Editing Luffa (section)

===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 }}</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" />