Correlation functions for predicting properties of heterogeneous materials. III. Effective elastic moduli of two‐phase solids

1974 ◽  
Vol 45 (7) ◽  
pp. 3171-3179 ◽  
Author(s):  
Peter B. Corson
Keyword(s):  
Correlation Functions ◽  
Elastic Moduli ◽  
Heterogeneous Materials ◽  
Effective Elastic Moduli ◽  
Two Phase

Rigorous Link Between the Electrical and Mechanical Properties of Composite Materials

1995 ◽  
Vol 411 ◽  
Author(s):  
S. Torquato ◽  
L. V. Gibiansky
Keyword(s):  
Mechanical Properties ◽  
Electrical Conductivity ◽  
Dielectric Constant ◽  
Composite Materials ◽  
Elastic Moduli ◽  
Effective Elastic Moduli ◽  
Two Phase ◽  
Property Relations ◽  
Isotropic Composite ◽  
Effective Electrical Conductivity

ABSTRACTCross-property relations that link rigorously the effective electrical conductivity (or dielectric constant) and the effective elastic moduli of two-phase, isotropic composite materials are discussed. The cross-property relations can be optimal in some cases, i.e., they are realized by particular microstructures. The relations are applied to specific two-phase composites as well as to cracked media.

Homogenization of a fibre/sphere with an inhomogeneous interphase for the effective elastic moduli of composites

2005 ◽  
Vol 461 (2057) ◽  
pp. 1475-1504 ◽  
Author(s):  
Lianxi Shen ◽  
Jackie Li
Keyword(s):  
Strain Energy ◽  
Elastic Moduli ◽  
Radial Direction ◽  
Analytical Models ◽  
Effective Elastic Moduli ◽  
The Finite Element Method ◽  
Central Idea ◽  
Two Phase ◽  
Three Phase ◽  
Replacement Model

An effective interphase model (EIM) and a uniform replacement model (URM) are proposed to study the effect of an inhomogeneous interphase with varying elastic properties in the radial direction on the effective elastic moduli of composites reinforced by fibres/spheres. The central idea of these models is to convert a fibre/sphere with its interphase into a two-phase or homogeneous fibre/sphere. Then, the strain energy changes can be obtained using the three-phase model or Eshelby's solution. Detailed comparisons with the finite-element method (FEM) results of the strain energy changes for various possible material combinations of fibre/sphere, interphase and matrix are carried out to check the validity of the two models. Moreover, the other two existing models, the uniform interphase model (UIM) and differential replacement model (DRM), are compared with the new ones. It is shown that the validity of these analytical models depends on the material combinations. The EIM can be valid for general cases, while the simple URM is only valid for some cases. The validity ranges of the two existing models lie between those of the two new ones. Finally, the expressions of the effective elastic moduli of composites involving an inhomogeneous interphase are given by combining these models and the Mori–Tanaka method. The application of these expressions is illustrated through three examples and further comparisons with FEM results are also given.

The Elastic Moduli of Heterogeneous Materials

1962 ◽  
Vol 29 (1) ◽  
pp. 143-150 ◽  
Author(s):  
Zvi Hashin
Keyword(s):  
Approximate Method ◽  
Elastic Moduli ◽  
Heterogeneous Materials ◽  
Theory Of Elasticity ◽  
Experimental Results ◽  
Two Phase ◽  
Concentric Spheres ◽  
Theoretical Results ◽  
Nonhomogeneous Materials ◽  
Good Agreement

Bounds and expressions for the elastic moduli of two or many phase nonhomogeneous materials are obtained by an approximate method based on the variational theorems of the theory of elasticity and on a concentric-spheres model. Theoretical results are in good agreement with experimental results for a two-phase alloy.

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