scholarly journals Effective elastic properties of one-dimensional hexagonal quasicrystal composites

2021 ◽  
Vol 42 (10) ◽  
pp. 1439-1448
Author(s):  
Shuang Li ◽  
Lianhe Li
Keyword(s):  
Composite Materials ◽  
Explicit Expression ◽  
Elastic Properties ◽  
Function Method ◽  
Volume Fraction ◽  
Effective Properties ◽  
Elliptic Cylinder ◽  
One Dimensional ◽  
Special Cases ◽  
Analytical Expressions

AbstractThe explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

scholarly journals Interaction of a Screw Dislocation with Interface and Wedge-Shaped Cracks in One-Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Lian he Li ◽  
Yue Zhao
Keyword(s):  
Screw Dislocation ◽  
Electric Fields ◽  
Electric Displacement ◽  
Image Force ◽  
Coupling Constants ◽  
Geometrical Parameters ◽  
Intensity Factors ◽  
One Dimensional ◽  
Special Cases ◽  
Analytical Expressions

Interaction of a screw dislocation with wedge-shaped cracks in one-dimensional hexagonal piezoelectric quasicrystals bimaterial is considered. The general solutions of the elastic and electric fields are derived by complex variable method. Then the analytical expressions for the phonon stresses, phason stresses, and electric displacements are given. The stresses and electric displacement intensity factors of the cracks are also calculated, as well as the force on dislocation. The effects of the coupling constants, the geometrical parameters of cracks, and the dislocation location on stresses intensity factors and image force are shown graphically. The distribution characteristics with regard to the phonon stresses, phason stresses, and electric displacements are discussed in detail. The solutions of several special cases are obtained as the results of the present conclusion.

ON THE DEPENDENCE OF THE ELASTIC PROPERTIES OF A POROUS ROCK ON THE COMPRESSIBILITY OF THE PORE FLUID

Geophysics ◽  
1975 ◽  
Vol 40 (4) ◽  
pp. 608-616 ◽  
Author(s):  
Robert J. S. Brown ◽  
Jan Korringa
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Fluid Pressure ◽  
Reciprocity Theorem ◽  
Pore Fluid ◽  
Pore System ◽  
Porous Rock ◽  
Special Cases ◽  
The One ◽  
Interconnected Pore

An equation is derived for the dependence of the elastic properties of a porous material on the compressibility of the pore fluid. More generally, the elastic properties of a container of arbitrary shape are related to the compressibility of the fluid filling a cavity in the container. If the pore system or cavity under consideration is filled with a fluid of compressibility [Formula: see text], the compressibility κ* of the closed container is given by [Formula: see text] Here [Formula: see text] is the compressibility of the container with the fluid pressure held constant in the interconnected pore system or cavity. Fluids in other pores or cavities not connected with the one in question contribute to the value of [Formula: see text]. ϕ is the porosity, i.e., the volume fraction corresponding to the pore system or cavity in question. The equation contains two distinct effective compressibilities, [Formula: see text] and [Formula: see text], of the material exclusive of the pore fluid. When this material is homogeneous, one has [Formula: see text], and the equation reduces to a well‐known relation by Gassmann. For the other elastic properties, we also obtain expressions which generalize Gassmann’s work and which also differ from it only in the appearance of [Formula: see text] instead of [Formula: see text] in one term. Our result is intimately related to the reciprocity theorem of elasticity. Special cases are discussed.

scholarly journals Second order homogenization of quasi-periodic structures

2018 ◽  
Vol 40 (4) ◽  
pp. 325-348
Author(s):  
Duc Trung Le ◽  
Jean-Jacques Marigo
Keyword(s):  
General Framework ◽  
Volume Fraction ◽  
Effective Properties ◽  
Periodic Structures ◽  
Expansion Method ◽  
Second Order ◽  
Unit Cell ◽  
One Dimensional ◽  
Minimization Problems ◽  
Asymptotic Expansion Method

The paper develops a general framework to derive the effective properties of quasi-periodic elastic medium. By using the asymptotic expansion method, the solution is expanded to the second order by solving a sequence of minimization problems. The effective stiffness tensors fields entering in the expression of the macroscopic energy are obtained by solving several families of microscopic problems posed on the unit cell and which bring into play only the microstructure. As an illustrative example, we consider an anti-plane elastic case of a heterogeneous cylinder made of a bi-layer laminate and submitted to the gravity. The unit cell being one-dimensional, all the associated elementary problems can be solved in a closed form and one shows that the effective energy of the medium expanded up to the second order depends not only on the strain gradient, but also on the gradient of the volume fraction \(\theta\) characterizing the repartition of the two materials in the laminate.

scholarly journals Static component of photothermal response in non-transparent samples

2012 ◽  
Vol 25 (3) ◽  
pp. 213-224 ◽  
Author(s):  
Zlatan Soskic ◽  
Slobodanka Galovic ◽  
Nebojsa Bogojevic ◽  
Slobodan Todosijevic
Keyword(s):  
Temperature Distribution ◽  
Mean Value ◽  
Optical Absorption Coefficient ◽  
Back Side ◽  
One Dimensional ◽  
Static Component ◽  
Special Cases ◽  
Static Part ◽  
The Mean ◽  
Analytical Expressions

The paper presents the analysis of the static component of temperature distribution in non-transparent samples during photothermal measurements. Analytical expressions for static part of temperature distribution in the irradiated sample and in its surroundings are determined using one dimensional model of heat transfer in a typical photothermal environment. It is established that the dominant factors that influence the shape and the mean value of the temperature distribution are optical absorption coefficient and thermal conductances of the sample and the surroundings. Important special cases are described and analytical expressions for temperatures of the front and the back side of the sample are derived.

Effective Moduli of Solids With Cavities of Various Shapes

1994 ◽  
Vol 47 (1S) ◽  
pp. S151-S174 ◽  
Author(s):  
M. Kachanov ◽  
I. Tsukrov ◽  
B. Shafiro
Keyword(s):  
Stress Field ◽  
Elastic Properties ◽  
Effective Properties ◽  
Average Stress ◽  
Effective Moduli ◽  
Effective Elastic Properties ◽  
Elastic Potentials ◽  
Special Cases ◽  
Elliptical Holes ◽  
Unified Description

Effective elastic properties of solids with cavities of various shapes are derived in two approximations: the approximation of non-interacting cavities and the approximation of the average stress field (Mori-Tanaka’s scheme); the latter appears to be appropriate when mutual positions of defects are random. We construct the elastic potential of a solid with cavities. Such an approach covers, in a unified way, cavities of various shapes and any mixture of them. No degeneracies (or a need in a special limiting procedure) arise when cavities shrink to cracks. It also provides a unified description of both isotropic and anisotropic effective properties and recovers results available in the literature for special cases. Elastic potentials dictate the choice of proper parameters of cavity density. These parameters depend on defect shapes. Even in the case of random orientations, the isotropic overall properties cannot be characterized in terms of porosity alone; for elliptical holes, for example, a second parameter - “eccentricity” - is needed.

Modeling of the Effective Elastic Properties of Multifunctional Carbon Nanocomposites Due to Agglomeration of Straight Circular Carbon Nanotubes in a Polymer Matrix

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Chetan Shivaputra Jarali ◽  
Somaraddi R. Basavaraddi ◽  
Björn Kiefer ◽  
Sharanabasava C. Pilli ◽  
Y. Charles Lu
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Properties ◽  
Transverse Isotropy ◽  
Effective Elastic Moduli ◽  
Effective Elastic Properties ◽  
The Matrix ◽  
Nanotube Composites

In the present study, the effective elastic properties of multifunctional carbon nanotube composites are derived due to the agglomeration of straight circular carbon nanotubes dispersed in soft polymer matrices. The agglomeration of CNTs is common due to the size of nanotubes, which is at nanoscales. Furthermore, it has been proved that straight circular CNTs provide higher stiffness and elastic properties than any other shape of the nanofibers. Therefore, in the present study, the agglomeration effect on the effective elastic moduli of the CNT polymer nanocomposites is investigated when circular CNTs are aligned straight as well as distributed randomly in the matrix. The Mori–Tanaka micromechanics theory is adopted to newly derive the expressions for the effective elastic moduli of the CNT composites including the effect of agglomeration. In this direction, analytical expressions are developed to establish the volume fraction relationships for the agglomeration regions with high, and dilute CNT concentrations. The volume of the matrix in which there may not be any CNTs due to agglomeration is also included in the present formulation. The agglomeration volume fractions are subsequently adopted to develop the effective relations of the composites for transverse isotropy and isotropic straight CNTs. The validation of the modeling technique is assessed with results reported, and the variations in the effective properties for high and dilute agglomeration concentrations are investigated.

scholarly journals Refinement of the Maxwell formula for a composite reinforced by circular cross-section fibres. Part II: using Padé approximants

2020 ◽  
Vol 231 (12) ◽  
pp. 5145-5157
Author(s):  
Igor I. Andrianov ◽  
Jan Awrejcewicz ◽  
Galina A. Starushenko ◽  
Vladimir A. Gabrinets
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Volume Fraction ◽  
Effective Properties ◽  
Circular Cross Section ◽  
The Novel ◽  
High Contrast ◽  
Asymptotic Results ◽  
Reinforced Composite ◽  
Coefficient Of Thermal Conductivity

Abstract The effective properties of the fiber-reinforced composite materials with fibers of circle cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For an analytical solution of the periodically repeated cell problem the Schwarz alternating process (SAP) was employed. Convergence of this method was proved by S. Mikhlin, S. Sobolev, V. Mityushev. Unfortunately, the rate of the convergence is often slow, especially for nondilute high-contrast composite materials. For improving this drawback we used Padé approximations for various forms of SAP solutions with the following additive matching of obtained expressions. As a result, the solutions in our paper are obtained in a fairly simple and convenient form. They can be used even for a volume fraction of inclusion very near the physically possible maximum value as well as for high-contrast composite constituents. The results are confirmed by comparison with known numerical and asymptotic results.

Three-Phase Cylinder Model of One-Dimensional Hexagonal Piezoelectric Quasi-Crystal Composites

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Junhong Guo ◽  
Ernian Pan
Keyword(s):  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Interphase Layer ◽  
Effective Moduli ◽  
Fiber Volume ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Three Phase ◽  
Cylinder Model

A three-phase cylinder model (inclusion/matrix/composite) is proposed and analyzed for one-dimensional (1D) piezoelectric quasi-crystal composites. The exact closed-form solutions of the stresses of the phonon and phason fields and the electric field are derived under far-field antiplane mechanical and in-plane electric loadings via the Laurent expansion technique. Numerical results show that the thickness and material properties of the interphase layer can significantly affect the induced fields in the inclusion and interphase layer. Furthermore, the generalized self-consistent method is applied to predict analytically the effective moduli of the piezoelectric quasi-crystal composites. It is observed from the numerical examples that the effective moduli of piezoelectric quasi-crystal composites are very sensitive to the fiber volume fraction as well as to the individual material properties of the fiber and matrix. By comparing QC/PE with QC1/QC2, PE/QC, and PZT-7/epoxy, we found that using QC as fiber could, in general, enhance the effective properties, a conclusion which is in agreement with the recent experimental results.

scholarly journals Global Sensitivity Analysis for the Polymeric Microcapsules in Self-Healing Cementitious Composites

Polymers ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2990 ◽  
Author(s):  
Shuai Zhou ◽  
Yue Jia ◽  
Chong Wang
Keyword(s):  
Sensitivity Analysis ◽  
Elastic Properties ◽  
Global Sensitivity Analysis ◽  
Volume Fraction ◽  
Effective Properties ◽  
Micromechanical Model ◽  
Cementitious Composites ◽  
Self Healing ◽  
Effective Elastic Properties ◽  
Global Sensitivity

Cementitious composites with microencapsulated healing agents are appealing due to the advantages of self-healing. The polymeric shell and polymeric healing agents in microcapsules have been proven effective in self-healing, while these microcapsules decrease the effective elastic properties of cementitious composites before self-healing happens. The reduction of effective elastic properties can be evaluated by micromechanics. The substantial complicacy included in micromechanical models leads to the need of specifying a large number of parameters and inputs. Meanwhile, there are nonlinearities in input–output relationships. Hence, it is a prerequisite to know the sensitivity of the models. A micromechanical model which can evaluate the effective properties of the microcapsule-contained cementitious material is proposed. Subsequently, a quantitative global sensitivity analysis technique, the Extended Fourier Amplitude Sensitivity Test (EFAST), is applied to identify which parameters are required for knowledge improvement to achieve the desired level of confidence in the results. Sensitivity indices for first-order effects are computed. Results show the volume fraction of microcapsules is the most important factor which influences the effective properties of self-healing cementitious composites before self-healing. The influence of interfacial properties cannot be neglected. The research sheds new light on the influence of parameters on microcapsule-contained self-healing composites.

Design and Effective Properties of a Functionally Graded Unidirectional Fiber-Reinforced Composite

2015 ◽  
Author(s):  
Satyajit Panda
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Coupled Analysis ◽  
Sigmoid Function ◽  
Thickness Direction ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Representative Volume ◽  
Reinforced Composite

The present work deals with the design of a fiber-reinforced composite lamina with varying fiber-volume fraction (FVF) along its thickness direction. In the available elastic analyses of this kind of composite, the elastic properties are evaluated based on the assumptions like continuous variation of FVF and existence of decoupled representative volume element (RVE) at every point along the thickness direction. In order to predict the graded material properties without any of these assumptions at present, first a micro-structure of similar graded composite is designed for the variation of FVF according to a sigmoid function of thickness coordinate. Next, a continuum micro-mechanics finite element model of the corresponding representative volume (RV) is derived. The RV is basically composed of several micro-volumes of different FVFs and the classical homogenization treatment is implemented over these micro-volumes without decoupling them from the overall volume of RV. The importance of this coupled analysis is verified through a parallel decoupled analysis. The effect of the total number of micro-volumes within a specified thickness of lamina on its graded elastic properties is presented. The characteristics of graded elastic properties according to the sigmoid function are also discussed.

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