scholarly journals Overall dynamic properties of three-dimensional periodic elastic composites

2011 ◽  
Vol 468 (2137) ◽  
pp. 269-287 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Effective Properties ◽  
Dynamic Properties ◽  
Mass Density ◽  
Three Dimensional ◽  
Linear Momentum ◽  
Three Dimensions ◽  
Theoretical Treatment ◽  
Periodic Composite ◽  
Constitutive Parameters ◽  
Elastic Composites

This article presents a method for the homogenization of three-dimensional periodic elastic composites. It allows for the evaluation of the averaged overall frequency-dependent dynamic material constitutive tensors relating the averaged dynamic field variable tensors of velocity, strain, stress and linear momentum. Although the form of the dynamic constitutive relation for three-dimensional elastodynamic wave propagation has been known, this is the first time that explicit calculations of the effective parameters (for three dimensions) are presented. We show that for three-dimensional periodic composites, the overall compliance (stiffness) tensor, as produced directly by our formulation, is Hermitian, regardless of whether the corresponding unit cell is geometrically or materially symmetric. Overall, mass density is shown to be a tensor and, like the overall compliance tensor, always Hermitian. The average strain and linear momentum tensors are, however, coupled, and the coupling tensors are shown to be each others' Hermitian transpose. Finally, we present a numerical example of a three-dimensional periodic composite composed of elastic cubes periodically distributed in an elastic matrix. The presented results corroborate the predictions of the theoretical treatment illustrating the frequency dependence of the constitutive parameters. We also show that the effective properties calculated in this paper satisfy the dispersion relation of the composite.

scholarly journals Anti-plane shear waves in periodic elastic composites: band structure and anomalous wave refraction

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150152 ◽  
Author(s):  
Sia Nemat-Nasser
Keyword(s):  
Band Structure ◽  
Phase Velocity ◽  
Negative Refraction ◽  
Mass Density ◽  
Shear Waves ◽  
Variable Mass ◽  
Three Dimensional ◽  
Positive Energy ◽  
Plane Shear ◽  
Elastic Composites

For anti-plane shear waves in periodic elastic composites, it is shown that negative energy refraction can be accompanied by positive phase-velocity refraction and positive energy refraction can be accompanied by negative phase-velocity refraction , and that this can happen over a broad range of frequencies. Hence, in general, negative refraction does not necessarily require antiparallel group and phase-velocity vectors. Details are given for layered composites and the results are extended to, and illustrated for, two-dimensional periodic composites, revealing a wealth of information about the refractive characteristics of this class of composites. The composite's unit cell may consist of any number of constituents of any variable mass density and elastic modulus, admitting large discontinuities . A powerful variational-based solution method is used that applies to one-, two- and three-dimensional composites, irrespective of their constituents being homogeneous or heterogeneous. The calculations are direct, accurate and efficient, yielding the band structure, group-velocity, energy-flux and phase-velocity vectors as functions of the frequency and wavevector components, over an entire frequency band.

Simulation and Modelling the Heterogeneous Effects of the Microstructure MOX Fuels on their Effective Properties in Nominal Pressure Water Reactor Conditions

2010 ◽  
Vol 73 ◽  
pp. 91-96 ◽  
Author(s):  
Rodrigue Largenton ◽  
Victor Blanc ◽  
Philippe Thevenin ◽  
Daniel Baron
Keyword(s):  
Effective Properties ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Numerical Representation ◽  
Two Dimensional ◽  
Heterogeneous Microstructure ◽  
Heterogeneous Effects ◽  
Nominal Pressure ◽  
Sequential Absorption ◽  
The Moment

The experimental Electron Probe Micro Analysis (EPMA) characterizations on the MOX fuels evidence a heterogeneous microstructure, containing several phases. This heterogeneity must be accounted for in the numerical simulation. The first phase of this work, presented here, concerns exclusively the numerical representation of the MOX microstructure in three dimensions. Three identified steps were realized. The first one consisted in the acquisition and the treatment of two-dimensional experimental pictures thanks to a soft-ware already developed [1]. From the made treatments, the following bi-dimensional data were acquired: the surface fraction of every phase, the various diameters of inclusions within a phase as well as their surfaces fractions. However, within the framework of our study, we wished to represent our heterogeneous microstructure in three dimensions. Except, the data, supplied by this soft-ware, were bi-dimensional. Therefore, the second step of our works deal with the stereological domain. The model of Saltykov [2] was used to go back up the two-dimensional statistical information in three-dimensional. Finally, the last step of our works was to develop a tool able to build a meshed periodic numerical representation of the MOX microstructure. This innovative tool, based on a Random Sequential Absorption technique, represents MOX fuels already irradiated in reactor or any heterogeneous fuels envisaged in the future as well. For example it models two or three phases MOX fuel or any multi-phases fuels as well. Moreover, the sizes of the inclusions can vary within each phase. At the moment, the tool models spherical inclusions but nothing prevents from evolving towards more complex morphologies.

scholarly journals Spin Waves in Two and Three Dimensional Magnetic Materials

2015 ◽  
Vol 49 ◽  
pp. 35-47 ◽  
Author(s):  
H.S. Wijesinhe ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Spin Waves ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Second Order ◽  
Three Dimensions ◽  
Operator Representation ◽  
Computer Based ◽  
Canonical Ensembles

The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

Applicability of Dynamic Homogenization for Acoustic Metamaterials

2014 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Negative Refraction ◽  
Effective Properties ◽  
Dynamic Properties ◽  
Low Frequency ◽  
Bloch Wave ◽  
Acoustic Metamaterials ◽  
Infinite Domain ◽  
True Negative ◽  
Periodic Composite ◽  
Frequency Regime

Dynamic homogenization seeks to define frequency dependent effective properties for heterogeneous composites for the purpose of studying wave propagation in them. These properties can be used to predict and design for metamaterial behavior. However, there is an approximation involved in replacing a heterogeneous composite with its homogenized equivalent. In this paper we propose a quantification to this approximation. By way of explicit examples we show that a comprehensive homogenization scheme proposed in earlier papers is applicable in a finite composite setting and in the low frequency regime. We also show that there exist good arguments for considering the second branch of a locally resonant composite a true negative branch. Furthermore, we note that infinite-domain homogenization is more applicable to finite cases of locally resonant metamaterial composites than it is to 2-phase composites. We also study the effect of the interface location on the applicability of homogenization. The results open intriguing questions regarding the effects of replacing a semi-infinite periodic composite with its Bloch-wave (infinite domain) dynamic properties on such phenomenon as negative refraction.

scholarly journals Three-dimensional coherent X-ray diffractive imaging of whole frozen-hydrated cells

IUCrJ ◽  
2015 ◽  
Vol 2 (5) ◽  
pp. 575-583 ◽  
Author(s):  
Jose A. Rodriguez ◽  
Rui Xu ◽  
Chien-Chun Chen ◽  
Zhifeng Huang ◽  
Huaidong Jiang ◽  
...  
Keyword(s):  
Neospora Caninum ◽  
Mass Density ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Natural State ◽  
X Rays ◽  
Diffractive Imaging ◽  
Three Dimensional Imaging ◽  
Whole Cells ◽  
Dimensional Reconstruction

A structural understanding of whole cells in three dimensions at high spatial resolution remains a significant challenge and, in the case of X-rays, has been limited by radiation damage. By alleviating this limitation, cryogenic coherent diffractive imaging (cryo-CDI) can in principle be used to bridge the important resolution gap between optical and electron microscopy in bio-imaging. Here, the first experimental demonstration of cryo-CDI for quantitative three-dimensional imaging of whole frozen-hydrated cells using 8 keV X-rays is reported. As a proof of principle, a tilt series of 72 diffraction patterns was collected from a frozen-hydratedNeospora caninumcell and the three-dimensional mass density of the cell was reconstructed and quantified based on its natural contrast. This three-dimensional reconstruction reveals the surface and internal morphology of the cell, including its complex polarized sub-cellular structure. It is believed that this work represents an experimental milestone towards routine quantitative three-dimensional imaging of whole cells in their natural state with spatial resolutions in the tens of nanometres.

scholarly journals Moore–Gibson–Thompson thermoelasticity

2019 ◽  
Vol 24 (12) ◽  
pp. 4020-4031 ◽  
Author(s):  
Ramón Quintanilla
Keyword(s):  
Three Dimensional ◽  
Relaxation Parameter ◽  
Three Dimensions ◽  
One Dimension ◽  
Well Posedness ◽  
Stability Of Solutions ◽  
The Stability ◽  
The One ◽  
Constitutive Parameters ◽  
Thermoelastic Theory

We consider a thermoelastic theory where the heat conduction is described by the Moore–Gibson–Thompson equation. In fact, this equation can be obtained after the introduction of a relaxation parameter in the Green–Naghdi type III model. We analyse the one- and three-dimensional cases. In three dimensions, we obtain the well-posedness and the stability of solutions. In one dimension, we obtain the exponential decay and the instability of the solutions depending on the conditions over the system of constitutive parameters. We also propose possible extensions for these theories.

2d And 3d Acoustic Metamaterials Using Space Coil Design

2015 ◽  
Vol 1753 ◽  
Author(s):  
Santosh K. Maurya ◽  
Manu Sahay ◽  
Shobha Shukla ◽  
Sumit Saxena
Keyword(s):  
Acoustic Wave ◽  
Mass Density ◽  
3D Structure ◽  
Three Dimensional ◽  
Acoustic Metamaterials ◽  
Coil Design ◽  
Frequency Range ◽  
2D And 3D ◽  
Constitutive Parameters ◽  
Sub Wavelength

ABSTRACTVarious promising applications such as acoustic cloaking, sub-wavelength imaging, acoustic wave manipulation, transmission or reflection control etc. are feasible because of the ability of manipulating sounds and vibrations using artificially engineered “Acoustics meta-materials”. Recent works on space-coiling acoustic metamaterials show their extreme constitutive parameters like large refractive index, double negativity and zero mass density. Three dimensional structures have a wide application in sub-wavelength broadband acoustic wave suppression due to huge attenuation. Here we report the study of propagated and transmitted wave through 3D acoustic metamaterials structure using finite element method. Our simulations on 3D structure show a huge absorption/damping over few hundreds kilohertz frequency range.

Image restoration of thick biological specimens using a through focus series as applied to electron tomography

1994 ◽  
Vol 52 ◽  
pp. 338-339
Author(s):  
Karen F. Han ◽  
John W. Sedat ◽  
David A. Agard
Keyword(s):  
Electron Tomography ◽  
Mass Density ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Electron ◽  
Accurate Representation ◽  
Exit Surface ◽  
Ewald Sphere ◽  
Electron Energy Loss ◽  
Simple Fashion

The main focus of our laboratory is the study of higher order chromatin structure using three dimensional electron microscope tomography. Three dimensional tomography involves the reconstruction of an object by combining multiple projection views of the object at different tilt angles. It is thus imperative to obtain an accurate representation of the projected object mass density to reconstruct the object correctly in three dimensions. Due to the effects of electron-specimen interactions and microscope lens aberrations, image intensities are not always related to the projected mass density in a simple fashion. We are using a variety of techniques to interpret collected images. In previous work, we have analyzed image formation for thick (0.3-0.7um) biological specimens by electron energy loss spectroscopy and imaging, as well as Ewald sphere construction analysis. In this work, we have modified existing techniques to restore images with only three focus levels using the exit surface wave reconstruction as a reference for comparison.

scholarly journals Band Gaps and Vibration Isolation of a Three-dimensional Metamaterial with a Star Structure

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3812 ◽  
Author(s):  
Heng Jiang ◽  
Mangong Zhang ◽  
Yu Liu ◽  
Dongliang Pei ◽  
Meng Chen ◽  
...  
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Mass Density ◽  
Three Dimensional ◽  
Low Frequency ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Star Structure

Elastic metamaterials have promising applications in wave control and vibration isolation, due to their extraordinary characteristics, e.g., negative Poisson ratio, band gaps, effective negative mass density and effective negative modulus. How to develop new functional metamaterials using a special structure has always been a hot topic in this field. In this study, a three-dimensional (3D) star structure is designed to construct metamaterials with both negative static and dynamic properties. The results show that the 3D star structure formed a wide band gap at lower frequency and had a negative Poisson’s ratio. Different from conventional acoustic metamaterials, the main physical mechanism behind the low-frequency band gap of the 3D star structure is the resonance mode formed by the bending deformation of each rib plate, which made it easier to achieve effective isolation of low-frequency elastic waves with a low mass density. In addition, many structural parameters of the 3D star structure can be modulated to effectively adjust the band gap frequency by changing the angle between the concave nodes and aspect ratio. This study provides a new way to design the 3D acoustic metamaterials and develop the lightweight vibration isolation devices.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

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