The Effective Properties of Composite Materials With Constant Reinforcement Density by the Linear Mori-Tanaka Method

1994 ◽  
Vol 116 (3) ◽  
pp. 428-437 ◽  
Author(s):  
J. R. Zuiker ◽  
G. J. Dvorak
Keyword(s):  
Composite Materials ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Local Fields ◽  
Original Form ◽  
Constant Field ◽  
Inhomogeneous Materials ◽  
Reinforcement Density ◽  
Variable Reinforcement

In its original form, the Mori-Tanaka method estimates constant overall properties of statistically homogeneous composite materials subjected to uniform overall stresses, strain or temperature changes, from averages of local fields in the phases. To permit applications involving large overall stress and/or temperature gradients, and functionally graded materials with a variable reinforcement density, the method has been extended to linearly variable overall and local fields by Zuiker and Dvorak (Composites Engineering, Vol. 4, 19–35, 1994) as a first step toward application of the method to statistically inhomogeneous materials with variable reinforcement density. Here, the effective properties are examined in detail. Non-zero components of the stiffness matrix are shown to satisfy invariance requirements and to vary with reinforcement volume fraction and size of the representative volume. It is shown that the linear and constant field approaches provide different estimates of overall properties for small representative volumes, but nearly identical estimates for large volumes.

scholarly journals Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 79 ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Elastic Response ◽  
Governing Equations ◽  
Third Order ◽  
Reinforced Composite

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

Challenge problems for the benchmarking of micromechanics analysis: Level I initial results

2017 ◽  
Vol 52 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Hamsasew M Sertse ◽  
Johnathan Goodsell ◽  
Andrew J Ritchey ◽  
R Byron Pipes ◽  
Wenbin Yu
Keyword(s):  
Composite Materials ◽  
Resource Constraints ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Short Fiber ◽  
Local Fields ◽  
Element Analysis ◽  
Software Packages ◽  
Weave Fabric ◽  
Level I

Because of composite materials’ inherent heterogeneity, the field of micromechanics provides essential tools for understanding and analyzing composite materials and structures. Micromechanics serves two purposes: homogenization or prediction of effective properties and dehomogenization or recovery of local fields in the original heterogeneous microstructure. Many micromechanical tools have been developed and codified, including commercially available software packages that offer micromechanical analyses as stand-alone tools or as part of an analysis chain. With the increasing number of tools available, the practitioner must determine which tool(s) provides the most value for the problem at hand given budget, time, and resource constraints. To date, simple benchmarking examples have been developed in an attempt to address this challenge. The present paper presents the benchmark cases and results from the Micromechanical Simulation Challenge hosted by the Composites Design and Manufacturing HUB. The challenge is a series of comprehensive benchmarking exercises in the field of micromechanics against which such tools can be compared. The Level I challenge problems consist of six microstructure cases, including aligned, continuous fibers in a matrix, with and without an interphase; a cross-ply laminate; spherical inclusions; a plain-weave fabric; and a short-fiber microstructure with “random” fiber orientation. In the present phase of the simulation challenge, the material constitutive relations are restricted to linear thermoelastic. Partial results from DIGIMAT-MF, ESI VPS, MAC/GMC, finite volume direct averaging method, Altair MDS, SwiftComp, and 3D finite element analysis are reported. As the challenge is intended to be ongoing, the full results are hosted and updated online at www.cdmHUB.org .

TORSIONAL BUCKLING OF FUNCTIONALLY GRADED CYLINDRICAL SHELLS WITH TEMPERATURE-DEPENDENT PROPERTIES

2013 ◽  
Vol 14 (01) ◽  
pp. 1350048 ◽  
Author(s):  
JIABIN SUN ◽  
XINSHENG XU ◽  
C. W. LIM
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Effective Properties ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Accurate Solution ◽  
Functionally Graded ◽  
Torsional Buckling ◽  
Temperature Dependent Properties ◽  
Transverse Boundary

Based on Hamilton's principle, a new accurate solution methodology is developed to study the torsional bifurcation buckling of functionally graded cylindrical shells in a thermal environment. The effective properties of functionally graded materials (FGMs) are assumed to be functions of the ambient temperature as well as the thickness coordinate of the shell. By applying Donnell's shell theory, the lower-order Hamiltonian canonical equations are established, from which the eigenvalues and eigenvectors are solved as the critical loads and buckling modes of the shell of concern, respectively. The effects of various aspects, including the combined in-plane and transverse boundary conditions, dimensionless geometric parameters, FGM parameters and changing thermal surroundings, are discussed in detail. The results reveal that the in-plane axial edge supports do have a certain influence on the buckling loads. On the other hand, the transverse boundary conditions only affect extremely short shells. With increasing thermal loads, the material volume fraction has a different influence on the critical stresses. It is concluded that the optimized FGM mixtures to withstand thermal torsional buckling are Si 3 N 4/SUS304 and Al 2 O 3/SUS304 among the materials studied in this paper.

scholarly journals Optimization of Functionally Graded Structural Members by Means of New Effective Properties Estimation Method

Materials ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3139
Author(s):  
Anna Wiśniewska ◽  
Halina Egner
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Estimation Method ◽  
Functionally Graded ◽  
Structural Members ◽  
Structural Element ◽  
Composite Configuration ◽  
Analytical Formulae ◽  
Circular Bar ◽  
Composite Properties

An innovative method of effective composite mechanical properties estimation is applied to optimize the distribution of reinforcement in a functionally graded structural element. The concept is based on the assumption of the mechanical equivalence between two configurations: The real heterogeneous composite configuration and the fictitious quasi-homogeneous one. It allows to obtain the analytical formulae describing the dependence of the effective elastic composite properties on the volume fraction of reinforcing inclusions. As an example of application, a circular bar subjected to torsion is considered.

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.

The Thermal Instability Analysis of Functionally Graded Carbon Nanotube Composite Plates Using Finite Element Method

2014 ◽  
Vol 695 ◽  
pp. 285-288 ◽  
Author(s):  
Z.A. Rasid ◽  
Hafizal Yahaya
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Carbon Nanotube ◽  
Critical Temperature ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Parametric Studies ◽  
Element Method

In recent years carbon nanotube (CNT) has been combined with polymers to take advantage of the extremely high strength and stiffness of the CNT. This paper reports a study on the thermal instability of carbon nanotube reinforced composites (CNTRC) plate subjected to uniform temperature rise. Finite element method (FEM) formulation was developed based on the first order shear deformation theory. The extended rule of mixture was used to determine the effective properties of the CNTRC plate. The CNTRC plate was functionally graded in its thickness direction. The results of the thermal instability were validated using past results and several parametric studies were then conducted using the developed formulation. The parametric studies showed that the critical temperature of the CNTRC was increased with the increase of the CNT volume fraction and the FG-4 configuration gave the highest critical temperature.

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.

Vibration Reduction of Laminated Plates With Various Piezoelectric Functionally Graded Actuators

2008 ◽  
Author(s):  
Marek Pietrzakowski
Keyword(s):  
Numerical Simulations ◽  
Volume Fraction ◽  
Effective Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Dynamic Responses ◽  
Electromechanical Properties ◽  
Classical Plate Theory ◽  
Fraction Distribution

The aim of the present study is to develop models of active laminated plates containing monolithic piezopolymer sensor layers and a new type of actuator layers made of Piezoelectric Functionally Graded (PFG) material, which is a mixture of piezoceramics and polymer or epoxy matrix. The electromechanical properties of the PFG layers can be tailored varying continuously the piezoceramic volume fraction across the thickness during the manufacturing process. The analysis and numerical simulations are focused on the relationship between the material compositional gradient and electromechanical properties and also dynamic responses of the structure obtained. Three types of functions, which describe the volume fraction distribution of constituents, are considered: exponential, parabolic and sigmoid. The effective properties of the PFG material, i.e. the Young’s modulus and piezoelectric coefficient gradations, are determined using to the rule of mixtures. A constant velocity feedback algorithm is used for the active damping of transverse plate vibration. The dynamic analysis concerns steady-state behavior of rectangular symmetrically laminated plates and is based on hypothesis of the classical plate theory. The numerical simulations are performed to recognize the influence of the applied pattern of the piezoceramic fraction distribution and its parameters on the gradient of elastic and piezoelectric properties within the PFG actuators and, as the final result, the active plate structural response presented in terms of amplitude-frequency characteristics. The changes in both the natural frequencies and resonant amplitudes are compared and the influence of the piezoceramic gradation on the control system operational effectiveness is also indicated and discussed.

scholarly journals Transient Analysis of a Functionally Graded Ceramic/Metal Layer considering Lord-Shulman Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Antonios M. Nikolarakis ◽  
Efstathios E. Theotokoglou
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Effective Properties ◽  
Metal Layer ◽  
Time Integration ◽  
Maximum Tensile Stress ◽  
Functionally Graded ◽  
Sigmoid Function ◽  
The One ◽  
Functionally Graded Layer

The transient displacement, temperature, and stress fields in a functionally graded ceramic/metal layer under uniform thermal shock conditions at the upper surface are numerically studied based on the Lord-Shulman model, employing a direct finite element method. The Newmark method is employed for the time integration of the problem. A Matlab finite element code is developed for the numerical analysis of the one-dimensional problem under consideration. The Voigt model (rule of mixture) is used for the estimation of the effective properties inside the functionally graded layer and the variation of the volume fraction of the materials follows the sigmoid function in terms of the introduced parameter p. Furthermore, a parametric study with respect to the parameter p follows, where three different combinations of ceramic/metal materials are considered. It is concluded that the value p=1, which corresponds to a linear variation of the properties, minimizes the maximum (tensile) stress applied at the middle of the functionally graded layer.

Sign in / Sign up

Export Citation Format

Share Document