of a luffa sponge and the relevant coordinate system for mechanical properties measurements]]
The hierarchical structure of luffa sponges results in mechanical properties that vary with the component of sponge tested. Specifically, the mechanical properties of fiber bundles differ from those of blocks from the bulk of the sponge, which differ from those of the [[Cross section (geometry)|cross sections]] of the entire sponge.<ref name=":0" />

===Fiber-bundles===
[[Tensile testing|Uniaxial tensile tests]] of fiber bundles isolated from the inner surface provide insight this basic [[strut]] element of the luffa sponges. These fiber bundles vary in [[diameter]] from 0.3 to 0.5&nbsp;mm.<ref name=":0" /> Each fiber bundle has a low density core region not occupied by fibers.<ref name=":1">{{doi|10.3390/ma10050479 }}</ref> The [[Stress–strain curve|stress-strain]] response of the fiber bundles is nearly [[Linear elasticity|linear elastic]] all the way until [[fracture]], suggesting the absence of [[work hardening]]. The [[slope]] of the [[Linearity|linear]] region of the stress-strain curve, or [[Young's modulus|Young’s modulus]], is 236* MPa. The highest stress achieved before fracture, or [[ultimate tensile strength]], is 103 MPa. The strain at which failure occurs, or failure strain, is small at only 5%. The mechanical properties of fiber bundles decrease dramatically when the size of the hollow region inside the bundle increases.  Despite their low tensile strength, the fiber bundles have a high [[specific modulus]] of 2.07– 4.05 MPa⋅m<sup>3</sup>/kg, and their overall properties are improved when a high ratio of their cross sectional area is occupied by fibers, they are evenly distributed, and there is strong adhesion between fibers.<ref name=":0" /><ref name=":1" />

===Bulk-sponge===
[[File:Stress_strain_of_luffa_sponge.jpg|thumb|Characteristic stress-strain curve of a luffa sponge in compression]]
Block samples (height: 12.69 ± 2.35mm, width: 11.30 ± 2.88mm, length: 13.10 ± 2.64mm) cut from the core region and hoop region of the luffa sponge exhibit different mechanical behaviors under compression depending on both the orientation they are loaded in as well as the location in the sponge they are sampled from. The hoop region consists of the section of sponge located around the outside between the inner and outer surfaces, while the core region is from the sponge center. Samples from both the hoop and core regions exhibited [[Yield (engineering)|yielding]] when compressed in the longitudinal direction due to the [[buckling]] of fibers. With the highly aligned fibers from the inner surface removed from the hoop region block samples, this yield behavior disappears. In general, the inner surface fibers most significantly impact the longitudinal properties of the luffa sponge column followed by the [[Circumference|circumferential]] properties. There is no noticeable contribution to the [[Radius|radial]] properties. Additionally, the core region exhibits lower [[Yield (engineering)|yield stress]] and energy absorption (as determined by the area under the stress-strain curve) compared to the hoop region due to its greater [[porosity]].<ref name=":0" />

Overall, the stress-strain curves of block samples exhibit three stages of mechanical behavior common to porous materials. Namely, the samples follow [[linear elasticity]] for strains less than 10%, followed by a plateau for strains from 10% to 60%, and finally a stress increase associated with densification at strains greater than 60%. Segment samples created from cross sections of the entire luffa sponge (diameter: 92.51 ± 6.15mm, height: 19.76 ± 4.95mm) when tested in compression exhibit this same characteristic behavior.<ref name=":0" /> The three stages can be described by the equations:

# Linear elasticity region: <math>\sigma=E^*\varepsilon
	
</math> for <math>\varepsilon\le\varepsilon_e</math>
# Plateau region: <math>\sigma=\sigma_p^* </math> for <math>\varepsilon_e<\varepsilon\le\varepsilon_D(1-1/D)</math>
# Densification region: <math>\sigma=\sigma_p^*/D{(\varepsilon_D/\varepsilon_D-\varepsilon)}^m </math> for <math> \varepsilon>\varepsilon_D(1-1/D)</math> <ref name=":2">{{Cite journal|last=Gibson|first=Lorna J.|date=March 2005|title=Biomechanics of cellular solids|url=https://linkinghub.elsevier.com/retrieve/pii/S0021929004004919|journal=Journal of Biomechanics|language=en|volume=38|issue=3|pages=211–223|doi=10.1016/j.jbiomech.2004.09.027|pmid=15652536 |url-access=subscription}}</ref>

In the above equations, <math>E^*</math> is the [[Young's modulus]] and <math>\sigma_p^*</math> the [[Yield (engineering)|yield strength]] of the sponge material. These are chosen to best fit [[experimental data]]. The strain at the [[Yield (engineering)|elastic limit]], where the plateau region begins, is denoted as <math>\varepsilon_e</math>, while the strain at the onset of the densification region is <math>\varepsilon_D</math>.<ref name=":2" />

<math>\varepsilon_D=1-1.4(\rho^*/\rho_s)</math>

Here <math>\rho^*</math> is the density of the bulk sponge <math>\rho_s</math> is the density of its constituent, the fiber bundle. The constant D defines the strain at the onset of densification as well as the stress relationship in the densification region. It is determined by fitting experimental data.<ref name=":2" />

===Dynamic loading===
The mechanical properties of Luffa sponges change under different [[strain rate]]s. Specifically, energy adsorption, [[compressive stress]], and plateau stress (which is in the case of foam materials corresponds to the yield stress) are enhanced by increasing the strain rate.<ref name=":0" /><ref name=":3">{{Cite journal|date=2013-07-01|title=Behaviour of luffa sponge material under dynamic loading|url=https://www.sciencedirect.com/science/article/abs/pii/S0734743X13000110|journal=International Journal of Impact Engineering|language=en|volume=57|pages=17–26|doi=10.1016/j.ijimpeng.2013.01.004|issn=0734-743X|last1=Shen |first1=Jianhu |last2=Xie |first2=Yi Min |last3=Huang |first3=Xiaodong |last4=Zhou |first4=Shiwei |last5=Ruan |first5=Dong |bibcode=2013IJIE...57...17S |url-access=subscription }}</ref> One explanation for this is that the luffa fibers undergo more axial deformation when dynamically loaded (high strain rates) than when [[Quasistatic loading|quasi-statically]] loaded (low strain rates).<ref name=":3" />