1. Modeling Atomic Scale Interfaces Using CZM in
Carbon Nanotube Based Composites
NAMAS CHANDRA
Department of Mechanical Engineering
Florida State/Florida A&M University
Tallahassee FL 32310
First I would like to thank Dr. Curtin for inviting me. We have fairly a good chance that we will strongly interact with Brown through MRSEC or other programs.
I like to take the opportunity to explain the uniqueness of FAMU-FSU College of Engineering in Tallahassee, Fl.
Santa Fe, New Mexico
AFOSR Contract Review Meeting
August 30- September 2, 2005

2. Quantum corral of 48 iron atoms on copper surface
The Scale of Things -- Nanometers and More
Things Natural
Things Manmade
The Microworld
0.1 nm
1 nanometer (nm)
0.01 mm
10 nm
0.1 mm
100 nm
1 micrometer (mm)
10 mm
100 mm
1 millimeter (mm)
1 cm
10-2 m
10-3 m
10-4 m
10-5 m
10-6 m
10-7 m
10-8 m
10-9 m
10-10 m
Visible
The Nanoworld
1,000 nanometers =
Infrared
Ultraviolet
Microwave
Soft x-ray
1,000,000 nanometers =
Ant
~ 5 mm
Head of a pin
1-2 mm
Dust mite
200 mm
21st Century Challenge
Combine nanoscale building blocks to make novel functional devices, e.g., a photosynthetic reaction center with integral semiconductor storage
MicroElectroMechanical devices
mm wide
Fly ash
~ mm
Human hair
~ mm wide
Red blood cells
with white cell
~ 2-5 mm
Red blood cells
Pollen grain
Zone plate x-ray “lens” Outermost ring spacing ~35 nm
ATP synthase
~10 nm diameter
Nanotube electrode
Nanotube transistor
Nanoscale science, engineering, and technology are emerging fields in which scientists and engineers are beginning to manipulate matter at the atomic and molecular scales level in order to obtain materials and systems with significantly improved properties. Ten nanometers is equal to one-thousandth the diameter of human hair. 
For decades, microstructures – which are thousands of times larger than nanostructures – have formed the basis for our current technologies, e.g., ceramics and alloy fabrication and electronics. Although microstructures are small on the scale of direct human experience, their physics is still largely the same as that of macroscopic systems. 
However, nanostructures are fundamentally different. Their characteristics – especially their electronic and magnetic characteristics – are often significantly different from the same material in the bulk. Nanostructures are, in a sense, a unique state of matter – one with particular promise for new and potentially very useful products.
Exploring the science of nanostructures has become, in just a few years, a new theme common to many disciplines. In electronics nanostructures represent the limiting extension of Moore's law and classical devices to small devices, and they represent the step into quantum devices and fundamentally new processor architectures. In catalysis, nanostructures are the templates and pores of zeolites and other vitally important structures. In condensed matter physics, the nanometer length scale is the largest one over which a crystal can be made essentially perfect. In materials sciences, fabrication using nanostructures results in alloys and composites with radically improved properties. In molecular biology, nanostructures are the fundamental machines that drive the cell – histones and proteosomes – and they are components of the mitochondrion, the chloroplast, the ribosome, and the replication and transcription complexes. The ability to precisely control the arrangements of impurities and defects with respect to each other, and the ability to integrate perfect inorganic and organic nanostructures, holds forth the promise of a completely new generation of advanced composites. 
As part of the National Nanotechnology Initiative, DOE’s Office of Science is supporting investigators in universities and national laboratories in various areas of nanoscience. In addition, new Nanoscale Science Research Centers will provide critically needed user facilities for synthesis, processing, fabrication, and analysis of materials at the nanoscale.
Quantum corral of 48 iron atoms on copper surface
positioned one at a time with an STM tip
Corral diameter 14 nm
Carbon nanotube
~2 nm diameter
DNA
~2-1/2 nm diameter
Atoms of silicon
spacing ~tenths of nm
Office of Basic Energy Sciences
Office of Science, U.S. DOE
Version

3. Note on Molecular Dynamics
Given for one instance an intelligence which would comprehend all forces by which nature is animated and the respective situation of beings who compose it ……… Nothing would be uncertain and the future , as the past, would be present to its eyes
Laplace, 1814
Limitations
Given a geometric configuration of atoms, we can compute all the future configurations if we can compute the motion of each atom as a function of time if we know how the atoms will move under mutually interacting forces
Interacting forces given by potential energy functions; Right function or series of functions critical
Space scale
1 μm3 of Al contains about 1010 atoms
Time Scale
1 step= 1fs : For simulation of 1μs need 109 steps
AMML

4. Carbon Nanotubes (CNTs)
CNTs can span 23,000 miles without failing due to its own weight.
CNTs are 100 times stronger than steel.
Many times stiffer than any known material
Conducts heat better than diamond
Can be a conductor or insulator without any doping.
Lighter than feather.
AMML

5. Carbon Nanotubes (CNT)
Carbon Nanotubes: Graphite sheet rolled into a tube
Single wall and Multiwall nanotubes
Zigzag, armchair and chiral nanotubes
Length ~ 100 nm to few m Diameter~ 1 nm
Carbon nanotube is one example of a nanoscale element; it is an example of a molecular structure that has extremely interesting electrical, magnetic, electronic, optical and structural properties. Combining them in novel ways give us multi functional capabilities. To the materials and mechanics community, CNT is an example of numerous macromolecules that will be soon available; how do we use them in practical applications? How do we process them and exploit their characteristics? How do we model them? To what extent, our continuum based knowledge be applied? What new theory, modeling, simulation tools and processing techniques are needed?
My belief is it is not a question of will they work; but when and how?
Applications
E ~ 1 TPa Strength ~150 GPa
Conductivity depends on chirality
High strength
composites
Energy
storage
Nano sensors
Medical applications
Nano
electronics
Functional
composites
Do these properties extend to
CNT reinforced composites ?
AMML

6. Do we realize the potentials of CNT in PMC?
Parallel model
Upper Bound
Answer is No-We do not
Series model
Lower Bound
First practical mechanics use is to use in polymeric matrix composites-no technical problem of using in metallic or ceramic matrices.
AMML

7. Factors affecting interfacial properties
Asperities
Interfacial chemistry
Mechanical effects
Origin: Surface irregularities inherent in the interface
Issues: Affects interface fracture process through mechanical loading and friction
Approach: Incorporate roughness effects in the interface model; Study effect of generating surface roughness using: Sinusoidal functions and fractal approach; Use push-back test data and measured roughness profile of push-out fibers for the model.
Residual stress
Origin: Chemical reaction during thermal-mechanical Processing and service conditions, e.g. Aging, Coatings, Exposures at high temp..
Issues: Chemistry and architecture effects on mechanical properties.
Approach: Analyze the effect of size of reaction zone and chemical bond strength (e.g. SCS-6/Ti matrix and SCS-6/Ti matrix )
Origin: CTE mismatch between fiber and matrix.
Issues: Significantly affects the state of stress at interface and hence fracture process
Approach: Isolate the effects of residual stress state by plastic straining of specimen; and validate with numerical models.
Metal/
ceramic/
polymer
Interface
CNTs
This then becomes well reasoned and studied. The interfaces-except now at nanosclaes; only problem is we do not even know how do we define a surface at atomic scale leave alone interfaces.
Properties affected
Trans. & long.
Stiffness/strength
Fatigue/Fracture
Thermal/electronic/magnetic
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8. Critical Scientific Issues
Critical issues in nanotube composites
Alignment
Dispersion
Load Transfer
Load transfer and to some extant Dispersion affected by interfaces
Interface  Bounding surface with physical / chemical / mechanical discontinuity
CNT-matrix interfaces
Vanderwall’s forces
Mechanical interlocking
Chemical bonding
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9. Some issues in Elastic Modulii computation
Energy based approach
Assumes existence of W. Then,
Validity of W based on potentials questionable under conditions such as temperature, pressure
Value of E depends on selection of strain.
Stress –Strain approach
Circumvents the above problems
Evaluation of local modulus for defect regions possible
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10. Stress Measures
Virial stress
BDT stress
Lutsko stress

11. Strain calculation in nanotubes
Defect free nanotube  mesh of hexagons
Strain calculated using displacements and derivatives shape functions in a local coordinate system formed by tangential (X) and radial (y) direction of centroid and tube axis
Area weighted averages of surrounding hexagons considered for strain at each atom
Similar procedure for pentagons and heptagons
Updated Lagrangian scheme is used in MD simulations

12. Elastic modulus of defect free CNT
-Defect free (9,0) nanotube
with periodic boundary
conditions
-Strains applied using
conjugate gradients energy
minimization
All stress and strain
measures yield a Young’s
modulus value of 1.002TPa
Values in literature range
from 0.5 to 5.5 Tpa. Mostly
around 1Tpa

13. Effect of Diameter
stiffness values of defects for various tubes with different diameters do not change significantly
Stiffness in the range of 0.61TPa to 0.63TPa for different (n,0) tubes
Mechanical properties of defect not significantly affected by the curvature of nanotube
stress strain curves for different (n,0)
tubes with varying diameters.

14. Residual stress at zero strain
Stress is present at zero strain values.
This corresponds to stress due to curvature
It is found to decrease with increasing diameter
Basis for stress calculation  graphene sheet
Brenner et. al.1 observed similar variation in energy at zero strain
Reflects the concept of processing induced residual stresses. We take the undeformed graphite sheets as the stress-free configuration.
1 Robertson DH, Brenner DW and Mintmire 1992
N. Chandra et. al., Phys. Rev B 69, (2004)

15. CNT with defect
Lutsko stress profile for (9,0) tube with type I defect shown below
Stress amplification observed in the defected region
This effect reduces with increasing applied strains
In (n,n) type of tubes there is a decrease in stress at the defect region
Next we examine the effect of defects on the local and global stiffness. This is the simplest form of defect with one rotated bond.
Shet and Chandra, J. Mat. Sci, 40, (2005)
Shet, Chandra, Namilae, Mech. Adv. Mat. Str,,55-65, (2005).

16. Evolution of stress and strain
Strain and stress evolution at 1,3,5 and 7 % applied strains
Stress based on BDT stress

17. Local elastic moduli of CNT with defects
Type I defect  E= 0.62 TPa
Type II defect  E=0.63 Tpa
Reduction in stiffness in the presence of defect from 1 Tpa
-Initial residual stress indicates additional forces at zero strain
-Analogous to formation energy
Namilae and Chandra, Chem.. Phy. Letters 387, 4-6, , (2004)

18. Functionalized Nanotubes
Change in hybridization (SP2 to SP3)
Experimental reports of different chemical attachments
Application in composites, medicine, sensors
Functionalized CNT are possibly fibers in composites
Sensors check how ? Pyrene what check?
How does functionalization affect the elastic and inelastic deformation behavior and fracture

19. Functionalized nanotubes
Increase in stiffness observed by functionalizing
Vinyl and Butyl
Hydrocarbons
T=77K and 3000K
Lutsko stress
Stiffness increase is more for higher number of chemical attachments
Stiffness increase higher for longer chemical attachments

20. Local Stiffness of Functionalized CNTs
Local Stiffness of Functionalized CNTs
Stiffness increase is more for higher number of chemical attachments
Stiffness increase higher for longer chemical attachments
Namilae and Chandra, Chem. Phy. Letters 387, 4-6, , (2004)

21. Contour plots Stress contours with one chemical attachment.
Stress fluctuations are present

22. Radius variation
Increased radius of curvature at the attachment because of change in hybridization
Radius of curvature lowered in adjoining area
Sp3 Hybridization here

23. Evolution of defects in tension
Keep the cnt_tension_defects.mov in the same folder (quicktime movie)
Defects Evolve at much lower strain of 6.5 % in CNT with chemical attachments
Onset of plastic deformation at lower strain. Reduced fracture strain
Defects Evolve
Effect of functionalization
on defect evolution

24. Different Fracture Mechanisms ?
Fracture Behavior Different
Fracture happens by formation of defects, coalescence of defects and final separation of damaged region in defect free CNT
In Functionalized CNT it happens in a brittle manner by breaking of bonds
Namilae and Chandra, Chem. Phy. Letters 387, 4-6, , (2004)

25. Compressive Behavior of CNT composites (weak)
Weak Interfaces
Compressive behavior of CNT in polymer matrix with
Weak interface

26. Compressive Behavior of CNT composites (strong)
Strong Interfaces
Deformation mechanism changes
Mechanical Response significantly altered
Strong Interfaces

27. Effect of interstitial on tensile behavior of MWNTs
Tensile simulation without functionalization
Tensile simulation with functionalization
Compressive response of (6,0)(15,0) nanotube with and without chemical bonding between the walls of nanotubes.
Interstitial atoms increase the load transfer in tension, and both stiffness and strength increase
Interstitial atoms in multiwall nanotubes
Paper under review

28. Atomic simulation of CNT pullout test
Simulation conditions
Corner atoms of hydrocarbon attachments fixed
Displacement applied as shown 0.02A/1500 steps
T=300K

29. Simulation of pull-out test
Energy for debonding of chemical attachment = 3eV

30. Interfacial shear
Interfacial shear measured as reaction force of fixed atoms
Max load
Typical interface shear force pattern. Note zero force after
Failure (separation of chemical attachment)
After Failure
250,000 steps

31. Debonding and Rebonding of Interfaces
Failure

32. Debonding and Rebonding
Matrix
Matrix
Energy for debonding of chemical attachment 3eV
Strain energy in force-displacement plot 20 ± 4 eV
Energy increase due to debonding-rebonding

33. Various types of Interface Behavior

34. Behavior of different lengths of interfaces
Increasing the length of attachment increases region ‘a’
Decreasing the number of attachments extends region ‘b’

35. Temperature dependence of pullout tests
Force to failure decreases with increasing temperature
Debonding-rebonding behavior at higher temperatures
does not alter the energy dissipation

36. Cohesive zone model for interfaces
Assumptions
Nanotubes deform in linear elastic manner
Interface character completely determined
by traction-displacement plot
Chandra et. a., IJSS, 39, , (2002)

37. Cohesive zone Models for nanoscale interfaces
Namilae and Chandra JEMT, , (2005).

38. Finite element simulation
ABAQUS with user element for cohesive zone model
Linear elastic model for both matrix and CNT
About 1000 elements and 100 elements at interface

39. Parametric studies Variation of CNT content for different interface
strengths

40. Parametric studies
Variation of matrix stiffness for different interface
strengths

41. Parametric studies
Variation of fiber stiffness for different interface
strengths

42. Summary Interfaces play a key role even at micro/nano scales.
Nanoscale effects can be effectively captured using molecular dynamics model (using the right potentials).
MD results can be integrated in an heirarchical model using CZM-Finite Element method
Using Atomistic scale we can determine atomic effect on macro effects.
Understanding the effects of nanoscale interfaces, and interface mechanics will be important in in a number of engineering applications.
AMML

43. Dr. Les Lee, AFOSR, Short Term Grant
Acknowledgement
Dr. Les Lee, AFOSR, Short Term Grant
Nanomechanics Group:
Prof. A. Srinivasan, U. Chandra
Dr. S. Namilae, C. Shet
S. Guan, M. Naveen, Girish, Yanan, J. Kohle, Jason Montgomery
First of all I would like to thank Professor Somnath Ghosh for the kind invitation. It is my great pleasure and privilege to present him with the official certificate as a FELLOW of ASME. He is a very prominent and young researchers in the field we are discussing today. He has some pioneering work in microstructure based numerical modeling using voronoi cell method. He gets the pin, and a badge. Today’s topic relates to modeling materials to build useful devices and structures. The issue is what is the best way to not only use existing materials but how can we help develop new materials. It turns out this modeling should be done at different levels. Hierarchy refers to a specific order.
FuAlso contributed by ARO, NSF, FSURF
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44. Further References MD Papers: AMML
N. Chandra, S. Namilae, and C. Shet, Local elastic properties of carbon nanotubes in the presence of Stone -Wales defects, Physical Review B, 69, , (2004).
S. Namilae, N. Chandra, and C. Shet, Mechanical behavior of functionalized nanotubes, Chemical Physics Letters 387, 4-6, , (2004)
N. Chandra and S. Namilae, Multi-scale modeling of nanocystalline materials, Materials Science Forum, , 19-27, (2004)..
C. Shet, N. Chandra, and S. Namilae, Defect-defect interaction in carbon nanotubes under mechanical loading, Mechanics of Advanced Materials and Structures, (2004) (in print).
C. Shet, N. Chandra, and S. Namilae, Defect annihilations in carbon nanotubes under thermo-mechanical loading, Journal of Material Sciences , (in print).
S. Namilae, C. Shet, N. Chandra and T.G. Nieh, Atomistic simulation of grain boundary sliding in pure and magnesium doped aluminum bicrystals, Scripta Materialia 46, (2002).
S. Namilae, C. Shet, N. Chandra and T.G. Nieh, Atomistic simulation of the effect of trace elements on grain boundary of aluminum, Materials Science Forum, , , (2001).
C. Shet, H. Li and N. Chandra, Interface Models for grain boundary sliding and migration, Materials Science Forum , , (2001).
N. Chandra and P. Dang, Atomistic Simulation of Grain Boundary Sliding and Migration, Journal of Materials Science, 34, 4, (1998).
N. Chandra, Mechanics of Superplastic Deformations at Atomic Scale, Materials Science Forum, 304, 3, (1998).
First of all I would like to thank Professor Somnath Ghosh for the kind invitation. It is my great pleasure and privilege to present him with the official certificate as a FELLOW of ASME. He is a very prominent and young researchers in the field we are discussing today. He has some pioneering work in microstructure based numerical modeling using voronoi cell method. He gets the pin, and a badge. Today’s topic relates to modeling materials to build useful devices and structures. The issue is what is the best way to not only use existing materials but how can we help develop new materials. It turns out this modeling should be done at different levels. Hierarchy refers to a specific order.
AMML

45. Further References Cohesive Zones: AMML
C. Shet and N. Chandra, The effect of the shape of the cohesive zone curves on the fracture responses, Mechanics of Advanced Materials and Structures, 11(3), , (2004).
N. Chandra and C. Shet, A Micromechanistic Perspective of Cohesive Zone Approach in Modeling Fracture. Computer Modeling in Engineering & Sciences, CMES, Computer Modeling in Engineering and Sciences, 5(1), 21-34, (2004))
H. Li and N. Chandra, Analysis of Crack Growth and Crack-tip Plasticity in Ductile Material Using Cohesive Zone Models, International Journal of Plasticity, 19, , (2003).
N. Chandra, Constitutive behavior of Superplastic materials, International Journal for nonlinear mechanics, 37, , (2002).
N. Chandra, H. Li, C. Shet and H. Ghonem, Some Issues in the Application of Cohesive Zone Models for Metal-ceramic Interface. International Journal of Solids and Structures, 39, , (2002).
C. Shet and N. Chandra, Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Process, ASME Journal of Engineering Materials and Technology, 124, , (2002).
N. Chandra, Evaluation of Interfacial Fracture Toughness Using Cohesive Zone Models, Composites Part A: Applied Science and Manufacturing, 33, , (2002).
C. Shet, H. Li and N. Chandra, Interface Models for grain boundary sliding and migration, Materials Science Forum , , (2001).
First of all I would like to thank Professor Somnath Ghosh for the kind invitation. It is my great pleasure and privilege to present him with the official certificate as a FELLOW of ASME. He is a very prominent and young researchers in the field we are discussing today. He has some pioneering work in microstructure based numerical modeling using voronoi cell method. He gets the pin, and a badge. Today’s topic relates to modeling materials to build useful devices and structures. The issue is what is the best way to not only use existing materials but how can we help develop new materials. It turns out this modeling should be done at different levels. Hierarchy refers to a specific order.
AMML

46. Further References Interface Mechanics: AMML
N. Chandra and H. Ghonem, Interfacial Mechanics of push-out tests: theory and experiments, Composites Part A: Applied Science and Manufacturing, 32, 3-4, , (2001).
D. Osborne, N. Chandra and, H. Ghonem, Interface Behavior of Ti Matrix Composites at elevated temperature, Composites Part A: Applied Science and Manufacturing, 32, 3-4, , (2001).
N. Chandra, S. C. Rama and Z. Chen, Process Modeling of Superplastic materials, Materials Transactions JIM, 40, 8, (1999).
S. R. Voleti, C. R. Ananth and N. Chandra, Effect of Fiber Fracture and Matrix Yielding on Load Sharing in Continuous Fiber Metal Matrix Composites, Journal of Composites Technology and Research, 20, 4, , (1998).
C.R. Ananth, S. R. Voleti and N. Chandra, Effect of Fiber Fracture and Interfacial Debonding on the Evolution of Damage in Metal Matrix Composites, Composites Part A, 29A, , (1998)
S. Mukherjee, C. R. Ananth and N. Chandra, Effect of Interface Chemistry on the Fracture Properties of Titanium Matrix Composites, Composites Part A, 29A, , (1998)
S. R. Voleti, C. R. Ananth and N. Chandra, Effect of Interfacial Properties on the Fiber Fragmentation Process in Polymer Matrix Composites, Journal of Composites Technology and Research, 20, 1, 16-26, (1998).
S. Mukherjee, C. R. Ananth and N. Chandra, Evaluation of Fracture Toughness of MMC Interfaces Using Thin-slice Push-out Tests, Scripta Materialia, 36, (1997).
C. R. Ananth, S. Mukherjee, and N. Chandra, Effect of Time Dependent Matrix Behavior on the Evolution of Processing-Induced Residual Stresses in Metal Matrix Composites, Journal of Composites Technology and Research 19, 3, , (1997).
S. Mukherjee, C. R. Ananth and N. Chandra, Effect of Residual Stresses on the Interfacial Fracture Behavior of Metal Matrix Composites, Composite Science and Technology, 57, , (1997).
C. R. Ananth and N. Chandra, Elevated temperature interfacial behavior of MMC: a computational study, Composites: Part A, 27A, (1996).
S. R. Voleti, N. Chandra and J R. Miller, Global-Local Analysis of Large-scale Composite Structures Using Finite Element Methods, Composites & Structures, 58, 3, , (1996).
C. R. Ananth and N. Chandra, Evaluation of Interfacial Properties of Metal Matrix Composites from Fiber Push-out Tests, Mechanics of Composite Materials and Structures, 2, (1995).
Xie, Z.Y. and N. Chandra, Application of GPS Tensors to Fiber Reinforced Composites, Journal of Composite Materials, 29, , (1995).
S. Mukherjee, H. Garmestani and N. Chandra, Experimental Investigation of Thermally Induced Plastic Deformation of MMCs Using Backscattered Kikuchi Method, Scripta Metallurgica et Materialia, 33, 1, (1995).
N. Chandra and C.R. Ananth, Analysis of Interfacial Behavior in MMCs and IMCs Using Thin Slice Push-out Tests', Composite Science and Technology, 54, 1 , , (1995).
C. R. Ananth and N. Chandra, Numerical Modeling of Fiber Push-Out Test in Metallic and Intermetallic Matrix Composites-Mechanics of the Failure Process', Journal of Composite Materials, 29, 11, , (1995).
N. Chandra., C.R. Ananth and H. Garmestani, Micromechanical Modeling of Process-Induced Residual Stresses in Ti-24Al-11Nb/SCS6 Composite', Journal of Composite Technology and Research, 17, 37-46, (1994).
Z. Xie and N. Chandra, Application of Equation Regulation Method to Multi-Phase Composites', International Journal of Non-linear Mechanics, 28, 6, , (1993).
First of all I would like to thank Professor Somnath Ghosh for the kind invitation. It is my great pleasure and privilege to present him with the official certificate as a FELLOW of ASME. He is a very prominent and young researchers in the field we are discussing today. He has some pioneering work in microstructure based numerical modeling using voronoi cell method. He gets the pin, and a badge. Today’s topic relates to modeling materials to build useful devices and structures. The issue is what is the best way to not only use existing materials but how can we help develop new materials. It turns out this modeling should be done at different levels. Hierarchy refers to a specific order.
AMML

47. Buckling Behavior-Neat CNT

48. Buckling Behavior-Functionalized CNT

49. Compressive loading of carbon nanotubes
Using surface modified CNT in composites improves resistance to buckling

50. Thermal Stresses
Thermal stress is higher for functionalized nanotube in polymer matrix

51. Effect of capped and uncapped on the compressive behavior of MWNTs
Capped compressive simulation
Energy per atom experienced by the inner tube in (6,0) (15,0) double walled
Uncapped compressive simulation
Inner tube is loaded in compression, even with weak inter wall interaction