1. Analysis of Elastic Behaviour of Honeycombs and
Auxetic Materials with Variation in its Cell Geometry
MS THESIS PRESENTED BY
VISHWATEJ MANE
ADVISOR- PROF. MAEN ALKHADER
DEPARTMENT OF MECHANICAL ENGINEERING
STONY BROOK UNIVERSITY

2. Introduction
Honeycombs used as core in sandwich panels of lightweight structure
Progressive collapse with retaining functionality
Auxetic materials exhibits NPR
Auxetic material has improved Shear, indentation resistance and fracture toughness
Potential applications in defense and aerospace
Relative density
Outline of the study

3. Deformation mechanism and Theory
Flexure, stretching and hinging mechanism
Cell Geometry and General Mathematical model
“ I.G. Masters and K E Evans, ”Models for the elastic deformation of honeycombs”, composite
strucutres,0263-8223/96

4. Models for FEA analysis
Sr. no. cell angle Wall thickness (in mm) Relative density (ρ*/ρs)
1. 30 0.15 0.178748
0.2 0.237965
0.25 0.297182
0.3 0.357496
2. 20 0.15 0.184136
0.2 0.2462415
0.25 0.307257
0.3 0.3693623
3. 10 0.15 0.1915415
0.2 0.281822
0.25 0.3525827
0.3 0.4233433
4. 5 0.15 0.2157475
0.2 0.28728
0.25 0.358822
0.3 0.431495
Sr. no. cell angle Wall thickness (in mm) Relative density (ρ*/ρs)
5. -5 0.15 0.255294
0.2 0.34
0.25 0.425
0.3 0.510589
6. -10 0.15 0.28385
0.2 0.379219
0.25 0.473463
0.3 0.568828
7. -20 0.15 0.369647
0.2 0.49368
0.25 0.616489
0.3 0.740524

5. FEA Model development
Development of Geometry for different cellular models
In Property module used Al 6061 as material
ρ=2700 kg/m3, E= 68950 MPa, ν= 0.3, plastic strain
Static, general analysis type
meshing - structured Quad shell elements (S4R)
Node Sets- TOP, BOTTOM, LEFT, RIGHT

6. BCs for Poisson’s ratio ν21
Hex30 model
U3=0
Bottom, U2=UR1=UR2=UR3=0
Top, UR1=UR2=UR3=0
U2= -2.5

7. BCs for Poisson’s ratio ν12
Hex30 model
U3= 0
LEFT, U1=UR1=UR2=UR3=0
RIGHT, UR1=UR2=UR3=0
U1= -2.5

8. FEA results and Trends for Honeycombs
Hex 30, t= 0.25mm Hex 10, t=0.3mm

9. Stress 22, Young’s Modulus E22 and Poisson’s ratio ν21 vs. Strain 22 for Hex05 model and Hex10 model

10. Stress 22, Young’s Modulus E22 and Poisson’s ratio ν21 vs. Strain 22 for Hex20 model and Hex30 model

11. FEA Results and Trends for Auxetics
Hex -05, t= 0.2mm Hex -10, t= 0.15mm

12. Stress 22, Young’s Modulus E22, Poisson’s ratio ν21 vs. Strain 22 for Hex-05 model and Hex-10 model

13. Stress 22, Young’s Modulus E22 and Poisson’s ratio ν21 vs. Strain 22 curve for Hex -20 model

14. FEA Results and Trends in honeycombs 11 direction
Hex30, t=0.3mm Hex20, t=0.25mm

15. Stress 11, Young’s Modulus E11 and Poisson’s ratio ν12 vs. Strain 11 for Hex 05 model and Hex10
model

16. Stress 11, Young’s Modulus E11 and Poisson’s ratio ν12 vs. Strain 11 for Hex20 model and Hex30
model

17. FEA Results and Trends in Auxetics
Hex-05, t=0.2mm Hex-10, t=0.15mm

18. Stress 11, Young’s Modulus E11 Poisson’s ratio ν12 vs. Strain 11 for Hex -05 model and Hex-10 model

19. Stress 11, Young’s Modulus E11 and Poisson’s ratio ν12 vs. Strain for Hex-20 model

20. Specifications of 3D printed models
MakerBot Replicator 2.0 3D printer
Sr No. Model by cell angle geometry
(wall thickness= 0.8mm)
Constant width= 15mm
Length
in mm
Height
in mm
1 -20 28.33 27.85
2 -10 24.94 25.45
3 -5 24.12 24.35
4 5 24.15 26.02
5 10 29.63 28.69
6 20 28.02 25.94
7 30 26.38 27.54

21. 3D printed Honeycombs test results
Stress vs Strain curves over entire period of compression test on MTS machine
0
5
10
15
20
25
0 0.1 0.2 0.3
StressY
Strain Y
Hex 05
0
2
4
6
8
10
12
14
16
18
0 0.05 0.1 0.15 0.2 0.25
StressY
Strain Y
Hex 10
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3
StressY
Strain Y
Hex 20
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3
StressY
Strain Y
Hex 30

22. Compression Test

23. 3D printed Auxetic test results
0
5
10
15
20
25
30
0 0.05 0.1 0.15 0.2 0.25 0.3
StressY
Strain Y
Hex-05
0
2
4
6
8
10
12
14
16
18
0 0.05 0.1 0.15 0.2 0.25 0.3
StressY
Strain Y
Hex-10
0
2
4
6
8
10
12
14
16
18
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
StressY
Strain Y
Hex-20

24. Compression Test

25. Elastic Region for honeycombs
Constant Modulus over these sections in elastic region
y = 480.47x - 3
R² = 0.9879
-5
0
5
10
15
20
25
0 0.02 0.04 0.06
StressY
Strain
Hex 05
y = 387.22x - 1
R² = 0.9957
-2
0
2
4
6
8
10
12
14
16
18
0 0.01 0.02 0.03 0.04 0.05
StressY
Strain Y
Hex 10
y = 198.42x - 0.25
R² = 0.9975
-1
0
1
2
3
4
5
6
0 0.01 0.02 0.03 0.04
StressY
Strain Y
Hex 20
y = 193.2x - 0.5
R² = 0.9968
-1
0
1
2
3
4
5
6
7
8
0 0.01 0.02 0.03 0.04
StressY
Strain Y
Hex 30

26. Elastic region for Auxetic
Constant Modulus over these sections in elastic region
y = 514.62x - 4
R² = 0.9838
-10
-5
0
5
10
15
20
25
30
0 0.01 0.02 0.03 0.04 0.05 0.06
StressY
Strain Y
Hex-05
y = 407.26x - 1.5
R² = 0.9946
-5
0
5
10
15
20
0 0.01 0.02 0.03 0.04 0.05
StressY
Strain Y
Hex-10
y = 422.82x - 2
R² = 0.9898
-4
-2
0
2
4
6
8
10
12
14
16
0 0.01 0.02 0.03 0.04 0.05
StressY
Strain Y
Hex-20

27. Poisson’s ratio ν21 for honeycombs
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.1 0.15 0.2 0.25 0.3 0.35
ν21
longitudnal strain
hex30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.05 0.1 0.15 0.2 0.25 0.3
ν21
longitudnal strain
hex20
0
0.2
0.4
0.6
0.8
1
1.2
0.05 0.1 0.15 0.2 0.25
ν21
longitudnal strain
hex10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.1 0.15 0.2 0.25 0.3
ν21
longitudnal strain
hex05

28. Poisson’s ratio ν21 for Auxetic
-2.5
-2
-1.5
-1
-0.5
0
0.05 0.1 0.15 0.2 0.25 0.3
ν21
longitudnal strain
hex-05
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.05 0.1 0.15 0.2 0.25 0.3
ν21
longitudnal strain
hex-10
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35
ν21
longitudnal strain
hex-20

29. 3D printed Honeycombs test results
Stress vs. strain curve for compression in 11-direction on MTS
0
1
2
3
4
5
6
7
0 0.05 0.1 0.15 0.2 0.25 0.3
Stress11
strain 11
Hex 05
0
1
2
3
4
5
6
0 0.1 0.2 0.3
stress11
Strain 11
Hex 10
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.05 0.1 0.15 0.2
Stress11
Strain 11
Hex 20
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4
Stress11
Strain 11
Hex 30

30. 3D printed Auxetic test results
Stress vs. strain curve for compression in 11-direction on MTS
0
1
2
3
4
5
6
7
8
9
0 0.05 0.1 0.15 0.2 0.25 0.3
Stress11
Strain 11
Hex -05
0
1
2
3
4
5
6
7
8
9
10
0 0.1 0.2 0.3 0.4
Stress11
Strain 11
Hex -10
0
2
4
6
8
10
12
14
16
18
0 0.05 0.1 0.15 0.2 0.25 0.3
Stress11
Strain 11
Hex -20

31. Compression Test

32. Compression Test

33. Elastic region for honeycombs
Constant modulus over these sections for compression 11-direction
y = 146.79x - 0.25
R² = 0.9986
-1
0
1
2
3
4
5
6
0 0.01 0.02 0.03 0.04 0.05
Stress
Strain
Hex 05
y = 107.61x - 0.2
R² = 0.9964
-1
0
1
2
3
4
5
0 0.01 0.02 0.03 0.04 0.05
Stress
strain
Hex 10
y = 79.143x - 0.1
R² = 0.9961
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
0 0.01 0.02 0.03 0.04 0.05
Stress
Strain
Hex 20
y = 181.33x - 0.5
R² = 0.9941
-1
0
1
2
3
4
5
6
0 0.01 0.02 0.03 0.04
Stress
Strain
Hex 30

34. Elastic region for Auxetics
Constant modulus over these sections for compression 11-direction
y = 161.12x - 1
R² = 0.9804
-2
-1
0
1
2
3
4
5
6
7
0 0.01 0.02 0.03 0.04 0.05
Stress
Strain
Hex -05
y = 70.312x - 0.1
R² = 0.9935
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.01 0.02 0.03 0.04 0.05 0.06
Stress
Strain
Hex -10
y = 132.51x - 0.5
R² = 0.9954
-1
0
1
2
3
4
5
6
0 0.01 0.02 0.03 0.04 0.05
stress
Strain
Hex -20

35. Poisson’s ratio ν12 for honeycombs
0
0.1
0.2
0.3
0.4
0.5
0.6
0.1 0.2 0.3 0.4 0.5
ν12
longitudnal strain
hex30
0
0.05
0.1
0.15
0.2
0.25
0.3
0.1 0.15 0.2 0.25 0.3 0.35
ν12
longitudnal strain
hex20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.1 0.15 0.2 0.25
ν12 longitudnal strain
hex10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.05 0.1 0.15 0.2 0.25 0.3
ν12
longitudnal strain
hex05

36. Poisson ratio ν12 for Auxetic
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.05 0.1 0.15 0.2 0.25 0.3 0.35
ν12
longitudnal strain
hex-10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.05 0.1 0.15 0.2 0.25 0.3
ν12
longitudnal strain
hex-20

37. Conclusions for honeycomb samples
FEA methods can be used to predict trends in elastic constants
E22 and E11 increases with increase in relative density
E22 increases with decrease in cell angle closer to zero
E11 increases with increase in angle closer to 30 degrees
Trends of ν21 and ν12 are linear and independent of relative density in elastic region
ν21 increase with decrease in cell angle closer to 0
ν12 increases with increase in cell angle closer to 30
Waviness in stress vs. strain trend in plastic region represents cell arrays collapse

38. Conclusions for Auxetic samples
E22 and E11 increases with relative density
Exhibits Negative Poisson’s ratio (NPR) property
Trends ν21 and ν12 independent of relative density in elastic region
ν21 increases with decrease in cell angle
ν12 decreases with increase in cell angle
Waviness in stress, Poisson’s ratio vs. strain trends represents cell arrays collapse

39. Young’s modulus 22 vs. cell angle
0
5000
10000
15000
20000
25000
30000
5 10 20 30 -5 -10 -20
Young'sModulusE22
Cell angle in degrees
t=0.15 mm t= 0.2 mm t= 0.25 mm t=0.3 mm

40. Poisson’s ratio 21 vs. cell angle
-6
-4
-2
0
2
4
6
5 10 20 30 -5 -10 -20
Poisson'sratioν21
Cell angle in degrees
t=0.15 mm t=0.2 mm t=0.25 mm t=0.3 mm

41. Young’s modulus 11 vs cell angle
0
500
1000
1500
2000
2500
3000
3500
5 10 20 30 -5 -10 -20
Young'sModulusE11
cell angles in degrees
t=0.15 mm t=0.2 mm t=0.25 mm t=0.3 mm

42. Poisson’s ratio12 vs cell angle
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
5 10 20 30 -5 -10 -20
Poisson'sratioν12
Cell angles in degrees
t=0.15 mm t=0.2 mm t=0.25 mm t=0.3 mm

43. Bibliography
I.G. Masters and K E Evans, “ Models for the elastic deformation of honeycombs”
composite structures,0263-8223/96
Q.Liu,” Literature Review: Material with Negative Poisson’s ratio and potential
applications to aerospace and defence” DSTO-GD-0472, August 2006
Yanping Liu and Hong Hu, “ A Review on Auxetic structures and polymeric materials”,
ISSN 1992-2248, May 2010
M. Bianchi, S. Frontoni, F. Scarpa, and C.W.Smith, “Density change during the
manufacturing process of PU-PE open cell Auxetic foams”, pssb.201083966, May 2010
Kim Alderson, Andrew Alderson, Naveen Ravirala, Virginia Simkins, and Philip Davies,
“Manufacture and characterization of thin flat and curved Auxetic foam sheets”,
pssb.201084215, March 2012