scholarly journals Generalized locally-exact homogenization theory for evaluation of electric conductivity and resistance of multiphase materials

2020 ◽  
Vol 9 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Guannan Wang ◽  
Qiang Chen ◽  
Mengyuan Gao ◽  
Bo Yang ◽  
David Hui
Keyword(s):  
Electric Fields ◽  
Unidirectional Composite ◽  
Homogenization Theory ◽  
Governing Equations ◽  
Multiphase Materials ◽  
Micromechanics Models ◽  
Present Technique ◽  
Unit Cells ◽  
Electric Behavior ◽  
Fiber Matrix

AbstractThe locally-exact homogenization theory is further extended to investigate the homogenized and localized electric behavior of unidirectional composite and porous materials. Distinct from the classical and numerical micromechanics models, the present technique is advantageous by developing exact analytical solutions of repeating unit cells (RUC) with hexagonal and rhomboid geometries that satisfy the internal governing equations and fiber/matrix interfacial continuities in a point-wise manner. A balanced variational principle is proposed to impose the periodic boundary conditions on mirror faces of an RUC, ensuring rapid convergence of homogenized and localized responses. The present simulations are validated against the generalized Eshelby solution with electric capability and the finite-volume direct averaging micromechanics, where excellent agreements are obtained. Several micromechanical parameters are then tested of their effects on the responses of composites, such as the fiber/matrix ratio and RUC geometry. The efficiency of the theory is also proved and only a few seconds are required to generate a full set of properties and concomitant local electric fields in an uncompiled MATLAB environment. Finally, the related programs may be encapsulated with an input/output (I/O) interface such that even non-professionals can execute the programs without learning the mathematical details.

A New Micromechanics Model for Predicting Thermal Properties of Heterogeneous Materials

2006 ◽  
Author(s):  
Wenbin Yu ◽  
Tian Tang
Keyword(s):  
Thermal Properties ◽  
Heterogeneous Materials ◽  
Present Theory ◽  
Unit Cell ◽  
Micromechanics Model ◽  
Micromechanics Models ◽  
Unit Cells ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Complete Set

A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is extended to predict thermal properties of heterogeneous anisotropic materials. In comparison to existing micromechanics models, VAMUCH is unique in the following three aspects: (1) it invokes only essential assumptions within the concept of micromechanics and achieves the same accuracy as mathematical homogenization theories; (2) it calculates the complete set of properties simultaneously without applying any loads; and (3) the dimensionality of the problem is determined by the dimension of the unit cell and the complete set of material properties can be obtained for one-dimensional unit cells. The present theory is implemented in the computer program VAMUCH, a recently developed, versatile engineering code for homogenization of heterogeneous materials. Several examples will be used to demonstrate the application and accuracy of the theory and the code of VAMUCH.

A Second Look at the Higher-Order Theory for Periodic Multiphase Materials

2005 ◽  
Vol 72 (2) ◽  
pp. 177-195 ◽  
Author(s):  
Yogesh Bansal ◽  
Marek-Jerzy Pindera
Keyword(s):  
Order Theory ◽  
Higher Order ◽  
Unit Cell ◽  
Material Symmetry ◽  
Original Formulation ◽  
Predictive Capability ◽  
Multiphase Materials ◽  
Periodic Composites ◽  
Unit Cells ◽  
Higher Order Theory

In this communication, we present a reformulation, based on the local/global stiffness matrix approach, of the recently developed higher-order theory for periodic multiphase materials, Aboudi et al. [“Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials,” J. Appl. Mech., 68(5), pp. 697–707]. This reformulation reveals that the higher-order theory employs an approximate, and standard, elasticity approach to the solution of the unit cell problem of periodic multiphase materials based on direct volume-averaging of the local field equations and satisfaction of the local continuity conditions in a surface-averge sense. This contrasts with the original formulation in which different moments of the local equilibrium equations were employed, suggesting that the theory is a variant of a micropolar, continuum-based model. The reformulation simplifies the derivation of the global system of equations governing the unit cell response, whose size is substantially reduced through elimination of redundant continuity equations employed in the original formulation, allowing one to test the theory’s predictive capability in most demanding situations. Herein, we do so by estimating the elastic moduli of periodic composites characterized by repeating unit cells obtained by rotation of an infinite square fiber array through an angle about the fiber axis. Such unit cells possess no planes of material symmetry in the rotated coordinate system, and may contain a few or many fibers, depending on the rotation angle, which the reformulated theory can easily accommodate. The excellent agreement with the corresponding results obtained from the standard transformation equations confirms the new model’s previously untested predictive capability for a class of periodic composites characterized by nonstandard, multi-inclusion repeating unit cells lacking planes of material symmetry. Comparison of the effective moduli and local stress fields with the corresponding results obtained from the original Generalized Method of Cells, which the higher-order theory supersedes, confirms the need for this new model, and dramatically highlights the original model’s shortcomings for a certain class of unidirectional composites.

A Locally Exact Homogenization Theory for Periodic Microstructures With Isotropic Phases

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Anthony S. Drago ◽  
Marek-Jerzy Pindera
Keyword(s):  
Fourier Series ◽  
Periodic Boundary ◽  
Series Representation ◽  
Heterogeneous Materials ◽  
Combined Loading ◽  
Homogenization Theory ◽  
Inclusion Problem ◽  
Local Displacement ◽  
Unit Cells ◽  
Periodic Microstructures

Elements of the homogenization theory are utilized to develop a new micromechanics approach for unit cells of periodic heterogeneous materials based on locally exact elasticity solutions. The interior inclusion problem is exactly solved by using Fourier series representation of the local displacement field. The exterior unit cell periodic boundary-value problem is tackled by using a new variational principle for this class of nonseparable elasticity problems, which leads to exceptionally fast and well-behaved convergence of the Fourier series coefficients. Closed-form expressions for the homogenized moduli of unidirectionally reinforced heterogeneous materials are obtained in terms of Hill’s strain concentration matrices valid under arbitrary combined loading, which yield homogenized Hooke’s law. Homogenized engineering moduli and local displacement and stress fields of unit cells with offset fibers, which require the use of periodic boundary conditions, are compared to corresponding finite-element results demonstrating excellent correlation.

The Effect of Electrostatic Forces on the Distribution of Drops in a Channel

2002 ◽  
Author(s):  
Arturo Ferna´ndez ◽  
Jiacai Lu ◽  
Asghar Esmaeeli ◽  
Gre´tar Tryggvason
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Hydrodynamic Interaction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Dielectric Fluids ◽  
Wide Range ◽  
Leaky Dielectric Model

Direct numerical simulations are used to examine the effect of electric fields on the behavior of suspension of drops in dielectric fluids. The effect of electric field is modeled using the “leaky dielectric” model, coupled with the full Navier-Stokes equations. The governing equations are solved using a front-tracking/finite volume technique. The interaction of the drops is strongly dependant on the conductivity and the permittivity ratio, but fibration, where drops line up into long columns, takes place over a wide range of these parameters. The hydrodynamic interaction due to fluid circulation induced by the electric field has a strong influence on the drop distribution and the rate of fibration.

MFS Heat Conduction Modeling of Composite Materials Reinforced by CNT-Fibers with Large Aspect Ratio

2013 ◽  
Vol 420 ◽  
pp. 202-208 ◽  
Author(s):  
Milan Žmindák ◽  
Zoran Pelagić ◽  
Martin Dudinsky
Keyword(s):  
Heat Conduction ◽  
Composite Materials ◽  
Aspect Ratio ◽  
Control Volume ◽  
Least Square ◽  
Governing Equations ◽  
Composite Matrix ◽  
Heat Flows ◽  
Fiber Matrix ◽  
Continuous Source

Carbon Nanotube (CNT) fibers, which are used to reinforce composite materials areoften associated within the aspect ratio values 103:1-106:1, sometimes even larger. The Method of Continuous Source Functions (MCSF) used for simulating fiber-matrix and fiber-fiber interaction uses 1D continuous source functions which are distributed along the fiber. The source functions serve as Trefftz (T-) functions, which can satisfy the governing equations which are inside the composite domain (composite matrix) and the boundary conditions on the fiber-matrix interfaces are satisfied through the collocation points along the fiber boundaries in the least square (LS) sense. For the presented heat conduction problems, the nanotube fibers are supposed to be super-conductive at the first stage. Temperatures and heat flows in the control volume (CV) enable to define homogenized material properties for corresponding patch of the investigated composite material.

scholarly journals Modeling of an AC-Electro-Osmosis Based Microfluidic Mixer

2017 ◽  
Author(s):  
H. Dilara Uslu ◽  
Çetin Canpolat ◽  
Barbaros Çetin
Keyword(s):  
Electric Fields ◽  
Comsol Multiphysics ◽  
Governing Equations ◽  
Ac Electroosmosis ◽  
Flow Rates ◽  
Microfluidic Mixer ◽  
Mixing Performance ◽  
Electro Osmosis ◽  
Micro Mixer ◽  
Electro Osmotic Flow

The purpose of this study is presenting an active micro-mixer, which is based on AC electro-osmotic flow driven on 3D micro wires. In order to solve governing equations of AC electroosmosis, a commercial software COMSOL Multiphysics® is implemented. Different wire configurations with various imposed electric fields and flow rates are tested for evaluating mixing efficiencies. The analyses show that mixing performance is significantly improved by number of the wires as well as wire orientation. It is also revealed that the degree of mixing can also be controlled by the tuning of the applied voltage for a given flow rate.

scholarly journals Effect of a Support on the Properties of Zinc Oxide Based Sorbents

Nanomaterials ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 89
Author(s):  
Maciej Chomiak ◽  
Bartłomiej M. Szyja ◽  
Marta Jędrysiak ◽  
Janusz Trawczyński
Keyword(s):  
Phase Composition ◽  
Hydrogen Sulphide ◽  
Computational Analysis ◽  
Subsequent Work ◽  
Multiphase Materials ◽  
Slurry Impregnation ◽  
Unit Cells ◽  
Hot Coal Gas ◽  
H2s Adsorption ◽  
Experimental Findings

We present the comparative analysis of three Zn-based sorbents for the process of sulphur removal from hot coal gas. The sorbents were prepared by a slurry impregnation of TiO2, SiO2 and Al2O3, resulting in complex, multiphase materials, with the dominant phases of Zn2TiO4, Zn2SiO4 and ZnAl2O4, respectively. We have analyzed the effect of supports on the phase composition, texture, reducibility and H2S sorption. We have found that the phase composition significantly influences the susceptibility of the investigated materials to reduction by hydrogen. Zn2TiO4 have been found to be the easiest to reduce which correlates with its ability to adsorb the largest amount of hydrogen sulphide—up to 4.2 gS/100 g—compared to the other sorbents, which absorb up to 2.2 gS/100 g. In the case of Zn2SiO4 and ZnAl2O4, this effect also correlates with reducibility—these sorbents have been found to be highly resistant to reduction by hydrogen and to absorb much less hydrogen sulphide. In addition, the capacity of ZnAl2O4 for H2S adsorption decreases in the subsequent work cycles—from 2.2 gS/100 g in the first cycle to 0.8 gS/100 g in the third one. Computational analysis on the DFT level has shown that these materials show different thermodynamic stability of sulphur sites within the unit cells of the sorbents. For Zn2TiO4 and Zn2SiO4, the adsorption is favorable in both the first and second layers of the former and only the top layer of the latter, while for zinc aluminate it is not favorable, which is consistent with the experimental findings.

scholarly journals Connecting Microstructures for Multiscale Topology Optimization With Connectivity Index Constraints

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Zongliang Du ◽  
Xiao-Yi Zhou ◽  
Renato Picelli ◽  
H. Alicia Kim
Keyword(s):  
Topology Optimization ◽  
Connectivity Index ◽  
Homogenization Theory ◽  
Advanced Manufacturing ◽  
Numerical Investigations ◽  
Repeated Unit ◽  
Unit Cells ◽  
Architected Material ◽  
Topological Connectivity ◽  
Additional Constraints

With the rapid developments of advanced manufacturing and its ability to manufacture microscale features, architected materials are receiving ever increasing attention in many physics fields. Such a design problem can be treated in topology optimization as architected material with repeated unit cells using the homogenization theory with the periodic boundary condition. When multiple architected materials with spatial variations in a structure are considered, a challenge arises in topological solutions, which may not be connected between adjacent material architecture. This paper introduces a new measure, connectivity index (CI), to quantify the topological connectivity, and adds it as a constraint in multiscale topology optimization to achieve connected architected materials. Numerical investigations reveal that the additional constraints lead to microstructural topologies, which are well connected and do not substantially compromise their optimalities.

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