Data Reduction And Error Analysis For The Physical Sciences

A comprehensive review is conducted on the modeling and simulation of isolated carbon nanotubes (CNTs) concentrating on all mechanical, buckling, vibrational and thermal properties Three different approaches consisting of atomistic modeling, continuum modeling and nano-scale continuum modeling are firstly explained and their applications toward understanding behavior of CNTs are discussed Different investigations available in literature focusing on mentioned behaviors are reviewed and their results are compared to show the applicability and efficiency of employed/developed technique Taking into account both runtime and accuracy of modeling, advantages and disadvantages of introduced methods are nominated and analyzed

On the modeling of carbon nanotubes: A critical review

Nano-cutting fluids are the mixtures of conventional cutting fluid and nanoparticles. Addition of the nanoparticles can alter wettability, lubricating properties, and convective heat transfer coefficient (cooling properties) of nano-cutting fluids. In the present work, nano-cutting fluid is made by adding 1% Al2O3 nanoparticles to conventional cutting fluid. The wettability characteristic of this nano-cutting fluid on a carbide tool tip is measured using the macroscopic contact angle method. Comparative study of tool wear, cutting force, workpiece surface roughness, and chip thickness among dry machining, machining with conventional cutting fluid as well as nano-cutting fluid has been undertaken. This study clearly reveals that the cutting force, workpiece surface roughness, tool wear, and chip thickness are reduced by the using nano-cutting fluid compared to dry machining and machining with conventional cutting fluid.

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Nano-Cutting Fluid for Enhancement of Metal Cutting Performance

In this study, free vibration analyses of embedded carbon and silica carbide nanotubes lying on an elastic matrix are performed based on Eringen’s nonlocal elasticity theory. These nanotubes are modeled as nanobeam and nanorod. Elastic matrix is considered as Winkler–Pasternak elastic foundation and axial elastic media for beam and rod models, respectively. The vibration formulations of the beam and rod are derived by utilizing Hamilton’s principle. The obtained equations of motions are solved by the method of separation of variables and finite element-based Hermite polynomials for various boundary conditions. The effects of boundary conditions, system modeling, structural sizes such as length, cross-sectional sizes, elastic matrix, mode number, and nonlocal parameters on the natural frequencies of these nanostructures are discussed in detail. Moreover, the availability of size-dependent finite element formulation is investigated in the vibration problem of nanobeams/rods resting on an elastic matrix.

Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method

The study using numerical methods on porous functionally graded (FG) nanoplates is still somewhat limited. This paper focuses on porosity-dependent nonlinear transient analysis of FG nanoplates using isogeometric finite element approach. In order to capture the small size effects, the Eringen's nonlocal elasticity based on higher order shear deformation theory (HSDT) are used to model the porous FG nanoplates. Two distributions of porosities inside FG materials are incorporated and defined via a modified rule of mixture. The nonlinear transient nonlocal governing equations under transverse dynamic loads are formulated by using the von Karman strains and are solved by Newmark time integration scheme to obtain geometrically nonlinear responses. It is indicated that nonlinear transient deflections of the porous FG nanoplate are significantly influenced by material composition, porosity, nonlocal parameters, volume fraction exponent, porosity distributions, geometrical parameters and dynamic load characteristics.

Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis

The elastostatic problem of a Bernoulli-Euler functionally graded nanobeam is formulated by adopting stress-driven nonlocal elasticity theory, recently proposed by G. Romano and R. Barretta. According to this model, elastic bending curvature is got by convoluting bending moment interaction with an attenuation function. The stress-driven integral relation is equivalent to a differential problem with higher-order homogeneous constitutive boundary conditions, when the special bi-exponential kernel introduced by Helmholtz is considered. Simple solution procedures, based on integral and differential formulations, are illustrated in detail to establish the exact expressions of nonlocal transverse displacements of inflected nano-beams of technical interest. It is also shown that all the considered nano-beams have no solution if Eringen's strain-driven integral model is adopted. The solutions of the stress-driven integral method indicate that the stiffness of nanobeams increases at smaller scales due to size effects. Local solutions are obtained as limit of the nonlocal ones when the characteristic length tends to zero.

Exact solutions of inflected functionally graded nano-beams in integral elasticity

An enhanced model of nonlocal torsion based on the Eringen theory is provided in this paper. The variational formulation is given and then the governing differential equation and boundary conditions of nonlocal nanobeams subjected to torsional loading are consistently derived. No higher-order boundary conditions are required for the enhanced model. It is assumed that the ends of nanobeams are not perfectly restrained thus focusing the attention also on the influence of elastically compliant boundary conditions on the behaviour of nonlocal models. Closed-form solutions are then provided for nanocantilevers and fully clamped nanobeams subject to distributed torsional loads. It is shown that the dimensionless small-scale parameter must fulfil a suitable inequality in order to avoid that a positive distributed torsional load provides a negative torsional rotation. The size-dependent static torsional behaviour of the proposed model in terms of torsional rotations and moments is tested. Contrary to the nonlocal Eringen model, the proposed enhanced model provides the small-scale effect also for nanobeams subjected to uniformly distributed torsional loads. Comparisons with Eringen model, gradient elasticity theory and classical (local) model are provided.

A closed-form model for torsion of nanobeams with an enhanced nonlocal formulation

Small-scale effects in carbon nanotubes are effectively assessed by resorting to the methods of nonlocal continuum mechanics. The crucial point of this approach consists in defining suitable constitutive laws which lead to reliable results. A nonlocal elastic law, diffusely adopted in literature, is that proposed by Eringen. According to this theory, the elastic equilibrium problem of a nonlocal nanostructure is equivalent to that of a corresponding local nanostructure subjected to suitable distortions simulating the nonlocality effect. Accordingly, transverse displacements and bending moments of a Bernoulli–Euler nonlocal nanobeam can be obtained by solving a corresponding linearly elastic (local) nanobeam, subjected to the same loading and kinematic constraint conditions of the nonlocal nanobeam, but with the prescription of suitable inelastic bending curvature fields. This observation leads naturally to the definition of a higher-order Eringen version for Bernoulli–Euler nanobeams, in which the elastic energy is assumed to be dependent on the total and inelastic bending curvatures and on their derivatives. Weak and strong formulations of elastic equilibrium of first-order gradient nanobeams are provided by a consistent thermodynamic approach. Exact solutions of fully clamped and cantilever nanobeams are given and compared with those of literature.

A higher-order Eringen model for Bernoulli–Euler nanobeams

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On the thermomechanical coupling in finite strain plasticity theory with non-linear kinematic hardening by means of incremental energy minimization

Nowadays, the modified nonlocal strain gradient theory provides a mathematically well-posed and technically reliable methodology to assess scale effects in inflected nano-structures. Such an approach is extended in this paper to investigate the extensional behavior of nano-rods. The considered integral elasticity model, involving axial force and strain fields, is conveniently shown to be equivalent to a nonlocal differential problem equipped with constitutive boundary conditions. Unlike treatments in the literature, no higher-order boundary conditions are required to close the nonlocal problem. Closed-form solutions of elastic nano-rods under selected loadings and kinematic boundary conditions are provided. As an innovative implication, Young’s moduli of Single-Walled Carbon Nanotubes (SWCNT) weare assessed and compared with predictions of Molecular Dynamics (MD). New benchmarks for numerical analyses were also detected.

Marko Canadija

Papers

Exact solutions of inflected functionally graded nano-beams in integral elasticity

A closed-form model for torsion of nanobeams with an enhanced nonlocal formulation

A higher-order Eringen model for Bernoulli–Euler nanobeams

On the thermomechanical coupling in finite strain plasticity theory with non-linear kinematic hardening by means of incremental energy minimization

Modified Nonlocal Strain Gradient Elasticity for Nano-Rods and Application to Carbon Nanotubes