One Inclusion in the Infinite Peristatic Matrix

2018 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Dynamic Properties ◽  
Homogeneous Medium ◽  
Initial Approximation ◽  
Inclusion Size ◽  
Linear Displacement ◽  
Function Technique ◽  
External Boundary ◽  
Infinite Matrix ◽  
Infinite Domain ◽  
Perturbation Field

A basic problem of of micromechanics is analysis of one inclusion in the infinite matrix subjected to a homogeneous remote loading. A heterogeneous medium with the bond-based peri-dynamic properties (see Silling, J. Mech. Phys. Solids 2000; 48:175–209) of constituents is considered. At first a volumetric boundary conditions are set up at the external boundary of a final domain obtained from the original infinite domain by truncation. An alternative sort of truncation method is periodisation method when a unite cell (UC) size is increased while the inclusion size is fixed. In the second approach, the displacement field is decomposed as linear displacement corresponding to the homogeneous loading of the infinite homogeneous medium and a perturbation field introduced by one inclusion. This perturbation field is found by the Green function technique as well as by the iteration method for entirely infinite sample with an initial approximation given by a driving term which has a compact support. The methods are demonstrated by numerical examples for 1D case. A convergence of numerical results for the peristatic composite bar to the corresponding exact evaluation for the local elastic theory are shown.

An Investigation of the Structural Dynamics of a Racing Yacht

1999 ◽  
Author(s):  
Frederic Louarn ◽  
Pandeli Temarel
Keyword(s):  
Dynamic Properties ◽  
Three Dimensional ◽  
Element Model ◽  
Point Of View ◽  
Mode Shapes ◽  
Function Technique ◽  
Operational Conditions ◽  
Principal Coordinates ◽  
Modal Summation ◽  
Structural Responses

The dynamic behaviour of a WOR 60 is investigated using three dimensional hydroelasticity theory. Global structural responses (e.g. stresses) in waves are obtained corresponding to the upright as well as to the more realistic heeled sailing configurations, revealing the connection between the ballast keel and the hull as being a critical area of the structure. For the "dry hull" analysis, a global finite element model has been developed, incorporating the hull and deck shell, the internal structure, the ballast keel and the rig together with rigging loads. The modular nature of the model has been used to assess the relative influence of each of the aforementioned components upon the required characteristic dynamic properties (e.g. natural frequencies and principal mode shapes). Regarding the "wet hull" analysis, a three dimensional Green's function technique, using pulsating sources distributed over the wetted surface, provides a numerical solution to the case of the yacht sailing in regular waves at arbitrary heading. Principal coordinates for the rigid body motions and flexible distortions of interest are evaluated and the latter are used to obtain the dynamic stresses in waves using modal summation. This paper will describe the modelling techniques used and discuss the applicability / limitations of hydroelasticity theory regarding this type of structures in the light of the results obtained for the upright and heeled operational conditions, as well as from the point of view of design aspects such as "L" and "T" keel configurations. The ABS design criteria will provide a practical reference for comparing the results from the dynamic analysis.

Nonequilibrium Green’s Function Approach to Dynamic Properties of Resonant-Tunneling through Double-Barrier Structures

1992 ◽  
Vol 06 (07) ◽  
pp. 1099-1118
Author(s):  
L.Y. Chen ◽  
C.S. Ting
Keyword(s):  
Green’S Function ◽  
Bias Voltage ◽  
Green's Function ◽  
Resonant Tunneling ◽  
Dynamic Properties ◽  
Function Technique ◽  
Double Barrier ◽  
Nonequilibrium Green's Function ◽  
Dc Bias ◽  
Nonequilibrium Green’S Function

In this paper, we review a recently developed approach to the dynamic properties of double barrier resonant tunneling systems, based on the nonequilibrium Green’s function technique and the Feynman path integral theory. The transient behavior of tunneling current, immediately after the switch-on of a dc bias voltage, is characterized by the building up process of tunneling electrons in the quantum well. The novel negative differential conductance demonstrates itself as a function of frequency of the small ac signal imposed upon a dc bias. The imaginary part of admittance is shown to be related to the conductance via a Kronig-Kramers relation. The noise characteristics clearly demonstrate a strong time correlation derived from the Pauli exclusion principle and have evident dependence upon the structure parameters and the bias voltage. All those theoretical results are compared with experiments and numerical simulations.

Matrix Cracking in Fiber-Reinforced Composite Materials

1991 ◽  
Vol 58 (3) ◽  
pp. 846-848 ◽  
Author(s):  
H. A. Luo ◽  
Y. Chen
Keyword(s):  
Composite Materials ◽  
Volume Fraction ◽  
Matrix Material ◽  
Homogeneous Medium ◽  
Circular Inclusion ◽  
Matrix Cracking ◽  
Phase Model ◽  
Infinite Matrix ◽  
Finite Concentration ◽  
Three Phase

Matrix cracking is a major pattern of the failure of composite materials. A crack can form in the matrix during manufacturing, or be produced during loading. Erdogan, Gupta, and Ratwani (1974) first considered the interaction between an isolated circular inclusion and a line crack embedded in infinite matrix. As commented by Erdogan et al., their model is applicable to the composite materials which contain sparsely distributed inclusions. For composites filled with finite concentration of inclusions, it is commonly understood that the stress and strain fields near the crack depend considerably on the microstructure around it. One notable simplified model is the so-called three-phase model which was introduced by Christensen and Lo (1979). The three-phase model considers that in the immediate neighborhood of the inclusion there is a layer of matrix material, but at certain distance the heterogeneous medium can be substituted by a homogeneous medium with the equivalent properties of the composite. Thus, for the problems of which the interest is in the field near the inclusion, it can reasonably be accepted as a good model. The two-dimensional version of the three-phase model consists of three concentric cylindrical layers with the outer one, labeled by 3, extended to infinity. The external radii a and b of the inner and intermediate phases, labeled by 1 and 2, respectively, are related by (a/b)2 =c, where c is the volume fraction of the fiber in composite.

scholarly journals Evanescent wave boundary layers in metamaterials and sidestepping them through a variational approach

2017 ◽  
Vol 473 (2200) ◽  
pp. 20160765 ◽  
Author(s):  
Ankit Srivastava ◽  
John R. Willis
Keyword(s):  
Boundary Layers ◽  
Variational Approach ◽  
Homogeneous Medium ◽  
Layered Composite ◽  
Evanescent Waves ◽  
Infinite Domain ◽  
Long Wavelength ◽  
Infinite Domains ◽  
Scattering Coefficients ◽  
Finite Samples

All metamaterial applications are based upon the idea that extreme material properties can be achieved through appropriate dynamic homogenization of composites. This homogenization is almost always done for infinite domains and the results are then applied to finite samples. This process ignores the evanescent waves which appear at the boundaries of such finite samples. In this paper, we first clarify the emergence and purpose of these evanescent waves in a model problem consisting of an interface between a layered composite and a homogeneous medium. We show that these evanescent waves form boundary layers on either side of the interface beyond which the composite can be represented by appropriate infinite domain homogenized relations. We show that if one ignores the boundary layers, then the displacement and stress fields are discontinuous across the interface. Therefore, the scattering coefficients at such an interface cannot be determined through the conventional continuity conditions involving only propagating modes. Here, we propose an approximate variational approach for sidestepping these boundary layers. The aim is to determine the scattering coefficients without the knowledge of evanescent modes. Through various numerical examples we show that our technique gives very good estimates of the actual scattering coefficients beyond the long wavelength limit.

Simplified Micro-Mechanical Approach for Coated Viscoelastic Inclusion

2019 ◽  
Vol 820 ◽  
pp. 118-127
Author(s):  
Elmahdi Boulhafa ◽  
Kouddane Redouane ◽  
Hamza Ouadfel ◽  
Rachid Cheikh ◽  
M. Abbadi
Keyword(s):  
Effective Properties ◽  
Homogeneous Medium ◽  
Spherical Shape ◽  
Function Technique ◽  
The Matrix ◽  
Linear Viscoelastic ◽  
Mechanical Approach ◽  
Coated Inclusion ◽  
The Green Function ◽  
Analytical Resolution

The present work deals with the analytical resolution of the problem of viscoelastic coated inclusion embedded in a viscoelastic matrix.In a first step, we will study the problem of a linear viscoelastic inclusion, without coating, embedded in a linear viscoelastic matrix.Then, the problem of coated viscoelastic inclusion considering the coating as a thin layer whose viscoelastic properties are different from those of the inclusion and the matrix is performed.The resolution of this problem will be based simultaneously on the Green function technique as well as the interface operator. The analytical expression of the solution is obtained by assuming the isotropy of the matrix as well as the spherical shape of the coatedinclusion.These results are used to determine the effective properties of a heterogeneous medium from a self-consistent approach taking into accountthe interactions between coated inclusions and the equivalent homogeneous medium.

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.

The distribution of antigen on the surface of RBL-2H3 rat basophilic leukemia cells observed by back-scattered electron imaging

1986 ◽  
Vol 44 ◽  
pp. 274-275
Author(s):  
R.F. Stump ◽  
J.R. Pfeiffer ◽  
JC. Seagrave ◽  
D. Huskisson ◽  
J.M. Oliver
Keyword(s):  
Cell Surface ◽  
Dynamic Properties ◽  
Leukemia Cells ◽  
Antigen Binding ◽  
Scattered Electron ◽  
Ige Receptor ◽  
Receptor Complexes ◽  
Rat Basophilic Leukemia Cells ◽  
Electron Imaging ◽  
Basophilic Leukemia

In RBL-2H3 rat basophilic leukemia cells, antigen binding to cell surface IgE-receptor complexes stimulates the release of inflammatory mediators and initiates a series of membrane and cytoskeletal events including a transformation of the cell surface from a microvillous to a lamellar topography. It is likely that dynamic properties of the IgE receptor contribute to the activation of these responses. Fewtrell and Metzger have established that limited crosslinking of IgE-receptor complexes is essential to trigger secretion. In addition, Baird and colleagues have reported that antigen binding causes a rapid immobilization of IgE-receptor complexes, and we have demonstrated an apparent increase with time in the affinity of IgE-receptor complexes for antigen.

Nucleosome dynamics

2006 ◽  
Vol 73 ◽  
pp. 109-119 ◽  
Author(s):  
Chris Stockdale ◽  
Michael Bruno ◽  
Helder Ferreira ◽  
Elisa Garcia-Wilson ◽  
Nicola Wiechens ◽  
...  
Keyword(s):  
High Resolution ◽  
Chromatin Structure ◽  
Current Knowledge ◽  
Dynamic Properties ◽  
Structure And Dynamics ◽  
Nucleosome Dynamics ◽  
Sharp Focus ◽  
Recent Advances ◽  
Insight Into ◽  
Chromatin Structure And Dynamics

In the 30 years since the discovery of the nucleosome, our picture of it has come into sharp focus. The recent high-resolution structures have provided a wealth of insight into the function of the nucleosome, but they are inherently static. Our current knowledge of how nucleosomes can be reconfigured dynamically is at a much earlier stage. Here, recent advances in the understanding of chromatin structure and dynamics are highlighted. The ways in which different modes of nucleosome reconfiguration are likely to influence each other are discussed, and some of the factors likely to regulate the dynamic properties of nucleosomes are considered.

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