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Ajeet Kumar's blog

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A singularity free approach for Kirchhoff rods having uniformly distributed electrostatic charge

We present a singularity free formulation and its efficient numerical implementation for the spatial deformation of Kirchhoff rods having uniformly distributed electrostatic charge. Due to the presence of continuously distributed charge, the governing equations of the Kirchhoff rod become a system of integro-differential equations which is singular at every arc-length. We show that this singularity is of removable type which, ones removed, makes the system well defined everywhere. No cutoff length or mollifier is used to remove this singularity.

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Microscopic definition of internal force, moment and associated stiffnesses in one-dimensional nanostructures at finite temperature

We present a one-dimensional variant of the Irving-Kirkwood-Noll procedure to derive microscopic expressions of internal contact force and moment in one-dimensional nanostructures. We show that these expressions must contain both the potential and kinetic parts: just the potential part does not yield meaningful continuum results. We further specialize these expressions for helically repeating one-dimensional nanostructures for their extension, torsion and bending deformation. As the Irving-Kirkwood-Noll procedure does not yield expressions of stiffnesses, we resort to a thermodynamic equilibrium approach to first obtain the Helmholtz free energy of the supercell of helically repeating nanostructures. We then obtain expressions of axial force, twisting moment, bending moment and the associated stiffnesses by taking the first and second derivatives of the Helmholtz free energy with respect to conjugate strain measures. The derived expressions are used in finite temperature molecular dynamics simulation to study extension, torsion and bending of single-walled carbon nanotubes and their buckling.
The article will soon appear in the Mathematics and Mechanics of Solids. The same can be accessed at the following link:

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Phonons in chiral nanorods and nanotubes: a Cosserat rod based continuum approach

A Cosserat rod based continuum approach is presented to obtain phonon dispersion curves of flexural, torsional, longitudinal, shearing and radial breathing modes in chiral nanorods and nanotubes. Upon substituting the continuum wave form in the linearized dynamic equations of stretched and twisted Cosserat rods, we obtain analytical expression of a coefficient matrix (in terms of the rod's stiffnesses, induced axial force and twisting moment) whose eigenvalues and eigenvectors give us frequencies and mode shapes, respectively, for each of the above phonon modes.

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An asymptotic numerical method for continuation of spatial equilibria of special Cosserat rods

We present an efficient numerical scheme based on asymptotic numerical method for continuation of spatial equilibria of special Cosserat rods. Using quaternions to represent rotation, the equations of static equilibria of special Cosserat rods are posed as a system of thirteen first order ordinary differential equations having cubic nonlinearity. The derivatives in these equations are further discretized to yield a system of cubic polynomial equations.

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A thermo-elasto-plastic theory for special Cosserat rods

A general framework is presented to model coupled thermo-elasto-plastic deformations in the theory of special Cosserat rods. The use of the one-dimensional form of the energy balance in conjunction with the one-dimensional entropy balance allows us to obtain an additional equation for the evolution of a temperature-like one-dimensional field variable together with constitutive relations for this theory. Reduction to the case of thermoelasticity leads us to the well known nonlinear theory of thermoelasticity for special Cosserat rods.

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Effect of surface elasticity on extensional and torsional stiffnesses of isotropic circular nanorods

We present a continuum formulation to obtain simple expressions demonstrating the effects of surface residual stress and surface elastic constants on extensional and torsional stiffnesses of isotropic circular nanorods. Unlike the case of rectangular nanorods, we show that the stiffnesses of circular nanorods also depend on surface residual stress components. This is attributed to non-zero surface curvature inherent in circular nanorods.

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Unusual couplings in elastic tubes - negative poisson effect and overwinding on being stretched

We demonstrate intersting extension-torsion-inflation coupling in intrinsically twisted chiral tubes. In particular, we show that by tuning its intrinsic twist and the material constants, such tubes can show negative poison effect on being stretched. Similarly, such tubes can overwind initially when stretched - the same unusual behavior has been reported earlier when a DNA molecule is stretched.

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Research Associate/Postdoc position at IIT Delhi

Job title: Research Associate/Postdoc

Minimum qualification: PhD in Solid Mechanics/Mathematics

Research area: Thermoelastic Modeling of nano and Contunuum Rods – A Molecular Approach

Salary: Rs 36000 per month + 30% HRA

Walk in interview: 3rd of Nov 2016 in Department of Applied Mechanics, IIT Delhi

Contact person: Prof. Ajeet Kumar,

See the attachment for more details.

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PhD/Postdoc position at IIT Delhi

A PhD/Postdoc position is available for Indian nationals in my group to work in the broad area of "Molecular origin of elastic/plastic deformations in nanorods". This is a collaborative project with Germany and may require a semester or two stay in Germany. The PhD applicant should have good background in mathematics and solid mechanics. The postdoc candidate should preferably also be familiar with molecular modeling of materials.

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Effect of material nonlinearity on spatial buckling of nanorods and nanotubes

You may be interested in reading our following article: We show the importance of incorporating material nonlinearity for accurate simulation of nanorods and nanotubes. The linear material laws are shown to give completely erroneous results. The nonlinear material laws for nanorods were obtained using the recently proposed "Helical Cauchy-Born rule". We also discuss how surface stress affects buckling in such nanostructures.

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A one-dimensional Rod Model for Carbon Nanotubes

We recently published a paper in International Journal of Solids and Structures titled "A rod model for three dimensional deformations of single walled carbon nanotubes".(paper attached)

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