Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials

1992 ◽  
Vol 59 (3) ◽  
pp. 539-546 ◽  
Author(s):  
Tungyang Chen ◽  
George J. Dvorak ◽  
Yakov Benveniste
Keyword(s):  
Composite Materials ◽  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Effective Elastic Moduli ◽  
Explicit Formulae ◽  
Cylindrically Orthotropic ◽  
Multiphase Composite

Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.

scholarly journals On the Theory of Elasticity of Microinhomogeneous Media with Account for Stochastic Changes in the Connectivity of Constituent Components

2021 ◽  
pp. 132-143
Author(s):  
L. A Saraev
Keyword(s):  
Differential Equation ◽  
Composite Material ◽  
Composite Materials ◽  
Numerical Solution ◽  
Elastic Moduli ◽  
Production Factor ◽  
Effective Elastic Moduli ◽  
Connectivity Function ◽  
Isotropic Composite ◽  
Random Connectivity

The paper proposes a mathematical model aimed at calculating the effective elastic moduli of a micro-inhomogeneous two-component isotropic composite material, which components are connected randomly depending on the level of their relative volumetric contents. A stochastic equation is formulated for the connectivity parameter of the constituent components, according to which, with an increase in the volumetric content of the filler, individual inclusions build the structures of the matrix mixture in the form of interpenetrating frameworks, and then turn into a new binding matrix with individual inclusions from the material of the rest of the old matrix. The algorithm for the numerical solution of this stochastic differential equation is constructed in accordance with the Euler-Maruyama method. For each implementation of this algorithm, the corresponding stochastic trajectories are constructed for the random connectivity function of the constituent components of the composite material. A variant of the method aimed at calculating the mathematical expectation of a random connectivity function of the constituent components has been developed and the corresponding differential equation has been obtained for it. It is shown that the numerical solution of this equation and the average value of the production factor function calculated for all realizations of stochastic trajectories give close numerical values. New macroscopic constitutive relations are found for microinhomogeneous materials with a variable microstructure and their effective elastic moduli are calculated. It is noted that the formulas for these effective elastic moduli generalize the known results for isotropic composite materials. The values of the effective elastic moduli, constructed according to the expressions obtained in the paper, lie within the Khashin-Shtrikman range for the lower and upper bounds of the effective elastic moduli of the composite materials. The numerical analysis of the developed models showed a good agreement with the known experimental data.

scholarly journals Evaluation of Effective Elastic Properties of Nitride NWs/Polymer Composite Materials Using Laser-Generated Surface Acoustic Waves

2018 ◽  
Vol 8 (11) ◽  
pp. 2319 ◽  
Author(s):  
Evgeny Glushkov ◽  
Natalia Glushkova ◽  
Bernard Bonello ◽  
Lu Lu ◽  
Eric Charron ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Composite Materials ◽  
Elastic Constants ◽  
Acoustic Waves ◽  
Composite Structures ◽  
Elastic Moduli ◽  
Surface Acoustic Waves ◽  
Dispersion Curves ◽  
Effective Elastic Moduli ◽  
Asymptotic Representations

In this paper we demonstrate a high potential of transient grating method to study the behavior of surface acoustic waves in nanowires-based composite structures. The investigation of dispersion curves is done by adjusting the calculated dispersion curves to the experimental results. The wave propagation is simulated using the explicit integral and asymptotic representations for laser-generated surface acoustic waves in layered anisotropic waveguides. The analysis of the behavior permits to determine all elastic constants and effective elastic moduli of constituent materials, which is important both for technological applications of these materials and for basic scientific studies of their physical properties.

Effective Elastic Moduli of Ribbon-Reinforced Composites

1990 ◽  
Vol 57 (1) ◽  
pp. 158-167 ◽  
Author(s):  
Y. H. Zhao ◽  
G. J. Weng
Keyword(s):  
Aspect Ratio ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Isotropic Case ◽  
Effective Elastic Moduli ◽  
Cross Sectional ◽  
Isotropic Composite ◽  
The Matrix ◽  
The Hill

Based on the Eshelby-Mori-Tanaka theory the nine effective elastic constants of an orthotropic composite reinforced with monotonically aligned elliptic cylinders, and the five elastic moduli of a transversely isotropic composite reinforced with two-dimensional randomly-oriented elliptic cylinders, are derived. These moduli are given in terms of the cross-sectional aspect ratio and the volume fraction of the elliptic cylinders. When the aspect ratio approaches zero, the elliptic cylinders exist as thin ribbons, and these moduli are given in very simple, explicit forms as a function of volume fraction. It turns out that, in the transversely isotropic case, the effective elastic moduli of the composite coincide with Hill’s and Hashin’s upper bounds if ribbons are harder than the matrix, and coincide with their lower bounds if ribbons are softer. These results are in direct contrast to those of circular fibers. Since the width of the Hill-Hashin bounds can be very wide when the constituents have high modular ratios, this analysis suggests that the ribbon reinforcement is far more effective than the traditional fiber reinforcement.

Sign in / Sign up

Export Citation Format

Share Document