Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities

1994 ◽  
Vol 103 (1-4) ◽  
pp. 123-144 ◽  
Author(s):  
J. W. Ju ◽  
T. M. Chen
Keyword(s):  
Elastic Moduli ◽  
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.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

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