A new integral equation approach to elastodynamic homogenization

2008 ◽  
Vol 464 (2094) ◽  
pp. 1461-1482 ◽  
Author(s):  
William J Parnell ◽  
I. David Abrahams
Keyword(s):  
Integral Equation ◽  
Volume Fraction ◽  
Effective Properties ◽  
Order Approximation ◽  
High Volume ◽  
Leading Order ◽  
Cross Sectional ◽  
Integral Equation Approach ◽  
Order Scheme ◽  
Sectional Shape

A new theory of elastodynamic homogenization is proposed, which exploits the integral equation form of Navier's equations and relationships between length scales within composite media. The scheme is introduced by focusing on its leading-order approximation for orthotropic, periodic fibre-reinforced media where fibres have arbitrary cross-sectional shape. The methodology is general but here it is shown for horizontally polarized shear (SH) wave propagation for ease of exposition. The resulting effective properties are shown to possess rich structure in that four terms account separately for the physical detail of the composite (associated with fibre cross-sectional shape, elastic properties, lattice geometry and volume fraction). In particular, the appropriate component of Eshelby's tensor arises naturally in order to deal with the shape of the fibre cross section. Results are plotted for circular fibres and compared with extant methods, including the method of asymptotic homogenization. The leading-order scheme is shown to be in excellent agreement even for relatively high volume fractions.

scholarly journals An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170080 ◽  
Author(s):  
Duncan Joyce ◽  
William J. Parnell ◽  
Raphaël C. Assier ◽  
I. David Abrahams
Keyword(s):  
Cross Section ◽  
Volume Fraction ◽  
Effective Properties ◽  
Circular Cross Section ◽  
Rational Functions ◽  
High Volume ◽  
Cross Sectional ◽  
Antiplane Elasticity ◽  
Unidirectional Fibre ◽  
Explicit Expressions

In Parnell & Abrahams (2008 Proc. R. Soc. A 464 , 1461–1482. ( doi:10.1098/rspa.2007.0254 )), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme.

On Thermal Interface Materials With Polydisperse Fillers: Packing Algorithm and Effective Properties

2018 ◽  
Author(s):  
Piyas Chowdhury ◽  
Kamal Sikka ◽  
Anuja De Silva ◽  
Indira Seshadri
Keyword(s):  
Thermal Conductivity ◽  
Elastic Modulus ◽  
Volume Fraction ◽  
Effective Properties ◽  
Material Design ◽  
High Volume ◽  
Thermal Interface Materials ◽  
Thermal Interface ◽  
Packing Algorithm ◽  
Interface Materials

Thermal interface materials (TIMs), which transmit heat from semiconductor chips, are indispensable in today’s microelectronic devices. Designing superior TIMs for increasingly demanding integration requirements, especially for server-level hardware with high power density chips, remains a particularly coveted yet challenging objective. This is because achieving desired degrees of thermal-mechanical attributes (e.g. high thermal conductivity, low elastic modulus, low viscosity) poses contradictory challenges. For instance, embedding thermally conductive fillers (e.g. metallic particles) into a compliant yet considerably less conductive matrix (e.g. polymer) enhances heat transmission, however at the expense of overall compliance. This leads to extensive trial-and-error based empirical approaches for optimal material design. Specifically, high volume fraction filler loading, role of filler size distribution, mixing of various filler types are some outstanding issues that need further clarification. To that end, we first forward a generic packing algorithm with ability to simulate a variety of filler types and distributions. Secondly, by modeling the physics of heat/force flux, we predict effective thermal conductivity, elastic modulus and viscosity for various packing cases.

scholarly journals Flush Flow Behaviour Affected by the Morphology of Intravascular Endoscope: A Numerical Simulation and Experimental Study

2021 ◽  
Vol 12 ◽  
Author(s):  
Yujie Li ◽  
Mingzi Zhang ◽  
Simon Tupin ◽  
Kohei Mitsuzuka ◽  
Toshio Nakayama ◽  
...  
Keyword(s):  
Computational Models ◽  
Volume Fraction ◽  
High Volume ◽  
Strong Impact ◽  
Cross Sectional ◽  
Injection Speed ◽  
Vascular Segment ◽  
Sectional Plane ◽  
The Cross

Background: Whilst intravascular endoscopy can be used to identify lesions and assess the deployment of endovascular devices, it requires temporary blockage of the local blood flow during observation, posing a serious risk of ischaemia.Objective: To aid the design of a novel flow-blockage-free intravascular endoscope, we explored changes in the haemodynamic behaviour of the flush flow with respect to the flow injection speed and the system design.Methods: We first constructed the computational models for three candidate endoscope designs (i.e., Model A, B, and C). Using each of the three endoscopes, flow patterns in the target vessels (straight, bent, and twisted) under three different sets of boundary conditions (i.e., injection speed of the flush flow and the background blood flowrate) were then resolved through use of computational fluid dynamics and in vitro flow experiments. The design of endoscope and its optimal operating condition were evaluated in terms of the volume fraction within the vascular segment of interest, as well as the percentage of high-volume-fraction area (PHVFA) corresponding to three cross-sectional planes distal to the microcatheter tip.Results: With a mild narrowing at the endoscope neck, Model B exhibited the highest PHVFA, irrespective of location of the cross-sectional plane, compared with Models A and C which, respectively, had no narrowing and a moderate narrowing. The greatest difference in the PHVFA between the three models was observed on the cross-sectional plane 2 mm distal to the tip of the microcatheter (Model B: 33% vs. Model A: 18%). The background blood flowrate was found to have a strong impact on the resulting volume fraction of the flush flow close to the vascular wall, with the greatest difference being 44% (Model A).Conclusion: We found that the haemodynamic performance of endoscope Model B outperformed that of Models A and C, as it generated a flush flow that occupied the largest volume within the vascular segment of interest, suggesting that the endoscope design with a diameter narrowing of 30% at the endoscope neck might yield images of a better quality.

Utility of 2D Finite Element Simulations for Predicting Effective Thermomechanical Properties of Particle-Reinforced Composites

2018 ◽  
Author(s):  
Kamran Makarian ◽  
Sridhar Santhanam
Keyword(s):  
Finite Element ◽  
Failure Modes ◽  
Volume Fraction ◽  
Effective Properties ◽  
Coefficient Of Thermal Expansion ◽  
High Volume ◽  
Thermomechanical Properties ◽  
Reinforced Composites ◽  
Fe Simulations ◽  
Particle Reinforced Composites

In the last two decades, researchers have implemented two-dimensional (2D) Finite Element (FE) simulations of particle-reinforced composites for various purposes, including prediction of effective properties and failure modes. The present work aspires to examine the validity of the hypothesis that 2D FE simulations can provide accurate predictions for various thermomechanical properties of high volume fraction (VF) particle-reinforced composites. For this purpose, the random sequential adsorption (RSA) algorithm is implemented to generate FE simulations of various composites. The uniqueness in the methodology of the present work is in the generation of FE simulation of composites with more than two material types as reinforcement, as well as thorough and concurrent comparison of multiple thermal and mechanical properties. The adequacy of the simulations is verified statistically, and the results are compared to predictions from established schemes as well as certain experimental findings. These comparisons show that the predictive power of 2D FE simulations is lower for elastic properties, and higher for coefficient of thermal expansion (CTE) and thermal conductivity of particle-reinforced composites. The findings of this research can guide the researchers in making better decisions for implementing Finite Element Method (FEM) for designing high VF composites.

Morphology, Distribution and Identification of Micro-Constituents Along Grain Boundaries in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 176-177
Author(s):  
D. E. Fornwalt ◽  
A. R. Geary ◽  
B. H. Kear
Keyword(s):  
Electron Microscope ◽  
Grain Boundaries ◽  
Volume Fraction ◽  
Rupture Life ◽  
Stress Rupture ◽  
High Volume ◽  
Precipitate Morphology ◽  
Stress Rupture Life ◽  
Nickel Base ◽  
Scanning Electron

A systematic study has been made of the effects of various heat treatments on the microstructures of several experimental high volume fraction γ’ precipitation hardened nickel-base alloys, after doping with ∼2 w/o Hf so as to improve the stress rupture life and ductility. The most significant microstructural chan§e brought about by prolonged aging at temperatures in the range 1600°-1900°F was the decoration of grain boundaries with precipitate particles.Precipitation along the grain boundaries was first detected by optical microscopy, but it was necessary to use the scanning electron microscope to reveal the details of the precipitate morphology. Figure 1(a) shows the grain boundary precipitates in relief, after partial dissolution of the surrounding γ + γ’ matrix.

On the cross-sectional shape of the cellulose crystallites in the tunicate Halocynthia papillosa

1990 ◽  
Vol 48 (3) ◽  
pp. 566-567
Author(s):  
J.-F. Revol ◽  
Y. Van Daele ◽  
F. Gaill
Keyword(s):  
Contrast Imaging ◽  
Animal Kingdom ◽  
Bright Field ◽  
Field Mode ◽  
Cross Sectional ◽  
Ultrathin Sections ◽  
The Cross ◽  
Sectional Shape ◽  
Valonia Ventricosa ◽  
C Nmr

The only form of cellulose which could unequivocally be ascribed to the animal kingdom is the tunicin that occurs in the tests of the tunicates. Recently, high-resolution solid-state l3C NMR revealed that tunicin belongs to the Iβ form of cellulose as opposed to the Iα form found in Valonia and bacterial celluloses. The high perfection of the tunicin crystallites led us to study its crosssectional shape and to compare it with the shape of those in Valonia ventricosa (V.v.), the goal being to relate the cross-section of cellulose crystallites with the two allomorphs Iα and Iβ.In the present work the source of tunicin was the test of the ascidian Halocvnthia papillosa (H.p.). Diffraction contrast imaging in the bright field mode was applied on ultrathin sections of the V.v. cell wall and H.p. test with cellulose crystallites perpendicular to the plane of the sections. The electron microscope, a Philips 400T, was operated at 120 kV in a low intensity beam condition.

The stabilization of B.C.C. Cu in Cu/Nb nanolayered composites

1996 ◽  
Vol 54 ◽  
pp. 228-229
Author(s):  
H. Kung ◽  
A.J. Griffin ◽  
Y.C. Lu ◽  
K.E. Sickafus ◽  
T.E. Mitchell ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Layer Thickness ◽  
Volume Fraction ◽  
Ion Beam ◽  
High Strength ◽  
Cross Sectional ◽  
Metastable Structure ◽  
High Resolution Tem ◽  
Potential Improvement ◽  
Two Phases

Materials with compositionally modulated structures have gained much attention recently due to potential improvement in electrical, magnetic and mechanical properties. Specifically, Cu-Nb laminate systems have been extensively studied mainly due to the combination of high strength, and superior thermal and electrical conductivity that can be obtained and optimized for the different applications. The effect of layer thickness on the hardness, residual stress and electrical resistivity has been investigated. In general, increases in hardness and electrical resistivity have been observed with decreasing layer thickness. In addition, reduction in structural scale has caused the formation of a metastable structure which exhibits uniquely different properties. In this study, we report the formation of b.c.c. Cu in highly textured Cu/Nb nanolayers. A series of Cu/Nb nanolayered films, with alternating Cu and Nb layers, were prepared by dc magnetron sputtering onto Si {100} wafers. The nominal total thickness of each layered film was 1 μm. The layer thickness was varied between 1 nm and 500 nm with the volume fraction of the two phases kept constant at 50%. The deposition rates and film densities were determined through a combination of profilometry and ion beam analysis techniques. Cross-sectional transmission electron microscopy (XTEM) was used to examine the structure, phase and grain size distribution of the as-sputtered films. A JEOL 3000F high resolution TEM was used to characterize the microstructure.

AN INTEGRAL EQUATION APPROACH TO PHASE TRANSITIONS IN FERROFLUIDS

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1847-C8-1848
Author(s):  
G. A. R. Martin ◽  
A. Bradbury ◽  
R. W. Chantrell
Keyword(s):  
Integral Equation ◽  
Phase Transitions ◽  
Equation Approach ◽  
Integral Equation Approach

HOT CORROSION OF CERIA-YTTRIA STABILIZED ZIRCONIA PLASMA SPRAYED THERMAL BARRIER COATING BY EUTECTIC VANDIUM PENTAOXIDE-SODIUM SULFATE

2018 ◽  
Vol 18 (1) ◽  
pp. 182-192 ◽  
Author(s):  
Mohammed J Kadhim ◽  
Mohammed H Hafiz ◽  
Maryam A Ali Bash
Keyword(s):  
Thermal Barrier Coating ◽  
Hot Corrosion ◽  
Monoclinic Phase ◽  
Volume Fraction ◽  
High Volume ◽  
Thermal Barrier ◽  
Air Plasma ◽  
Plan View ◽  
Barrier Coating ◽  
Plasma Sprayed

The high temperature corrosion behavior of thermal barrier coating (TBC) systemconsisting of IN-738 LC superalloy substrate, air plasma sprayed Ni24.5Cr6Al0.4Y (wt%)bond coat and air plasma sprayed ZrO2-20 wt% ceria-3.6 wt% yttria (CYSZ) ceramic coatwere characterized. The upper surfaces of CYSZ covered with 30 mg/cm2 , mixed 45 wt%Na2SO4-55 wt% V2O5 salt were exposed at different temperatures from 800 to 1000 oC andinteraction times from 1 up to 8 h. The upper surface plan view of the coatings wereidentified for topography, roughness, chemical composition, phases and reaction productsusing scanning electron microscopy, energy dispersive spectroscopy, talysurf, and X-raydiffraction. XRD analyses of the plasma sprayed coatings after hot corrosion confirmed thephase transformation of nontransformable tetragonal (t') into monoclinic phase, presence ofYVO4 and CeVO4 products. Analysis of the hot corrosion CYSZ coating confirmed theformation of high volume fraction of YVO4, with low volume fractions of CeOV4 and CeO2.The formation of these compounds were combined with formation of monoclinic phase (m)from transformation of nontransformable tetragonal phase (t').

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