PEER-REVIEWED ARTICLE bioresources...luffa sponge material, defined by the ratio of the force to the...
Transcript of PEER-REVIEWED ARTICLE bioresources...luffa sponge material, defined by the ratio of the force to the...
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8426
Compression Responses of Bio-Cellular Luffa Sponges
Xiyue An,a,b Qianqian Sui,a Fangfang Sun,a Zhiyuan Ma,a Shu Jiang,a Bing Ji,a and
Hualin Fan a,b
Crushing behaviors of luffa sponges were studied through mechanical experiments. Controlled by four-order hierarchical and anisotropic structures, luffa sponges exhibit anisotropic responses along axial, radial, and circumferential directions. The ultra-thin but stiff inner surface layer dominates the crushing behavior, endowing the axially compressed luffa cylinder with structural integrity, enhancing the elastic deformation and yielding strength. In radial, circumferential, and lateral compressions, after removing the inner surface layer, luffa sponges are compliant and have large quasi-linear deformation before densification, without a plateau characterized by yielding and deformation. Immersed into water, crushed luffa sponge cylinders recover their geometry completely. However, compression strength is only partially restored. Gradual damage of the inner surface layer in water immersing/drying cycles greatly weakens the compression strength. In the case of removal of the inner surface layer, crushed luffa sponge cylinders completely restore their quasi-linear deformation ability during the water immersing/drying cycles.
Keywords: Natural cellular luffa sponge; Hierarchical structure; Mechanical properties;
Mechanical testing
Contact information: a: College of Mechanics and Materials, Hohai University, Nanjing 210098, China;
b: State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of
Aeronautics and Astronautics, Nanjing 210016, China;
Corresponding authors: [email protected] (Hualin Fan); [email protected] (Fangfang Sun)
INTRODUCTION
Bio-cellular materials, observed in biological systems, have hierarchical structures
(Lakes 1993; Fratzl and Weinkamer 2007; Chen and Pugno 2013); these materials exhibit
excellent mechanical properties at remarkably low density (Taylor et al. 2011; Fan et al.
2014; Wang et al. 2014; Anbukarasi and Kalaiselvam 2015). The luffa sponge is one such
material containing a complex, interconnecting pore structure (Shen et al. 2012; 2013;
2014; Chen et al. 2014). Investigation into the structure and properties of biological foam-
like materials may enable scientists and engineers to reveal novel functional mechanisms
and further develop biologically inspired materials with engineered properties. Shen et al.
(2012, 2013, 2014) reported measurements of stiffness, strength, and energy absorption
characteristics of the luffa sponge. Chen et al. (2014) revealed that the structure influences
the mechanical behavior of the luffa sponge. Their study revealed the anisotropic properties
of luffa sponges through crushing experiments. The tensile strength of a single fiber was
reported to be approximately 100 MPa (Chen et al. 2014).
Based on studies of Shen et al. (2012, 2013, 2014) and Chen et al. (2014), the
anisotropy and hierarchy of luffa sponges and their influences to the crushing behaviors
were explored quantitatively in this paper.
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8427
LUFFA SPONGE STRUCTURE
The luffa sponge has a hierarchical cellular structure. Macroscopically, the luffa sponge is
a cylinder (the 1st order structure) and the cylinder contains macro-pore structures with
three parts (the 2nd order structure): a cylindrical shell, a core structure, and more than three
macro-pores, forming a hollow cellular cylinder, as shown in Fig. 1. The letters X, Y, and
Z denote axial, circumferential, and radial directions, respectively. Mesoscopically, the
cylindrical shell and the core structure are cellular structures (the 3rd order structure),
containing interconnected struts and open meso-pores, as shown in Fig. 2. Microscopically,
the strut of the luffa sponge exhibits a two-order hierarchical hollow cellular tube (the 4th
order structure). Four-order hierarchical porosities make the luffa sponge ultra-light and
usually lighter than 0.1 g/cm3.
(a) (b) (c)
Fig. 1. Macro-structure of a luffa sponge from the (a) outside surface, (b) cross section, and (c) inner surface
Mesoscopically, luffa sponges have highly complex anisotropic properties. On the
outer surface, fibers extend along the circumferential direction (X-axis), and there are only
a few continuous fibers in the vertical direction (Y-axis), as shown in Fig. 2. The inside
surface contains an ultra-thin and stiff planar network of fibers that primarily extend in the
vertical direction, as shown in Fig. 2. Therefore, the cylindrical shell has two parts, similar
to that of stiff lamellae in a compliant matrix. One part is the outside surface layer, whose
thickness is close to that of the cylindrical shell and has fibers distributing circumferentially.
The second part is an ultra-thin and stiff lamina, with thickness of a single fiber strut and
fibers mainly extending vertically.
(a) (b) (c)
Fig. 2. Mesostructure of a luffa sponge showing the (a) outside surface, (b) cross section, and (c) inner surface, using an optical microscope
X
Y
X
Z
X
Y
X
Y Z X
Y Z
Cylindrical shell
Core
Pore Pore
Pore
Inner surface layer
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8428
EXPERIMENTS
Luffa sponges were bought from Shi Wang Enterprise Co., Ltd. (China). These
sponges are usually used as cleaning materials in China. The store-bought luffa sponge
cylinders were approximately 15 cm long. The ends of the cylinders were removed, and
the test samples were cut from the central part. To understand the mechanical performances
of luffa sponges, uniaxial compression experiments were performed using a 50-kN Instron
(USA) test machine at a loading rate of 2 to 5 mm/min. Characteristics of the samples are
listed in Table 1.
Table 1. Characteristics of Luffa Sponge Cylinders
Sample Length (cm)
Cylinder Dimensions
(long axis, short axis; cm)
Pore Dimensions (long axis, short axis; cm)
Weight (g)
Core
A1 4.0 (5.4,4.5) (2.1,1.2);(1.7,1.5);(1.9,1.4);(1.9,1.5) 3.5 With
A2 3.2 (7.3,5.7) (3.0,1.7);(2.5,2.0);(2.2,1.8) 4.9 With
A3 3.5 (6.3,5.4) (2.2,1.2);(2.1,1.5);(2.0,1.5) 5.0 With
A4 4.0 (4.8,4.2) (3.5,2.8) 3.0 Without
A5 3.0 (6.9,6.0) (5.0,4.0) 3.2 Without
A6 3.5 (6.5,5.4) (4.0,3.5) 4.6 Without
A7 8.0 (4.8, 4.2) (2.4, 1.3); (2.4, 1.5); (1.7, 1.5) 10.2 With
A8 7.2 (6.9, 6.0) (2.2, 1.2); (2.0, 1.3); (1.6, 1.6) 7.2 With
A9 7.9 (6.5, 5.4) (2.5, 1.5); (2.0, 1.2); (2.0, 2.0) 15.0 With
A10 7.5 (6.2,5.8) (4.0,4.0) 8.4 Without
A11 7.6 (6.4,5.6) (5.0,4.0) 7.9 Without
A12 8.0 (6.4,5.0) (5.0,3.5) 6.8 Without
A13 1.7 (5.8, 4.8) (4.4,3.8) 1.6 Without
A14 2.3 (6.5, 5.4) (4.3,3.5) 2.3 Without
C1 6.9 (6.5, 5.8) Not measured. 8.3 With
C2 7.7 (6.2, 4.9) Not measured. 8.5 With
C3 7.1 (6.7, 6.2) Not measured. 9.2 With
C4 7.2 (7.8, 7.0) Not measured. 12.9 With
C5 6.7 (7.1, 5.0) Not measured. 10.0 With
C6 7.1 (7.6, 5.9) Not measured. 15.2 With
To reveal the influence of water, the crushed luffa sponge cylinders, listed in Table
2, were immersed into water for 24 h and dried at room temperature for one week. Then,
the water-immersed and dried cylinders (WDCs) were uniaxially compressed.
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8429
Table 2. Characteristics of Luffa Sponge Cylinders after Water-Immersing/Drying Cycles
Sample Length (cm)
Cylinder Diameter (long axis, short axis;
cm)
Pore Diameter (long axis, short axis; cm)
Core Inner
Surface Layer
1a 2.1 (7.5, 6.5) (3.2, 1.7); (2.0, 1.7); (3.0, 2.0) With Without
1b 2.0 (7.3, 6.6) (3.1, 1.3); (2.6, 1.3); (2.9, 1.4) With With
2a 2.0 (6.2, 5.2) (2.0, 1.5); (2.0, 2.0); (2.0,1.6) With Without
2b 2.2 (5.9, 4.5) (2.2, 1.1); (1.9, 1.2); (1.9, 1.6) With With
3a 2.0 (7.0, 6.1) (2.4, 1.8); (2.6, 2.0); (3.1, 1.9) With Without
3b 2.1 (6.7, 5.5) (2.9, 1.5); (2.5, 1.7); (2.4, 1.8) With With
4a 1.8 (6.3, 4.1) (3.0, 1.5); (1.8, 1.7); (2.2, 1.0) With Without
4b 2.0 (6.1, 4.9) (2.4, 1.4); (1.9, 1.7); (2.4, 1.1) With With
5a 2.0 (7.5, 5.7) (6.0, 4.5) Without Without
5b 2.1 (7.5, 5.6) (6.0, 4.5) Without With
6a 2.0 (6.5, 5.4) (5.3, 4.0) Without Without
6b 2.0 (6.4, 5.2) (4.9, 4.1) Without With
7a 2.2 (6.0, 5.0) (4.5,4.0) Without Without
7b 2.2 (6.0, 5.2) (4.5, 4.0) Without With
8a 2.2 (5.2, 4.7) (4.7, 3.9) Without Without
8b 2.1 (5.9, 4.5) (4.5, 3.5) Without With
RESULTS AND DISCUSSION
Crushing Behaviors
As shown in Fig. 3, uniaxial crushing curves of luffa sponge cylinders have three
stages: elastic deformation, stable crushing deformation plateau, and densification. When
the core part of the cylinder is removed (Fig. 3(b) and 3(d)), the samples have identical
deformation curves to those with the core (Fig. 3(a) and 3(c)). For samples without the core,
a macro-shell buckling mode was observed, as shown in Fig. 4(a). Other cylinders failed
at local sites of crimpling, as shown in Fig. 4(b). The uniaxial compression strength of the
luffa sponge material, defined by the ratio of the force to the area of the luffa sponge
material from the shell and the core (Area of the macro-pore structure was not included),
was approximately 0.3 MPa. The crushing ratio (densification strain) is usually greater than
0.7 for luffa sponge materials. Thus, the level of energy absorption is approximately 0.21
J/cm3 (Fig. 3(d), A10). When the density of the material is approximately 0.07 g/cm3, the
energy absorption is 3.0 J/g (Fig. 3(d), A10). The energy absorption capacities of luffa
sponges are better than those of polymer and aluminum foams (Shen et al. 2012).
Compared to lattice materials (Fan et al. 2014), luffa sponge materials exhibit improved
specific energy absorptions, as shown in Fig. 3. A fourth-order hierarchical structure
enables luffa sponges to be more weight-efficient than second-order hierarchical hollow-
strut Ni–P micro-lattices (Schaedler et al. 2011).
The inner surface layers of samples 1a to 8a were removed and the samples were
compressed to determine if the inner surface layer would impact the strength, as shown in
Fig. 5. For all samples, the strength greatly decreased when removing the inner surface
layer. For samples without the core, the strength was below 0.15 MPa, about a 50%
reduction from the initial value, as shown in Fig. 5(a). The deformation curves had different
characteristics.
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8430
0.00 0.15 0.30 0.45 0.60 0.75 0.900.0
0.2
0.4
0.6
0.8
1.0
1.2
Str
ess (
MP
a)
Strain
A1
A2
A3
(a)
Elastic deformation
Deformation plateau
Densification
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Str
ess (
MP
a)
Strain
A4
A5
A6
(b)
0.0 0.2 0.4 0.6 0.80.0
0.2
0.4
0.6
0.8
Densification
Stable crushing deformation plateau
Str
ess (
MP
a)
Strain
A7
A8
A9
(c)
Elastic deformation
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
Str
ess (
MP
a)
Strain
A10
A11
A12
(d)
0.01 0.1 1
0.1
1
10
100 Luffa sponge
Woven textile panel
Woven Kagome truss
Lattice structure
Polymer lattice truss
Hollow lattice truss
Hollow pyramidal truss
Microlattices [18]
En
erg
y a
bso
rptio
n (
J/c
m3)
Density (g/cm3)
(e)
0.01 0.1 10
3
6
9
12
15
Luffa sponge
Woven textile panel
Woven Kagome truss
Lattice structure
Polymer lattice truss
Hollow lattice truss
Hollow truss
Microlattices [18]
En
erg
y a
bso
rptio
n (
J/g
)
Density (g/cm3)
(f)
Fig. 3. Crushing behaviors of luffa sponges (a) A1-A3; (b) A4-A6; (c) A7-A9 and (d) A10-A12, and energy absorbing abilities per unit (e) volume and (f) mass
(a) (b)
Fig. 4. Crushing modes of luffa sponges (a) without or (b) with core structures
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8431
For samples without core, the deformation curve was quasi-linear before the
densification strain reached 0.8, as shown in Fig. 5(b). Yielding and deformation plateaus
were not observed in any of the samples; therefore, it is difficult to define the strength
based on such a deformation curve. The linear deformation stiffness, d
E , is calculated by
/d d d
E (1)
whered
is the densification strain andd
is the densification strength of the luffa sponge
material. Assuming 0 .8d
, / 1 .2 5d d
E .
Without the inner surface layer, the modulus of the luffa sponge is comparable to
its densification strength. Energy absorption (W ) is calculated by
/ 2d d
W (2)
Without the inner surface layer, luffa sponges were found to have decreased energy
absorption at a rate of 0.16 J/cm3. This was approximately 30% less than the energy
absorption of luffa sponges with the inner surface layer in place.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0
0.1
0.2
0.3
0.4
Str
ess (
MP
a)
Strain
1a
2a
3a
4a
1b
2b
3b
4b
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
1.2
Str
ess (
MP
a)
Strain
5a
6a
7a
8a
5b
6b
7b
8b
(b)
Linear deforamtion
Fig. 5. Uniaxial crushing behaviors of luffa sponges (a) with and (b) without core structures. The dotted line denotes that the inner surface layer of the sample has been removed.
Block materials cut from the cylindrical shell, as shown in Fig. 1(c), were
compressed along the radial direction. As shown in Fig. 6(a), the deformation curves are
quasi-linear before the strain approaches the densification strain, which is similar to the
uniaxial compression curve of the luffa sponge material without inner surface layer (Fig.
5). The results reveal that the inner surface layer has little contribution to the radial crushing
behavior.
Block materials were compressed along the circumferential direction, as shown in
Fig. 6(b). The deformation curve in circumferential compression was different from the
quasi-linear curve in radial compression. With circumferentially distributed fibers, the
block exhibited three deformation stages: elastic deformation, linear deformation after
yielding, and densification. The strength was usually smaller than 0.1 MPa. After yielding,
the deformation was linear before densification.
Linear deformation
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8432
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0
0.2
0.4
0.6
0.8
1.0
1.2 J1: 7.22.10.8 cm
J2: 7.22.40.5 cm
J3: 7.82.50.6 cm
Str
ess (
MP
a)
Strain
(a)
Linear deformation
Densification
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Str
ess (
MP
a)
Strain
H1: 2.00.61.0 cm
H2: 2.20.50.8 cm
H3: 2.10.511.0 cm
(b)
Elastic deformation
Linear deformation
Densification
Fig. 6. Crushing behaviors in the (a) radial and (b) circumferential directions
Luffa sponge cylinders were compressed laterally, as shown in Figs. 7 and 8.
Characteristics of samples are listed in Table 1. Before densification, the curves are quasi-
linear, as shown in Fig. 7. When mechanically compressed, the cellular foam in the
cylindrical shell was condensed; however, the pore structure did not deform, as shown in
Fig. 8.
As the compressed area gradually increased, it subsequently increased the stress
load on the fibers. Then the pores were compressed and plastic hinges formed in the shell.
The inner surface layer had little contribution to these plastic hinges because it exhibited
reduced bending motion. Contractions among fibers supply anti-crushing stability to resist
lateral compression.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Str
ess (
MP
a)
Strain
C1
C2
C3
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.00
0.05
0.10
0.15
0.20
0.25
0.30
Str
ess (
MP
a)
Strain
C4
C5
C6
(b)
Fig. 7. Lateral crushing behaviors of luffa sponges along the (a) long and (b) short axes
Behavior after Water-Immersing/Drying Process
Five water-immersing/drying cycles were tested, as shown in Fig. 9. After these
cycles, crushed cylinders were restored their initial geometric shape completely, similar to
results by Shen et al. (2014). The WDCs exhibited similar geometric deformation curves
as the initial samples. But the yielding strength was less than one-third of the initial strength.
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8433
(a) (b)
Fig. 8. Lateral crushing modes of luffa sponges along the(a) long and (b) short axes.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Str
ess (
Mp
a)
Strain
A7
A7-NO_1
A7-NO_2
A7-NO_3
A7-NO_4
A7-NO_5
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
Str
ess (
Mp
a)
Strain
A8
A8-NO_1
A8-NO_2
A8-NO_3
A8-NO_4
A8-NO_5
(b)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Str
ess (
Mp
a)
Strain
A9
A9-NO_1
A9-NO_2
A9-NO_3
A9-NO_4
A9-NO_5
(c)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Str
ess (
Mp
a)
Strain
A10
A10-NO_1
A10-NO_2
A10-NO_3
A10-NO_4
A10-NO_5
(d)
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8434
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
Str
ess (
Mp
a)
Strain
A11
A11-NO_1
A11-NO_2
A11-NO_3
A11-NO_4
A11-NO_5
(e)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
Str
ess (
Mp
a)
Strain
A12
A12-NO_1
A12-NO_2
A12-NO_3
A12-NO_4
A12-NO_5
(f)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Str
ess (
Mp
a)
Strain
A13
A13-NO_1
A13-NO_2
A13-NO_3
A13-NO_4
A13-NO_5
(g)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
Str
ess (
Mp
a)
Strain
A14
A14-NO_1
A14-NO_2
A14-NO_3
A14-NO_4
A14-NO_5
(h)
Fig. 9. Crushing behaviors after the water immersing/drying cycles for (a) A7, (b) A8,(c) A9, (d) A10, (e) A11, (f) A12, (g)A13, and (h) A14
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.1
0.2
0.3
0.4
0.5
0.6
Str
ess(M
Pa
)
Strain
1a
2a
3a
4a
1b
2b
3b
4b
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.0
0.2
0.4
0.6
0.8
1.0
Str
ess (
MP
a)
Strain
5a
6a
7a
8a
5b
6b
7b
8b
(b)
Fig. 10. Uniaxial crushing behaviors of luffa sponges (a) with and (b) without core structures after one water-immersing/drying cycle. The dotted lines denote samples with the inner surface layer removed.
When the inner surface layer was removed, different responses after the water-
immersing/drying process were acquired, as shown in Fig. 10. Linear deformation
characterizes the response of WDCs without inner surface layer. Furthermore, the curves
were consistent with those of initially compressed samples before water-immersing/drying
cycles. Therefore, the results indicate that the anti-crushing ability of WDCs without the
inner surface layer was nearly restored.
Compared with observations of Shen et al. (2014), advanced understanding on the
water-responsive rapid recovery of natural cellular material has been achieved. Damage of
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8435
the inner surface layer of the luffa sponge may decrease the strength in water-
immersing/drying cycles. Without this layer, water-responsive rapid recovery is ideal
because of the deformation resistance from interactions among fibers.
Mechanism
The cylindrical shell structure behaves as an ultra-thin lamella covering a thick and
compliant bio-cellular matrix. The ultra-thin and stiff lamellae may bear the load, while the
thick but compliant cellular matrix supports the ultra-thin layer from buckling. Without the
stiff lamellae, the cylinder deforms linearly and has ultra-low load capacity. Without the
compliant matrix, membrane buckling controls the failure.
The modulus of elasticity and strength of the cylinder, c
E andc s
, can be predicted
using the following equations:
0 o
0 o
=
/
c i i
c s is i i
E E E
E E
(3)
i f fE E (4)
c s fs i f (5)
01
i (6)
2 2
4 /i i i o i
D t D D (7)
/f f f
t d (8)
In these equations,i
and 0
denote the volume fraction of the inner stiff shell and
the soft matrix, respectively.i
E and o
E denote the modulus of the inner stiff cylindrical
shell and the soft matrix, respectively.f
E and f s
are the modulus and strength of a single
fiber, respectively.i
t and f
t denote the thickness and width of a single fiber, respectively.
fd is the distance between neighboring vertical fiber in the inner surface layer,
f is the
volume fraction of the vertical fiber in the inner surface layer,i
D and o
D denote the inside
and outside diameters of the cylindrical shell, respectively, and is the area ratio of the
inner surface after removing the joint area with the core part. As suggested by Chen et al.
(2014), characteristics of luffa sponge cylinders are listed in Table 3. Considering errors in
estimating the dimension of the hierarchical structure, Eq. 3 suggests consistent results with
the experiments.
Table 3. Characteristics of Luffa Sponge Cylinders (from Chen et al. 2014)
f s
it f
d i
ft
f c s
100 MPa 0.3-0.5
mm
4.35-
5.88 mm
0.024-
0.04 1 mm
0.17-
0.23 0.7
0.28-0.65
MPa
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8436
When the inner surface layer is removed, luffa sponge materials deform linearly
before densification. The modulus is comparable to the stress. As shown in Fig. 2, fibers
are perpendicular to the compression load; therefore, fibers have minimal bending and axial
compression deformation. Under compression, fibers are in close contact and laterally
compressed. The slope of the macro-linear deformation curve depends on the amount of
the contact area. The stress and strain, and , are linearly associated using the equation
below:
/d d
(9)
Contacts among fibers enhance the anti-crushing ability in lateral compression.
Contact area (c
A ) is a variable to evaluate the stress and determined by the following
equations,
/ /d c
A A (10)
/d c
A A (11)
where A is the ultimate compression area of the sample.
Removing the inner surface layer, water-immersing/drying cycles have little
influence on the crushing behaviors. Damage of the inner surface layer decreases the yield
strength. However, the densification strength is identical to that of the sample without inner
surface layer. Damage to the material ( D ) in the th
n cycle is calculated using the following
equation,
0 .8 5(1 )D n
(12)
and the strength of the WDCs in the th
n cycle is used to determinen
in the following
equation,
0 .85
0 0(1 )
nD n n
(13)
where0
denotes the strength of the sample without water immersion. The exponent, 0.85,
from Fig. 11(b) describes the weakening response of other samples. It is similar to the
relationship described by Shen et al. (2014), where the exponent is 0.65. Ni-P microlattices
have a similar regularity in repetitive loadings (Schaedler et al. 2011).
0 1 2 3 4 50.00
0.09
0.18
0.27
0.36
0.45 A7
A8
A9
A10
A12
Str
en
gth
(M
Pa
)
Cycles
(a)
n=
D(n);
D(n)=/(1+n)^0.85
0 1 2 3 4 50.10
0.15
0.20
0.25
0.30
0.35
n=
D(n); D(n)=/(1+15n)^0.4
Tested data (Xie et al. 2014)
Fitting
Str
en
gth
(M
Pa
)
Cycles
(b)
n=
D(n); D(n)=/(1+n)^0.65
0.000
0.002
0.004
0.006
0.008
0.010
0.012
Str
ess (
MP
a)
Tested data (Schaedler et al. 2011)
Fitting
Fig. 11. Crushing behaviors after WDCs in (a) this study compared with (b) previous results from Schaedler et al. (2011) and Xie et al. (2014)
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8437
CONCLUSIONS
1. The hierarchy and anisotropy of the luffa sponge were investigated using quantitative
analysis of the crushing behavior. Accordingly, the luffa sponge cylinder was modeled
as an ultra-thin and stiff membrane surrounded by a thick and soft supporting matrix.
The ultra-thin and stiff inner surface layer endows the axially compressed luffa cylinder
with structural properties characterized by elastic deformation and yielding strength.
2. The luffa cylinders exhibit quasi-linear deformation characteristics and anisotropic
responses along axial, radial, and circumferential directions. Four-order hierarchical
structures permit the luffa sponge to be quite weight-efficient in resisting compression.
3. The ultra-thin and stiff inner surface dominates the crushing capabilities, leading to
elastic deformation, yielding deformation plateau, and densification. A soft matrix,
supporting stiff lamellae model was proposed and was consistent with the prediction of
strength.
4. For radial, circumferential, and lateral compressions with or without the inner surface
layer, luffa sponges exhibit quasi-linear large deformation before densification, without
yielding or plateau. Contacts among fibers supply anti-crushing capability.
5. When immersed into water, crushed cylinders restore their geometric shape
completely, and the load-bearing capacity can be partly restored. Damage of the inner
surface layer during the water immersing/drying cycles decreases the strength of the
fibers. Removing the inner surface layer, cylinders are able to completely restore their
large quasi-linear deformation during water immersing/drying cycles.
ACKNOWLEDGMENTS
Support from the National Natural Science Foundation of China (11172089,
11372095), Program for New Century Excellent Talents in University (NCET-11-0629),
State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-
0212G01, MCMS-0215G01), and Fund of State Key Laboratory of Structural Analysis for
Industrial Equipment (GZ1306) are gratefully acknowledged.
REFERENCES CITED
Anbukarasi, K., and Kalaiselvam, S. (2015). "Study of effect of fibre volume and
dimension on mechanical, thermal, and water absorption behaviour of luffa reinforced
epoxy composites," Mater. Des. 66, 321-330. DOI:10.1016/j.matdes.2014.10.078
Chen, Q., and Pugno, N. (2013)."Bio-mimetic mechanisms of natural hierarchical
materials: A review," J. Mech. Behav. Biomed. Mater.19, 3-33.DOI:
10.1016/j.jmbbm.2012.10.012
Chen, Q., Shi, Q., Gorb, S. N., and Li, Z. (2014). "A multiscale study on the structural
and mechanical properties of the luffa sponge from Luffa cylindrical plant," J.
Biomech. 47(6), 1332-1339. DOI:10.1016/j.jbiomech.2014.02.010
PEER-REVIEWED ARTICLE bioresources.com
An et al. (2015). “Luffa sponge crushing,” BioResources 10(4), 8426-8438. 8438
Fan, H. L., Qu, Z. X., Xia, Z. C., and Sun, F. (2014). "Designing and compression
behaviors of ductile hierarchical pyramidal lattice composites," Mater.Des. 58, 363-
367. DOI:10.1016/j.matdes.2014.01.011
Fratzl, P., and Weinkamer, R. (2007). "Nature's hierarchical materials," Prog. Mater. Sci.
52,1263-1334.DOI:10.1016/j.pmatsci.2007.06.001
Lakes, R. (1993). "Materials with structural hierarchy," Nature 361, 511-516.
DOI:10.1038/361511a0
Shen, J., Xie, Y. M., Huang, X. D., Zhou, S., and Ruan, D. (2012). "Mechanical
properties of luffa sponge," J. Mech. Behav. Biomed. Mater.15, 141-152.
DOI:10.1016/j.jmbbm.2012.07.004
Shen, J., Xie, Y. M., Huang, X. D., Zhou, S., and Ruan, D. (2013). "Behavior of luffa
sponge material under dynamic loading," Int. J. Impact Eng. 57, 17-26.
DOI:10.1016/j.ijimpeng.2013.01.004
Shen, J., Xie, Y. M., Zhou, S. W., Huang, X. D., and Ruan, D. (2014). "Water-responsive
rapid recovery of natural cellular material," J. Mech. Behav. Biomed. Mater. 34, 283-
293. DOI:10.1016/j.jmbbm.2014.02.022
Schaedler, T. A., Jacobsen, A. J., Torrents, A., Sorensen, A. E., Lian, J., Greer, J.
R.,Valdevit, L., and Carter, W. B. (2011). "Ultralight metallic microlattices," Science
334(6058), 962-965. DOI:10.1126/science.1211649
Taylor, C. M., Smith, C. W., Miller, W., and Evans, K. E. (2011). "The effects of
hierarchy on the in-plane elastic properties of honeycombs," Int. J. Solids Struct.
48(9), 1330-1339.DOI:10.1016/j.ijsolstr.2011.01.017
Wang, X. J., Shen, J. H., Zuo, Z. H., Huang, X., Zhou, S., and Xie, Y. M. (2014).
"Numerical investigation of compressive behaviour of luffa-filled tubes," Compos.
Part B: Eng.73, 149-157. DOI:10.1016/j.compositesb.2014.12.017
Article submitted: February 13, 2015; Peer review completed: July 30, 2015; Revised
version received: August 1, 2015; Accepted: August 16, 2015; Published: October 30,
2015.
DOI: 10.15376/biores.10.4.8426-8438