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Damodara Reddy's picture

What are the appropriate values of Young's modulus and wall thickness of single-walled carbon nanotubes (SWCNTs)?

Hi All, Simulations and experimental results show the wide range of values for Young’s modulus (0.5 to 5.5 TPa) and wall thickness (0.066 to 0.34 nm) of carbon nanotubes (CNTs) in literature. Most of the published results say that the set of values (Young’s modulus and wall thickness of CNT) are 1 TPa  and 0.34 nm, and the product is around 0.34 TPa-nm. In my point of view this set of values may be appropriate for multi-walled carbon nanotubes. Can we use the same set of values for analysis of single-walled carbon nanotubes (SWCNTs)?  The interlayer distance between the graphene layers is 0.34 nm. Can we use this value as wall thickness of SWCNT or do we need to use atomic thickness instead of 0.34 nm?


Perturbation analysis of a wavy film in a multi-layered structure

A free surface in a multi-layer can experience an undulation due to surface diffusion during fabrication or etching process. In order to analyze the undulation, the elasticity solution for the undulating film is needed. Considering the undulation as a perturbation of a flat surface, a boundary value problem for 2D elasticity is formulated. The solution procedure is straightforward, but very lengthy especially for a multi-layer.

Arun K. Subramaniyan's picture

Equivalence of Virial stress to Continuum Cauchy Stress

Calculating stresses in MD simulations is a controversial topic. There are two different schools of thought about the equivalence of the virial stress to the continuum Cauchy stress; for and against. Some argue based on momentum balance, that only the potential contribution to the virial stress should be considered as the continuum Cauchy stress. However, others assert that the total virial stress that contains both the kinetic and potential parts is indeed the quantity that corresponds to the Cauchy stress in continuum mechanics. We used a simple thermo-elastic analysis to verify the validity of using the total virial stress as the continuum Cauchy stress and found that the total virial stress is indeed the continuum Cauchy stress.

Guide vanes flutter/vibration

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Greetings co-researchers,

I am currently designing a full-scale Impulse turbine (2 to 3 m diameter, 0.5 hub to tip ratio) for extracting of energy from waves.The turbine will be connected to a shore based device oscillating water column (OWC), so the airflow through the turbine is bidirectional (i.e. reverses as the wave enters and recedes in the OWC). This means we have to use symmetrical entry and exit guide vanes. These vanes are fixed, not movable.·        The guide vanes are slender, approximately; height 700mm, chord length 600mm and thickness 2 to 5mm. Their role is to redirect the air flow from the axial direction to an angle of 60o ·        The rotor rotation speed is low (100 RPM to 1000 RPM). ·        The airflow is incompressible (Mach number < 0.3) and unsteady as it is related to the wave energy, which means the mass flow inlet to the turbine changes randomly (from zero to a maximum value say 10kg/s). One of the good approximations to this airflow is a sinusoid, but even this is extremely difficult to simulate in Fluent 6.2 CFD.I have done some preliminary forced vibration response analysis of the guide vanes. As far as I can see, the main cause of any vibration of the guide vanes would be the changes on pressure caused by the chopping of the flow by the rotor (i.e. the passing frequency of the rotor/guide vanes assembly). I plan to measure these pressure variations using pressure tapings on an experimental turbine test rig. 

Please could you comment whether in your experience the main source of guide vane vibration would be the chopping of the fluid flow by the rotor. Also I would appreciate it if you have done any experimental or analytical data on this problem.

atmaca's picture

Crack Propagation

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I have an investigation on Crack Propagation.

How can i predict the path of a crack.

Please help me!

Giuseppe Carbone's picture

Stick slip instabilities of hot cracks in rubber: The influence of flash temperature

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Here you find a preprint version of a paper published in PRL 95, 114301 (2005) [also see Eur. Phys. J. E. 17, 261-281 (2005)] where the authors present a theory to explain why instabilities, e.g. stick-slip motion, is observed when cracks propagate in rubber materials.

Mike Ciavarella's picture

friction and plasticity: new avenues of research?

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Based on some recent results by Anders Klabring, myself and Jim Barber, showing rigorously that Melan’s theorem only works for a very restricted class of frictional problems, we suggest possible ave

Mike Ciavarella's picture

Some notes on Luan and Robbin's papers on contact and adhesion at atomic scale

As I promised, I start with some brief notes on themes loved by Ken Johnson to hopefully raise some interest for discussion on iMechanica. Regards, Mike

L. Roy Xu's picture

Tensile strength and fracture toughness of nanocomposite materials

Are not as high as we expected although very stiff and strong nanotubes or nanofibers (Young’s modulus E~1000GPa) are added into soft polymer matrices like epoxy (E~4GPa).  In our early investigation on the  systematic mechanical property characterizations of nanocomposites (Xu et al., Journal of Composite Materials, 2004--among top 5 in 2005;and top 10 in 2006 of the Most-Frequently-Read Articles in Journal of Composite Materials.) have shown that there was a very small increase (sometimes even decrease) of critical ultimate tensile/bending strengths, and mode-I fracture toughnesses in spite of complete chemical treatments of the interfacial bonding area, and uniform dispersions of nanofibers (click to view a TEM image). Similar experimental results were often reported in recent years. Therefore, mechanics analysis is extremely valuable before we make these “expensive” nanocomposite materials. Our goal is to provide in-depth mechanics insight, and future directions for nanocomposite development. Till now, nanocomposite materials are promising as multi-functional materials, rather than structural materials. Here we mainly focus on two critical parameters for structural materials: tensile strength and fracture toughness. We notice that other mechanical parameters such as compressive strengths and Young’s moduli of nanocomposite materials have slight increase over their matrices.

Ashkan Vaziri's picture

"Persistence of a pinch in a pipe" by L. Mahadevan, Ashkan Vaziri and Moumita Das

The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology.

MichelleLOyen's picture

Viscoelastic Contacts

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I was a little bit surprised in the introduction of this new forum to see mention of elastic and plastic contacts but no specific mention of viscoelastic contacts.

In the era of commercially-available instruments for indentation testing, the examination of viscoelastic contact mechanics, both in the context of polymers and biological tissues, seems to have taken on new life. To a first approximation, for indentation testing in the time domain, the fundamental mechanics has not much advanced beyond a few classic papers of the 1960s: Lee and Radok, J. Appl. Mech. 27 (1960) 438 and Ting TCT, J. Appl. Mech. 88 (1966) 845. However, the implementation of techniques for analysis of experimental data has progressed substantially. With spherical indenters the use of linearly viscoelastic models for characterization of a material creep or relaxation function is straightforward. Recent experimental studies have confirmed this, while more lingering questions remain for sharp contacts including Berkovich pyramidal indenters (most commonly shipped with commercial indenters). Sharp contacts seem to give rise to nonlinearly viscoelastic responses. Other topics of recent interest include frequency-domain measurements and examination of oscillating contacts and adhesion. (Although not mentioned in the listing of KLJ's most-loved topics in contact mechanics, viscoelastic contact has been the subject of several recent KLJ publications!)  Although research in viscoelastic contact mechanics has been strong in recent years, perhaps a challenge remains in the dissemination of information and the establishment of approachable experimental techniques for use by non-experts.

Interfacial toughness and mode mixity

When I was a graduate student, I spent several months to measure interfacial toughness between metalic (Cu and Au) films and thick substrates(Si and Polycarbonate). My methods were bulge test (blistering test) and 4-point bending test. I had many problems such as making an initial crack(pre-cracking), changing load phase angle applied to specimens, preparing/patterning thin films, constructing my own test apparatus, etc. The biggest problem was to measure the interfacial toughness over a wide range of loading phase angle. For a bimaterial with a non-zero oscillatory index(epsilon), we don't know the phase angle for a minimum interfacial toughness beforehand. Therefore, we need to measure the interfacial toughness over a wide range of phage angle. For engineering purpose, we need a minimum interfacial toughness value for reliability design because this value will lead to a conservative design of systems.

arindam.chakraborty's picture

A paper on developing stochastic micromechanical model for elastic properties of functionally graded material (FGM)

Given link is for a stochastic micromechanical model developed for predicting probabilistic characteristics of elastic mechanical properties of an isotropic functionally graded material (FGM) subject to statistical uncertainties in material properties of constituents and their respective volume fractions.

Is there a shear instability in metal foams?

Last year I spent three months modeling the compressive behavior of aluminum alloy foams. I had hoped to find some evidence of the banding instability that is often observed in elastomeric foams [1]. Lakes writes that this sort of banding instability provides indirect experimental evidence for negative shear modulus [2].

Deformation of Top-Down and Bottom-Up Silver Nanowires

I wanted to share some our work on the deformation behavior of metal nanowires that was recently published in Advanced Functional Materials. In this work, we considered the tensile deformation of three experimentally observed silver nanowire geometries, including five-fold twinned, pentagonal nanowires. The manuscript abstract and urls to videos of the tensile deformation of the three nanowire geometries are below. A copy of the manuscript is attached.

Mark Tschopp's picture

Tension-Compression Asymmetry in Homogeneous Dislocation Nucleation

Abstract. This letter addresses the dependence of homogeneous dislocation nucleation on the crystallographic orientation of pure copper under uniaxial tension and compression.  Molecular dynamics simulation results with an embedded-atom method potential show that the stress required for homogeneous dislocation nucleation is highly dependent on the crystallographic orientation and the uniaxial loading conditions; certain orientations require a higher stress in compression (e.g., <110> and <111>) and other orientations require a higher stress in tension (<100>).  Furthermore, the resolved shear stress in the slip direction is unable to completely capture the dependence of homogeneous dislocation nucleation on crystal orientation and uniaxial loading conditions.

Mike Ciavarella's picture


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In this short note we remark that, at least for the theory of Fuller & Tabor for the adhesive contact of rough random surfaces, fractal surfaces have a limiting zero pull-off force, for all fractal dimensions or amplitudes of roughness. This paradoxical result raises some questions. I ask the iMechanica community for opinions, comparisons of experiments, etc.

Mike Ciavarella's picture

review on KLJ's most loved areas in contact mechanics

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If we read Ken Johnson’s Timoshenko medal 2006 speech also posted in iMechanica, the subjects Ken mentions in his brief and humorous speech are:-

  1. corrugation of railway rails,
  2. the damping at clamped joints,
  3. Hertz contact under the action of tangential friction forces,
  4. ‘tribology' (word invented by David Tabor along with F.P.Bowden in Cambridge),
  5. Atomic Force Microscope, Surface Force Apparatus & friction on the atomic scale,
  6. Relation between adhesion and friction.

These are probably the subjects Ken is most attached to. Some are older (but perhaps not solved, lke corrugation, for which the “short-pitch” fixed wavelength mechanism is still unclear despite Ken’s 40 years of efforts (!), and some are certainly fashionable today (like adhesion and friction at atomic scale). In starting this forum, why not start from here? Should we prepare a 1 page summary on each of these topics? Since I start this, I will do the effort on corrugation I promise in the next week or so!

Regards, Mike

Honghui Yu's picture

Integral Formulations for 2D Elasticity: 1. Anisotropic Materials

Might also be useful for simulating dislocation motion in a finite body.

Several sets of boundary integral equations for two dimensional elasticity are derived from Cauchy integral theorem.These equations reveal the relations between displacements and resultant forces, between displacements and tractions, and between the tangential derivatives of displacements and tractions on solid boundary.Special attention is given to the formulation that is based on tractions and the tangential derivatives of displacements on boundary, because its integral kernels have the weakest singularities.The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary without involving the linear superposition technique often used in the literature. Body forces and thermal effect are subsequently included. The general framework of setting up a boundary value problem is discussed and continuity conditions at a non-singular corner are derived.  The general procedure in obtaining the elastic field around a circular hole is described, and the stress fields with first and second order singularities are obtained. Some other analytical solutions are also derived by using the formulation. 

Rolling Moment Resistance of Particles on Surfaces

In the brief presentation attached, I am summarizing my lab's recent work in the field of adhesion and work-of-adhesion measurements, and hoping to see who else is working in the field.  Here is some intro to the topic (by no means, it is complete - maybe we can add some recent work to this list as discussions develop)

Martijn Feron's picture

Split singularities and dislocation injection in strained silicon

By Martijn Feron, Zhen Zhang and Zhigang Suo

The mobility of charge carriers in silicon can be significantly increased when silicon is subject to a field of strain.In a microelectronic device, however, the strain field may be intensified at a sharp feature, such as an edge or a corner, injecting dislocations into silicon and ultimately failing the device. The strain field at an edge is singular, and is often a linear superposition of two modes of different exponents. We characterize the relative contribution of the two modes by a mode angle, and determine the critical slip systems as the amplitude of the load increases. We calculate the critical residual stress in a thin-film stripe bonded on a silicon substrate.

Mike Ciavarella's picture

shakedown in friction --- where should we send it to?

Anders Klarbring, Jim Barber and I are preparing a paper on the subject of shakedown in elastic contact problems with Coulomb friction. In particular, we establish the (rather limited) conditions under which a frictional equivalent of Melan's theorem can be applied, and we counterprove the theorem in all other cases.There is no plasticity here - the contacting bodies are linear elastic - but the analogies between the Coulomb friction law and elastic plastic deformation make us think the plasticity community might be interested in the results.

Patrick J McCluskey's picture

An introductory paper on thermal combinatorial analysis of nano-scale materials

If you are interested in nano-calorimetry or combinatorial analysis, you might also find the following paper interesting. It was published as part of the MRS spring ‘06 meeting proceedings ( This paper describes the parallel nano-differential scanning calorimeter (PnDSC), a new device for measuring the thermal properties of nano-scale material systems using a combinatorial approach.

Pradeep Sharma's picture

Why is the reported elastic modulus of carbon nanotube so scattered? “Yakobsons Paradox” and Perspective from Huang et. al.

For many mechanicians and materials scientists one of the most confounding things (in the ever increasing literature on carbon nanotubes) is the reported theoretical value of the nanotube elastic modulus. Depending upon the specific paper at hand, the reported numerical values range from 1 -6 TPa!


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