Effect of cell shape of honeycomb structure on the toughness and bending
strength of the overall structure
2
(i) Abstract
Using a strong structure to construct an object is crucial to prevent it from rupturing due to
external forces such as bending. Honeycomb structures are widely used in constructing
bridges and airplanes due to its well-known rigidity. However, there’s a lack of research on
the effects of shapes on the overall strength of the honeycomb structure as most research
focus on the materials used in manufacturing them. In contrast, our research objective is to
investigate which common shape, namely circle, triangle, trapezium, square and hexagon
could provide the best toughness and bending strength for the honeycomb structure. The five
shapes of honeycomb structure were created using vanguard sheets and were tested by
loading a number of weights onto the centre until it collapsed. Meanwhile, static loading
method was used to provide even weight distribution throughout the honeycomb structure.
The average length of deflection of the honeycomb structure when handling different loads
were measured and graphs were plotted. The gradient and the area bounded by the graphs
were analyzed to determine the shape’s effectiveness on the honeycomb structures. The
experiment results revealed that hexagon gave the best toughness and bending strength to the
honeycomb structure mainly because of tessellation and three other factors. Due to
limitations, other tests regarding real life applications of the honeycomb structure were
unable to be carried out. Further research can be done regarding shock loading and etcetera,
which are more related to real life situations. Our research could contribute to the
manufacturing industry in picking the best shape, in producing honeycomb structures for
further usage.
(ii) Table of Contents
1.0 Introduction ............................................................. 4 – 5
2.0 Methods and Materials ........................................... 6 – 7
2.1 Apparatus and Materials .......................................... 6
2.2 Construction of Honeycomb Structures ................... 6
2.3 Methodology ............................................................ 7
3.0 Results and Discussions ........................................ 8 – 14
4.0 Conclusion and Recommendations .................... 15 – 16
5.0 References ........................................................... 17 – 18
6.0 Appendix ............................................................ 19 – 24
6.1 Appendix A ............................................................ 19
6.2 Appendix B ............................................................. 20
6.3 Appendix C ............................................................. 21
6.4 Appendix D .................................................... 22 – 24
4
1.0 Introduction
Honeycomb structure attained its name due to its resemblance to the bee hives (Blitzer,
1997). It commonly refers to a structure which consists of a core made up of a series of
orderly-arranged hollow cells and two facing sheets covering the surfaces of the cell pattern
(Figure 1).
Figure 1: Composite Honeycomb Sandwich
(Extracted from: Bitzer. T, 1997. Honeycomb Technology, (p. 36))
The earliest record of honeycomb structure usage dates back all the way to as early as the
19th century, whereby it was used in the construction of railroad bridge located in Wales
(Bitzer, 1997).
During World War I and II, honeycomb structure became popular in the aviation industry
(“Honeycomb Structure Fails”, para. 6). It was first implemented into the design of aircraft
wing panel in 1919 and later proved to be one of the best sandwich structures as it has high
strength-to-weight ratio which is essential to the aviation industry (Yu & Cleghorn, 2005;
Gaetano G. Galletti, 2007). The scientific research in the late 20th century discovered several
other unique physical properties of honeycomb such as its transverse compressive properties
(Thotakuri, 2004) which later led honeycomb structure to gain its recognition in other
industries such as the sports industry, the information and technology industry and furniture
industry (IKEA, 2004; Busch 2004).
5
The important parts of a honeycomb structure are the facing sheets of the structure and the
series of hollow cells, which help to withstand the longitudinal stress and carry the
transversal stress respectively. The individual cells as well as the facing sheets are bonded
together by the use of strong chemical adhesives (Galletti, Vinquist & Es-said, O.S, 2007).
This results in a highly rigid structure with relatively light weight. As shown in Figure 2,
structure 3 (honeycomb structure) is 37 times stiffer and 7 times stronger in bending strength
than structure 1 (non-honeycomb structure). Nonetheless, structure 3 is 9% heavier than
structure 1.
Figure 2: Rigidity Test
(Extracted from Bitzer. T, 1997, HoneycombTechnology, p 5)
In addition, it has been studied that when the honeycomb structure material is kept constant,
the variation of the cell’s geometries such as its angle, width and thickness affects the energy-
absorption property of the honeycomb structure (Veltin, 2009). There were many tests and
research conducted on regular hexagon honeycomb structure’s physical properties, but there
were limited research on the other common shapes such as triangle and square.
As variations in geometries of the cell play an important role in the honeycomb structure,
there lies a research gap of how other regular shaped cells will perform as compared to the
conventional hexagon cells. We aim to bridge the research gap by investigating the resulting
toughness and bending strength of a honeycomb structure when different shape cells are used
as the core of the structure. In our experiment, we will specifically test on the five common
shapes, namely, hexagon, circle, square, triangle, and trapezium.
1 2 3
6
2.0 Methods and Materials
Overview: To determine the cell shape that gives the highest bending strength and toughness
as the core of a honeycomb structure through the investigation of the rate of deflection and
the heaviest load that each honeycomb structure can withstand.
2.1 Apparatus and Materials
Apparatus
Ruler
Weights of 20 Newton (N) and 50N
Penknives
Scissors
Scientific Calculator
Mechanical Pencil
Materials
Vanguard Sheets
Super Glue
2.2 Construction of Honeycomb Structures
1. 5 different cell shapes namely: circle, triangle, square, trapezium and hexagon were
chosen to be the core of the honeycomb structure. Each honeycomb structure
consisted of 23 core cells, which were of the same shape.
2. The thickness of each cell was kept constant at 2 centimeter (cm) and the cross
sectional area was fixed at approximately 16cm
2
.
3. The vanguard sheets were first cut into strips of 2cm.
4. The square-shaped cells were the first to be made. The 2cm-thick strips were bent
according to the dimensions of the square. (Refer to Appendix B)
5. The bent strips were then sealed with super glue and the square-shaped cells were
formed.
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6. Once 23 square-shaped cells were formed, they were then glued together with a
formation of alternating rows of 5 cells and 4 cells (5-4-5-4-5). (Refer to Appendix C)
7. Two flat vanguard sheets were glued to the top and bottom of the cells formation
respectively. This is to create a sandwich composite structure.
8. Steps 4 to 7 were repeated to construct the remaining 4 cell shapes of the honeycomb
structure.
2.3 Methodology
1. The square honeycomb structure was the first to be experimented. It was placed on
two supports at the side. (Refer to appendix B)
2. A total weight of 70N (made up of a 20N weight and a 50N weight) was placed on top
of the honeycomb structure at the start of the experiment. The weights were placed at
the center of the structure by using the static loading method in order for the weights
to be evenly distributed among the cells.
3. The distance between the ground and the upper surface of the honeycomb structure
was measured. Readings were first taken from the front (L3) and back (L4) with the
help of a meter ruler. The average of the two readings was then calculated using the
formula (L3+L4)/2. The same step was repeated to calculate the average distance
between the ground and the lower surface of the honeycomb structure using the same
formula and the results were recorded. (Refer to Appendix B for experiment setup)
4. 20N weights were then added one by one onto the honeycomb structure and step 3
was repeated. A period of 10s was given in between loading intervals to ensure that
the honeycomb structure did not fail for that particular loading.
5. Step 4 was repeated until the square honeycomb structure collapsed.
6. Steps 1 to 5 were then repeated for the remaining 4 shapes of honeycomb structures.
7. The results for each cell shape were obtained, recorded and tabulated. (Refer to
appendix D)
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3.0 Results and Discussion
This section will discuss on the maximum weight, which the 5 different honeycomb
structures can withstand before collapsing and their rate of deflection. The results obtained
were analyzed and interpreted to compare the toughness and bending strength of the 5
different honeycomb structures. In this experiment, toughness is defined as the total weight a
structure can withstand before collapsing while bending strength is defined as a structure's
ability to resist deflection under load.
Figure 3 shows a graph of the average deflection versus the load on the honeycomb structure.
As toughness is defined to be the area under the graph of load versus deflection, we can use
Figure 3 to determine the toughness of each structure by calculating the area bounded by each
individual graph and the y-axis. Table 1 shows the area bounded by the y-axis
and each cell shape’s line graph.
Figure 3: Deflection of each cell shape under different loads.
9
Table 1: Area bounded by the y-axis and each cell shape’s line graph.
From table 1, hexagon honeycomb structure has an area of 1180 (N mm), which is 58.3%
larger than that of the next best structure, which is the square honeycomb structure. This
suggests that hexagon structure is much tougher than the other structures. On the other hand,
circle honeycomb structure is the weakest in terms of toughness as it has the smallest area of
only 335 (N mm).
Based on observation from Figure 3, the graph for hexagon honeycomb structure is placed
below the remaining 4 line graphs whereas the circle honeycomb structure is above the
others. In order to identify our findings regarding their bending strength, we proceed to
further analysis of calculating the gradient of each graph by making use of their best-fit-lines.
Figure 4 to Figure 8 show the best-fit-line of each individual graph whereby the gentler the
gradient, the lower the rate of deflection, and thus the higher the bending strength of the
honeycomb structure.
Cell Shape Area (Newton millimeter [N mm])
Circle 335
Square 745
Trapezium 570
Triangle 560
Hexagon 1180
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Figure 4: Best-fit-line for circle honeycomb structure.
Figure 5: Best-fit-line for square honeycomb structure.
11
Figure 6: Best-fit-line for trapezium honeycomb structure.
Figure 7: Best-fit-line for triangle honeycomb structure.
12
Figure 8: Best-fit-line for hexagon honeycomb structure.
By comparison, hexagon honeycomb structure has the highest bending strength as its line
graph has the gentlest slope, with a gradient of 0.0292mm/N. On the other hand, circle
structure’s line graph has the steepest slope, with a gradient of 0.0525mm/N, which is almost
twice as steep as that of hexagon structure. This suggests that circle honeycomb structure has
a bending strength, which is almost two times weaker than that of hexagon structure.
From the results obtained, it is observed that there is a relationship between toughness and
bending strength. Honeycomb structures with high bending strength tend to have high
toughness as well. Hence, observations for both physical properties shall be explained at the
same time.
The reason that hexagon honeycomb structure is the toughest and has the highest bending
strength is that its cells could be placed side by side repeatedly without any additional space.
This property of hexagon is known as tessellation (Jon Stefansson, 1999). It is the tessellation
of hexagon cells that provides the structure with outstanding capabilities to absorb energy
(McGill, 2010). When bending occurs, the cells receive maximum support from neighboring
cells that are not in line with the line of bending. Thus, hexagon honeycomb structure is able
to withstand more weight with the least deflection. On the contrary, circle honeycomb
13
structure does not have tessellation causing it to be the weakest in terms of both toughness
and bending strength.
The interlocking system of cells also plays a part in determining the toughness and bending
strength of the honeycomb structure. As seen from the arrangement of cells, hexagon and
circle structures have stronger interlocking system as compared to the remaining 3 structures
because there are no obvious divisive lines found between the rows of cells in the structure.
With a weaker interlocking system, stresses are not effectively distributed throughout the
structure, resulting in certain areas to be subjected to higher stress loads (Jaafar, Thanoon,
Najm, Abdulkadir, & Ali, 2006). Hence, hexagon and circle honeycomb structures are
stronger in terms of toughness and bending strength. However, according to the results
obtained, circle honeycomb structure is the weakest. This is possibly due to the fact that the
property of tessellation has a greater impact on the toughness and bending strength of the
honeycomb structure.
Another feature that is worth noting is the symmetry of the arrangements of cells. In our
experiment, we made use of 23 cells for all of the structures, arranging them in rows of four
and five. The only shape of which its cells cannot be arranged symmetrically is triangle. With
reference to the photos taken, it can be seen that the rows of four triangle cells are protruding
out of the structure when they are glued side by side with the rows of five triangle cells. As
pressure is defined as force per unit area (Stanbrough, 2008), this non-symmetrical
arrangement of triangle cells gave rise to a larger pressure and thus weaker support at one
side of the structure. Due to this, several cells reach their toughness limit earlier than the
others, thus weakening the overall structure. This explains why triangle honeycomb structure
is relatively weaker than the other structures.
Other than that, the number of symmetry axes in a cell shape may affect the toughness and
bending strength of the honeycomb structures. A higher number of symmetry axes suggest
that the structure has a higher bending strength and toughness because it has a higher number
bending orientations. Hexagon, having six symmetry axes, which is relatively higher than the
other shapes, contributes to its honeycomb structure having a high bending strength and
toughness.
The four factors that result in a structure having high bending strength and toughness are
tessellation, high degree of interlocking system, high number of symmetry axes in each cell
and a symmetrical arrangement of cells. Therefore, hexagon honeycomb structure is the
14
strongest among all the structures tested in this experiment as it possesses all of the properties
mentioned above.
15
4.0 Conclusion and Recommendations
In conclusion, this experiment was done with the aim of determining the cell shape that gives
the highest bending strength and toughness to the honeycomb structure. The objective was
achieved by investigating the deflection of each honeycomb structure when it was subjected
to increasing loads.
From the results obtained, it was found that hexagon honeycomb structure has the gentlest
gradient from its linear line graph as compared to the other 4 structures (trapezium, square,
triangle and circle). This shows that it has the strongest bending strength among the other
structures. On the other hand, hexagon honeycomb structure also has the largest area bounded
by the line graph and the y-axis, which proves that it is the toughest. The more significant
factors affecting the bending strength and toughness of the honeycomb structure are the
tessellation property and the degree of interlocking between cells. As a result, we can
conclude that hexagon is the best shape to be used as the core of the honeycomb structure.
Limitations were observed in the experiment which may lead to inaccurate results. When the
experiment was conducted, crackling sound was heard from the honeycomb structures before
failure occurred. Further investigations found that the crackling sounds were due to failure of
the bonding sections between cells. Hence, the structure might fail partly due to glue failure.
Since super glue is the strongest bonding agent available that can be applied onto the
vanguard sheet, a more suitable material that can withstand stronger bonding agents such as
solder should be used. This is to provide a more accurate result by minimizing the degree of
bonding failure.
In addition, due to apparatus limitation, there were only 20N weight plates available to be
used on the honeycomb structures. Hence, the exact weight at which each honeycomb
structure failed could not be determined precisely. This could undermine the actual results. It
is recommended that a greater variety of weight plates such as 1N weight plates to be used.
This will improve the accuracy of the results obtained.
Further studies on how the toughness and bending strength of the honeycomb structure is
affected by shock loading instead of static loading can be conducted. In real life situations,
most structures are subjected to both static and shock loading. In this experiment, the
honeycomb structure only experienced static loading as the weights were placed gently on the
structure. We suggest that the weights to be dropped onto the honeycomb structure from a
16
determined height so that it would experience shock loading.
Furthermore, cost is an important factor for manufacturers and industry players to maximize
their profits. Further studies can be done to determine the cost of manufacturing the five
different cell shape honeycomb structures. This enables them to find out which structure
provides the highest strength-to-cost ratio.
The findings from this research conclude that hexagon honeycomb structure is the strongest
in terms of toughness and bending strength. Manufacturers will be able to use these findings
to enhance the structural design of their products. This will enable them to build better quality
products which can withstand higher external forces.
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5.0 References
Barboutis, I., & Vassiliou, V. (2004). Strength properties of lightweight paper honeycomb
panels for the furniture. Retrieved from http://users.auth.gr/jbarb/Publications/lightweight
honeycomb furniture.pdf
Bitzer, T. (1997). Honeycomb technology. (1 ed., p. 235). Great Britain: Combridge
University Press. Retrieved from
http://books.google.com.sg/books?id=oBNSdDN84hIC&printsec=frontcover&source=gbs_g
e_summary_r&cad=0
Galletti, G. G., Vinquist, C., & Es-said, O. S. (2007). Theoretical design and analysis of a
honeycomb panel sandwich structure loaded in pure bending. Retrieved from
http://www.sciencedirect.com.ezlibproxy1.ntu.edu.sg/science/article/pii/S1350630707000842
Hohe, J., & Becker, W. (2000). A mechanical model for two-dimensional cellular sandwich
cores with general geometry. Retrieved from
http://www.sciencedirect.com/science/article/pii/S0927025600001452
Honeycomb structures fail. (n.d.). Retrieved from
http://www.ukessays.com/essays/engineering/honeycomb-structures-fail.php
Jaafar, M. S., Thanoon, W. A., Najm, A. M. S., Abdulkadir, M. R., & Ali, A. A. A. (2006).
Strength correlation between individual block, prism and basic wall panel for load bearing
interlocking mortarless hollow block masonry. Construction and Building Materials, 20(7),
492-498. Retrieved from
http://www.sciencedirect.com/science/article/pii/S0950061805000759
McGill. (2010). Multi-scale mechanics and design optimization lab. Retrieved from
http://mdog.mcgill.ca/research.html
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Stanbrough, J. L. (2009, November 21). Physics at bhs. Retrieved from
http://www.batesville.k12.in.us/physics/default.html
Stefensson, J. (n.d.). What is hexagonal. Retrieved from
http://www.ehow.com/about_6360694_hexagonal_.html
Thotakuri, M. (2004). Transverse compressive properties of honeycomb core under oblique
loading. Retrieved from
http://soar.wichita.edu/dspace/bitstream/handle/10057/1558/t07114.pdf?sequence=1
Veltin, B. A. (2009). Effect of geometric parameters on the in-plane crushing behavior of
honeycombs and honeycombs with facesheets. Retrieved from
http://www.engr.psu.edu/rcoe/theses/Atli-Veltin_Bilim.pdf
Xu, X. F., Qiao, P., & Davalos, J. F. (2001). Transverse shear stiffness of composite
honeycomb core. Retrieved from http://cee-faculty.ce.wsu.edu/Faculty/Qiao/j-data/22-
2001.pdf
Yu, S. D., & Cleghorn, W. L. (2005). Free flexural vibration analysis of symmetric
honeycomb panels. Retrieved from
http://www.sciencedirect.com/science/article/pii/S0022460X04005784
Zhu, H. X., & Chen, C. Y. (2007). Combined effects of relative density and material
distribution on the mechanical properties of metallic honeycombs. Retrieved from
http://www.sciencedirect.com/science/article/pii/S0167663611000329
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6.0 Appendix
6.1 Appendix A (Apparatus & Materials)
Apparatus
Ruler Weights Scientific Calculator
Mechanical Pencil Scissors Penknives
Materials
Vanguard Sheets Super Glue
20
6.2 Appendix B (Dimensions of Cell Shapes and Experiment Set Up)
Shapes Area(cm
2
) Perimeter(cm) Dimensions(cm)
Circle 16.0 14.20 14.2
Square 16.0 16.00 4+4+4+4
Triangle 16.0 18.30 6.1+6.1+6.1
Trapezium 16.0 16.20 4.1+4.1+3+5
Hexagon 16.0 15.00 2.5+2.5+2.5+2.5+2.5+2.5
21
6.3 Appendix C (5-4-5-4-5 Formation)
Hexagon Square Trapezium
Triangle Circle
22
6.4 Appendix D (Tabulation of Result)
Trapezium
L1 = 174mm L2 = 174mm L3 =191mm L4 = 193mm
Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290
L1’ (mm) 173 173 172 171 171 169 169 F
L2’ (mm) 173 172 171 170 169 169 168 F
L3’ (mm) 190 190 189 189 188 187 186 F
L4’ (mm) 192 191 191 190 189 189 188 F
Average
deflection,
δave (mm)
1 1.5 2.25 3 3.75 4.25 5.25
Circle
L1 = 174mm L2 = 174mm L3 =194mm L4 = 194mm
Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290
L1’ (mm) 172 171 171 169 F
L2’ (mm) 173 172 171 170 F
L3’ (mm) 192 191 189 189 F
L4’ (mm) 192 191 191 188 F
Average
deflection,
δave (mm)
1.75 2.75 3.5 5
23
Square
L1 = 177mm L2 = 173mm L3 =196mm L4 = 192mm
Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290
L1’ (mm) 175 174 173 173 172 172 171 169 F
L2’ (mm) 172 172 172 171 171 170 169 168 F
L3’ (mm) 194 193 193 193 192 192 191 190 F
L4’ (mm) 192 192 192 191 190 189 189 187 F
Average
deflection,
δave (mm)
1.25 1.75 2 2.5 3.25 3.75 4.5 6
Triangle
L1 = 174mm L2 = 173mm L3 =195mm L4 = 194mm
Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290
L1’ (mm) 173 172 172 171 170 169 F
L2’ (mm) 172 172 171 171 170 168 F
L3’ (mm) 194 193 193 191 190 189 F
L4’ (mm) 193 193 192 192 191 189 F
Average
deflection,
δave (mm)
1 1.5 2 2.75 3.75 5.25
24
Hexagon
L1 = 174mm L2 = 174mm L3 =194mm L4 = 195mm
Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290
L1’ (mm) 174 173 173 172 172 171 171 170 169 168 167 F
L2’ (mm) 174 173 172 172 172 171 170 170 170 170 168 F
L3’ (mm) 193 193 193 192 192 192 191 190 189 188 187 F
L4’ (mm) 194 194 193 193 193 192 192 191 190 189 188 F
Average
deflection,
δave (mm)
0.5 1 1.5 2 2 2.75 3.25 4 4.75 5.5 6.75
