Investigation of nanomechanical properties of multilayered hybrid nanocomposites

Nanocomposites manufactured by combining two nano-structured phases are quite rare. While industry is seeking materials to meet difficult challenges with unique properties, there is no “rule of mixtures” to identify how to mix multiple nanomaterials in a composite structure and make available all required properties. Filler–matrix adhesion and its relation to materials’ properties have been the subject of continuing study due to composites advanced applications. Further on, studies at the interphase created in the area between the constituent materials can provide important information concerning materials interaction and composites behavior; this issue becomes even more interesting when discussing about nano-interphases. In the present investigation, a study of multi-layered nanocomposites is conducted. More precisely, the following four different types of multilayered hybrid nanocomposites were manufactured and tested: Pure titanium–carbon nanotubes–epoxy; pure titanium–epoxy–carbon nanotubes; titanium dioxide nanotubes–carbon nanotubes–epoxy and titanium dioxide nanotubes–epoxy–carbon nanotubes. The nano-mechanical properties of the above-mentioned nanocomposites were investigated using nanoindentation technique. The main conclusion of the present work is that in the case of multilayered nanocomposites, even if nanoindentation is executed on the surface of the same material, results greatly depend on the underlying substrates’ nature and their stacking sequence. Also, nano-interphases created at the contact surfaces between different layers affect the experimentally measured values of the nanomechanical properties (Young’s modulus and hardness) of multilayered nanocomposites.     

Taxicab geometry in table of higher-order elements

Nonlinear Dynamics - The paper deals with the analysis of the order of the differential equation of motion describing the dynamics of a one-port network compounded of series or parallel connections...     

Experimental study on the microstructure and nanomechanical properties of the wing membrane of dragonfly

Detailed investigations on the microstructure and the mechanical properties of the wing membrane of the dragonfly are carried out. It is found that in the direction of the thickness the membrane was divided into three layers rather than a single entity as traditionally considered, and on the surfaces the membrane displays a random distribution rough microstructure that is composed of numerous nanometer scale columns coated by the cuticle wax secreted. The characteristics of the surface structure are measured and described. The mechanical properties of the membranes taken separately from the wings of live and dead dragonflies are investigated by the nanoindentation technique. The Young’s moduli obtained here are approximately two times greater than the previous result, and the reasons that yield the difference are discussed. The project supported by the National Natural Science Foundation of China (10372102 and 10672164).     

Waveguiding and anomalous properties of a periodic knife-type grating

It is shown that periodic knife-type gratings always have waveguiding and anomalous properties. The dispersion relations for waveguide modes are obtained and the passbands are determined. The asymptotical form of the dispersion relations is obtained with an infinite increase in the length of the cascade elements and a decrease in the wave number. The effect of the geometrical characteristics and the type of grating on its waveguiding and anomalous properties is investigated. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirisk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 46–56, November–December, 1998.     

An energy model for nanomechanical deflection of cantilever-DNA chip

Nanomechanical behavior of cantilever-DNA chip in label-free biodetection is investigated by the energy method. First, using an equation of state for DNA liquid crystals and an alternative two-variable model for laminated cantilever beams, a relationship between chip energy and some factors, such as nanogeometrical, physical, chemical characteristics of DNA molecules, microscopical geometric dimension, macroscopical mechanical properties of chip, etc., is formulated in consideration of electrostatic energy, hydration energy and configurational fluctuations of DNA layer as well as mechanical energy of chip. Second, theoretical predictions of nanomechanical deflection of DNA chip by the minimum principle of energy are compared with experimental data in Wu's experiments. Third, the influence of stochastic interchain distances and stochastic elastic modulus on chip deflection is investigated. The validity of the simplified two-layer-beam model is also studied. Numerical results show that chip deflection enhances with the increase in length of DNA chains, and the interchain distances should be carefully controlled no less than 4 nm during the process of probe molecules self-assembly.     

Towards a multiscale analysis of periodic masonry brickwork: A FEM algorithm with damage and friction

The aim of this paper is to present an effort towards a multiscale model of the inelastic behaviour of masonry brick panels and the relative solution algorithm. The essential features of the inelastic behaviour, such as the damage development within the bed joints and the frictional dissipation over cracks’ faces, are taken into account. Micromechanical solutions are adopted in order to trace the guidelines for modelling the mentioned phenomena, and FEM analyses of large-scale panels are shown.     

Effective elastic properties of periodic composite medium

A new method is presented for calculating the bulk effective elastic stiffness tensor of a two-component composite with a periodic microstructure. The basic features of this method are similar to the one introduced by Bergman and Dunn (1992) for the dielectric problem. It is based on a Fourier representation of an integro-differential equation for the displacement field, which is used to produce a continued-fraction expansion for the elastic moduli. The method enabled us to include a much larger number of Fourier components than some previously proposed Fourier methods. Consequently our method provides the possibility of performing reliable calculations of the effective elastic tensor of periodic composites that are neither dilute nor low contrast, and are not restricted to arrays of nonoverlapping inclusions. We present results for a cubic array of nonoverlapping spheres, intended to serve as a test of quality, as well as results for a cubic array of overlapping spheres and a two dimensional hexagonal array of circles (a model for a fiber reinforced material) for comparison with previous work.     

Simultaneous determination of position and mass of a particle by the vibration of a diaphragm-based nanomechanical resonator

We present a theoretical analysis of the vibration of a suspended circular diaphragm resonator with a particle at an arbitrary location when considering the effects of plate stiffness and membrane tension in the diaphragm. The analytical expression relating position and mass of a particle attached on a stretched diaphragm with varying residual stress to the resulting shifts in diaphragm resonant frequency is derived. It has been shown that the particle position and mass for the diaphragm configuration can be unambiguously resolved by combining resonant frequencies of the first three consecutive symmetric vibration modes. This finding is verified numerically in finite element modeling using a freestanding circular diaphragm with and without an added particle, and it proves that the method resolves the particle position and mass with high accuracy.     

On the performance of quadrilateral finite elements in the solution to the Stokes equations in periodic structures

The use of the finite element method in solving the problem of flow of a Newtonian fluid in periodically constricted tubes is explored. The performance of eight node serendipity and nine node Lagrangian elements is compared. It was found that the Lagrangian element results in unstable velocity fields when stagnant or recirculation regions are present. This is characteristic of tubes with large expansion zones. The eight node element does not exhibit instabilities. Both elements give accurate pressure fields. This behaviour is contrary to traditional results obtained for flow problems with similar geometrical characteristics. This suggests that the periodicity of the boundary conditions might be the cause of the instabilities in the numerical solution. The use of the continuity equation to simplify the viscous terms in the Stokes equations resulted, in this particular case, in a deterioration of the rate of convergence of the algorithm.     

Effective properties of elastic periodic composite media with fibers

A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended for rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites.     

Magnetoelastic problem for a bodywith periodic elastic inclusions

A general approach based on complex variable theory is proposed to determine the magnetoelastic state of a body with an infinite row of elliptic inclusions under the action of magnetic and elastic fields. Numerical solutions to a two-dimensional problem for a body made of Terfenol-D magnetostrictive material and piezomagnetic ceramic material and having circular, elliptic, and rectilinear inclusions made of a different material are presented depending on the geometry of the inclusions, their material characteristics, the spacing between them, and the type of applied load __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 32–40, September 2006.     

On the modelling of dynamic problems for plates with a periodic structure

Summary The subject of analysis is the bending of elastic plates exhibiting a nonhomogeneous periodic structure and/or a periodically variable thickness in a certain direction parallel to the plate's midplane. The fundamental modelling problem is how to obtain an effective 2D-model of a plate under consideration, i.e., a 2D-model represented by PDEs with constant coefficients. This problem for periodic plates has been solved independently in [5] and [10], using asymptotic homogenization. However, homogenization neglects dynamic phenomena related to the plate's rotational inertia and cannot be applied to the analysis of higher-order vibration frequences. The main aim of this contribution is to formulate a new non-asymptotic effective 2D-model of a periodic plate which is free from the mentioned drawbacks and describes the dynamic behaviour of plates having the thickness of the order of the period length. The proposed model is applied to the analysis of some vibration problems.     

Towards a Unified Field Theory for Classical Electrodynamics

In this paper we introduce a model which describes the relation of matter and the electromagnetic field from a unitarian standpoint in the spirit of ideas of Born and Infeld. In this model, based on a semilinear perturbation of Maxwell equations, the particles are finite-energy solitary waves due to the presence of the nonlinearity. In this respect the matter and the electromagnetic field have the same nature. Finite energy means that particles have finite mass and this makes electrodynamics consistent with the special relativity. We analyze the invariants of the motion of the semilinear Maxwell equations (SME) and their static solutions. In the magnetostatic case (i.e., when the electric field E = 0 and the magnetic field H does not depend on time) SME are reduced to the semilinear equation where × denotes the curloperator, f is the gradient of a strictly convex smooth function f:R³R and A:R³R³ is the gauge potential related to the magnetic field H (H = × A). Due to the presence of the curl operator, (1) is a strongly degenerate elliptic equation. Moreover, physical considerations impel f to be flat at zero (f(0)=0) and this fact leads us to study the problem in a functional setting related to the Orlicz space L^p+L^q. The existence of a nontrivial finite- energy solution of (1) is proved under suitable growth conditions on f. The proof is carried out by using a suitable variational framework related to the Hodge splitting of the vector field A.We thank Marino Badiale and Charles Stuart for their useful suggestions.     

Fourier averaging: a phase-averaging method for periodic flow

A new phase-averaging method, denoted as Fourier averaging, is presented for the investigation of periodic flows. In such flows, the moments of velocity, as estimated from a small number of samples, show fluctuations in their phasewise development. In previous methods these fluctuations are reduced by calculating moments from large phase intervals. Fourier averaging, in contrast, neglects high-frequency fluctuations and assumes that they are of no physical relevance. This method supplies additional information on amplitudes and phase angles of discrete frequencies, which may then be used for visualizations of flow fields at any desired phase increment. The Fourier averaging method was verified empirically by LDA measurements and compared to other methods. It is shown that the results obtained by Fourier averaging are more accurate than for previously known methods. Received: 15 June 1998/Accepted: 15 April 1999     

Plane contact problems for a periodic two-layered elastic composite

Summary This paper deals with the two-dimensional static punch problems in the presence of friction for a periodically layered half-space. Within the framework of the homogenized model of linear elasticity with microlocal parameters [8–11] the exact solutions of the considered problems are obtained. The case of the indentation of the composite body by a rigid rectangular punch has been discussed in detail.

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Ebene Kontaktprobleme für ein periodisches elastisches Zweischichten-Komposit

Übersicht In dieser Arbeit wird das zweidimensionale statische Stempelproblem mit Reibung für einen periodisch geschichteten Halbraum betrachtet. Im Rahmen eines Homogenisierungsmodells der linearen Elastizitätstheorie mit mikropolaren Parametern werden die exakten Lösungen der betrachteten Probleme gewonnen. Im Detail wird das Eindringen eines rechteckigen starren Stempels behandelt.