Size-dependent and strain rate effects in quantum dot nanostructures with molecular dynamic simulations

Size and strain rate effects are among several factors which play an important role in determining the response of nanostructures, such as their deformations, to the mechanical loadings. The mechanical deformations in nanostructure systems at finite temperatures are intrinsically dynamic processes. Most of the recent works in this context have been focused on nanowires [1, 2], but very little attention has been paid to such low dimensional nanostructures as quantum dots (QDs). In this contribution, molecular dynamics (MD) simulations with an embedded atom potential method(EAM) are carried out to analyse the size and strain rate effects in the silicon (Si) QDs, as an example. We consider various geometries of QDs such as spherical, cylindrical and cubic. We choose Si QDs as an example due to their major applications in solar cells and biosensing. The analysis has also been focused on the variation in the deformation mechanisms with the size and strain rate for Si QD embedded in a matrix of SiO2 [3] (other cases include SiN and SiC matrices).It is observed that the mechanical properties are the functions of the QD size, shape and strain rate as it is in the case for nanowires [2]. We also present the comparative study resulted from the application of different EAM potentials in particular, the Stillinger-Weber (SW) potential, the Tersoff potentials and the environment-dependent interatomic potential (EDIP) [1]. Finally, based on the stabilized structural properties we compute electronic bandstructures of our nanostructures using an envelope function approach and its finite element implementation.

Spectral Finite Element Formulation for Nanorods via Nonlocal Continuum Mechanics

In this article, the Eringen's nonlocal elasticity theory has been incorporated into classical/local Bernoulli-Euler rod model to capture unique properties of the nanorods under the umbrella of continuum mechanics theory. The spectral finite element (SFE) formulation of nanorods is performed. SFE formulation is carried out and the exact shape functions (frequency dependent) and dynamic stiffness matrix are obtained as function of nonlocal scale parameter. It has been found that the small scale affects the exact shape functions and the elements of the dynamic stiffness matrix. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave dispersion properties of carbon nanotubes.

Optimised form of acceleration correction algorithm within SPH-based simulations of impact mechanics

In the context of SPH-based simulations of impact dynamics, an optimised and automated form of the acceleration correction algorithm (Shaw and Reid, 2009a) is developed so as to remove spurious high frequency oscillations in computed responses whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. A rational framework for an insightful characterisation of the erstwhile acceleration correction method is first set up. This is followed by the proposal of an optimised version of the method, wherein the strength of the correction term in the momentum balance and energy equations is optimised. For the first time, this leads to an automated procedure to arrive at the artificial viscosity term. In particular, this is achieved by taking a spatially varying response-dependent support size for the kernel function through which the correction term is computed. The optimum value of the support size is deduced by minimising the (spatially localised) total variation of the high oscillation in the acceleration term with respect to its (local) mean. The derivation of the method, its advantages over the heuristic method and issues related to its numerical implementation are discussed in detail. (C) 2011 Elsevier Ltd. All rights reserved.

Fluid Mechanics of Aquatic Locomotion at Large Reynolds Numbers

Abstract | There exist a huge range of fish species besides other aquatic organisms like squids and salps that locomote in water at large Reynolds numbers, a regime of flow where inertial forces dominate viscous forces. In the present review, we discuss the fluid mechanics governing the locomotion of such organisms. Most fishes propel themselves by periodic undulatory motions of the body and tail, and the typical classification of their swimming modes is based on the fraction of their body that undergoes such undulatory motions. In the angulliform mode, or the eel type, the entire body undergoes undulatory motions in the form of a travelling wave that goes from head to tail, while in the other extreme case, the thunniform mode, only the rear tail (caudal fin) undergoes lateral oscillations. The thunniform mode of swimming is essentially based on the lift force generated by the airfoil like crosssection of the fish tail as it moves laterally through the water, while the anguilliform mode may be understood using the “reactive theory” of Lighthill. In pulsed jet propulsion, adopted by squids and salps, there are two components to the thrust; the first due to the familiar ejection of momentum and the other due to an over-pressure at the exit plane caused by the unsteadiness of the jet. The flow immediately downstream of the body in all three modes consists of vortex rings; the differentiating point being the vastly different orientations of the vortex rings. However, since all the bodies are self-propelling, the thrust force must be equal to the drag force (at steady speed), implying no net force on the body, and hence the wake or flow downstream must be momentumless. For such bodies, where there is no net force, it is difficult to directly define a propulsion efficiency, although it is possible to use some other very different measures like “cost of transportation” to broadly judge performance.

Down-to-earth temperatures: The mechanics of the thermal environment

This lecture describes some recent attempts at unravelling the mechanics of the temperature distribution near ground, especially during calm, clear nights. In particular, a resolution is offered of the so-called Ramdas paradox, connected with observations of a temperature minimum some decimetres above bare soil on calm clear nights, in apparent defiance of the Rayleigh criterion for instability due to thermal convection. The dynamics of the associated temperature distribution is governed by radiative and convective transport and by thermal conduction, and is characterised by two time constants, involving respectively quick radiative adjustments and slow diffusive relaxation. The theory underlying the work described here suggests that surface parameters like ground emissivity and soil thermal conductivity can exert appreciable influence on the development of nocturnal inversions.

Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches

Results from elasto-plastic numerical simulations of jointed rocks using both the equivalent continuum and discrete continuum approaches are presented, and are compared with experimental measurements. Initially triaxial compression tests on different types of rocks with wide variation in the uniaxial compressive strength are simulated using both the approaches and the results are compared. The applicability and relative merits and limitations of both the approaches for the simulation of jointed rocks are discussed. It is observed that both the approaches are reasonably good in predicting the real response. However, the equivalent continuum approach has predicted somewhat higher stiffness values at low strains. Considering the modelling effort involved in case of discrete continuum approach, for problems with complex geometry, it is suggested that a proper equivalent continuum model can be used, without compromising much on the accuracy of the results. Then the numerical analysis of a tunnel in Japan is taken up using the continuum approach. The deformations predicted are compared well against the field measurements and the predictions from discontinuum analysis. (C) 2012 Elsevier Ltd. All rights reserved.

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

Thermal vibration analysis of orthotropic nanoplates based on nonlocal continuum mechanics

This paper presents the thermal vibration analysis of orthotropic nanoplates such as graphene, using the two variable refined plate theory and nonlocal continuum mechanics for small scale effects. The nanoplate is modeled based on two variable refined plate theory and the axial stress caused by the thermal effects is also considered. The two variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the nanoplate are derived from the principle of virtual displacements. The closed form solution for thermal-vibration frequencies of a simply supported rectangular nanoplate has been obtained by using Navier's method of solution. Numerical results obtained by the present theory are compared with available solutions in the literature and the molecular dynamics results. The influences of the small scale coefficient, the room or low temperature, the high temparature, the half wave number and the aspect ratio of nanoplate on the natural frequencies are considered and discussed in detail. It can be concluded that the present theory, which does not require shear correction factor, is not only simple but also comparable to the first-order and higher order shear deformation theory. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplates. (C) 2012 Elsevier B.V. All rights reserved.

Geometrically non-linear dynamics of composite four-bar mechanisms

This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). (C) 2012 Elsevier Ltd. All rights reserved.