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Ajeet Kumar's blog

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Modeling ribbons/strips as a Cosserat rod

This study presents a computational approach to obtain nonlinearly elastic constitutive relations of strip/ribbon-like structures modeled as a special Cosserat rod. Starting with the description of strips as a general Cosserat plate, the strip is first subjected to a strain field which is uniform along its length. The Helical Cauchy-Born rule is used to impose this uniform strain field which deforms the strip into a six-parameter family of helical configurations-the six parameters here correspond to the six strain measures of rod theory.

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An electroelastic Kirchhoff rod theory incorporating free space electric energy

This work presents a geometrically exact Kirchhoff-like electroelastic rod theory wherein the contribution of free space energy is also factored in. In addition to the usual mechanical variables such as the rod's centerline and cross-section orientation, three electric potential parameters are also introduced to account for the variation in electric potential within the rod's cross-section as well as along the rod length. The free space energy is included through an electric flux-like variable acting on the lateral surface of the rod.

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Improved formulas of extensional and bending stiffnesses of rectangular nanorods

Improved formulas of extensional and bending stiffnesses of isotropic rectangular nanorods are derived. These formulas reduce to the existing widely used formulas for a special choice of material parameters, i.e., when the surface Poisson's ratio and the bulk Poisson's ratio match thus highlighting the limitation of the existing formulas.

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A slender body theory for the motion of special Cosserat filaments in Stokes flow

The motion of filament-like structures in fluid media has been a topic of interest since long. In this regard, a well known slender body theory exists wherein the fluid flow is assumed to be Stokesian while the filament is modeled as a Kirchhoff rod which can bend and twist but remains inextensible and unshearable. In this work, we relax the inextensibility and unshearability constraints on filaments, i.e., the filament is modeled as a special Cosserat rod.

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A magnetoelastic theory for Kirchhoff rods having uniformly distributed paramagnetic inclusions and its buckling

We present a theory for finite and spatial elastic deformation of rods under the influence of arbitrary magnetic field and boundary condition. The rod is modeled as a Kirchhoff rod and is assumed to have uniformly distributed array of uniaxial spheroidal paramagnetic inclusions embedded in it all pointing in the same direction in the undeformed state. The governing equations of the magnetoelastic rod are derived which are further non-dimensionalized and linearized to investigate buckling in such rods.

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Geometrically exact elastoplastic rods -determination of yield surface in terms of stress resultants

This work addresses the determination of yield surfaces for geometrically exact elastoplastic rods. Use is made of a formulation where the rod is subjected to an uniform strain field along its arc length, thereby reducing the elastoplastic problem of the full rod to just its cross-section. By integrating the plastic work and the stresses over the rod's cross-section, one then obtains discrete points of the yield surface in terms of stress resultants. Eventually, Lamé curves in their most general form are fitted to the discrete points by an appropriate optimisation method.

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A finite element formuation for a direct approach to elastoplasticity in special Cosserat rods

A finite element formulation is presented for a direct approach to model elastoplastic deformation in slender bodies using the special Cosserat rod theory. The direct theory has additional plastic strain and hardening variables, which are functions of just the rod's arc-length, to account for plastic deformation of the rod. Furthermore, the theory assumes the existence of an effective yield function in terms of stress resultants, i.e., force and moment in the cross-section and cross-section averaged hardening parameters.

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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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A variant of Irving-Kirkwood-Noll formulation for one-dimensional nanostructures

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: https://www.researchgate.net/publication/337873624_Microscopic_definitio...

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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, ajeetk@am.iitd.ac.in

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: http://link.springer.com/article/10.1007/s10659-016-9586-1. 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)

http://www.sciencedirect.com/science/article/pii/S0020768311002149

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