Effective Elastic Moduli of Composite Materials: Reduced Parameter Dependence

1997 ◽  
Vol 50 (11S) ◽  
pp. S39-S43 ◽  
Author(s):  
John Dundurs ◽  
Iwona Jasiuk
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Elastic Moduli ◽  
Plane Elasticity ◽  
Parameter Dependence ◽  
Effective Elastic Moduli ◽  
Independent Variables ◽  
Effective Elastic Constants

In this paper, we focus on the effective elastic constants of composite materials and pay attention to the possibility of reducing the number of independent variables. Surprisingly, this important issue has hardly been explored before. In our analysis, we rely on a new result in plane elasticity due to Cherkaev, Lurie, and Milton (1992), and use Dundurs constants (Dundurs, 1967, 1969). As an example, we consider a result for the effective elastic moduli of a composite containing a dilute concentration of perfectly-bonded circular inclusions.

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.

Elastic Moduli of Two Dimensional Materials With Polygonal and Elliptical Holes

1994 ◽  
Vol 47 (1S) ◽  
pp. S18-S28 ◽  
Author(s):  
I. Jasiuk ◽  
J. Chen ◽  
M. F. Thorpe
Keyword(s):  
Elastic Constants ◽  
Conformal Transformation ◽  
Elastic Moduli ◽  
Far Field ◽  
Effective Elastic Moduli ◽  
Two Dimensional ◽  
Effective Elastic Constants ◽  
Two Dimensional Materials ◽  
Elliptical Holes ◽  
General Relations

We study the effective elastic moduli of two-dimensional composite materials containing polygonal holes. In the analysis we use a complex variable method of elasticity involving a conformal transformation. Then we take a far field result and derive the effective elastic constants of composites with a dilute concentration of polygonal holes. In the discussion we use the recently-stated Cherkaev-Lurie-Milton theorem, which gives general relations between the effective elastic constants of two-dimensional composites. We also discuss known results for elliptical holes in the context of the present work.

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.

Environmentally-Induced Expansion of Heterogeneous Media

1989 ◽  
Vol 56 (3) ◽  
pp. 546-549 ◽  
Author(s):  
Kalman Schulgasser
Keyword(s):  
Composite Materials ◽  
Relative Humidity ◽  
Elastic Constants ◽  
Heterogeneous Media ◽  
Direct Method ◽  
Environmental Variable ◽  
Effective Elastic Constants ◽  
Effective Expansion ◽  
Expansion Behavior

Relationships between effective expansion behavior and effective elastic constants for composite materials have been known for many years. In the present work composites are considered for which more than one environmental variable (e.g., temperature and relative humidity) cause expansions. A simple direct method to relate effective expansions due to different causes is developed. It is shown that most of the previous elasticity-expansion behavior results are gotten as corollaries, and the applicability of these relationships is broadened.

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