scholarly journals Effective properties of two-phase disordered composite Media. I. Simplification of bounds on the conductivity and bulk modulus of dispersions of impenetrable spheres

1986 ◽  
Vol 33 (5) ◽  
pp. 3370-3378 ◽  
Author(s):  
F. Lado ◽  
S. Torquato
Keyword(s):  
Bulk Modulus ◽  
Effective Properties ◽  
Composite Media ◽  
Two Phase

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

Elastic Moduli of Thickly Coated Particle and Fiber-Reinforced Composites

1991 ◽  
Vol 58 (2) ◽  
pp. 388-398 ◽  
Author(s):  
Y. P. Qiu ◽  
G. J. Weng
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Elastic Moduli ◽  
Poisson Ratio ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Two Phase ◽  
Coated Particle ◽  
Replacement Method

Based on the models of Hashin (1962) and Hashin and Rosen (1964), the effective elastic moduli of thickly coated particle and fiber-reinforced composites are derived. The microgeometry of the composite is that of a progressively filled composite sphere or cylinder element model. The exact solutions of the effective bulk modulus κ of the particle-reinforced composite and those of the plain-strain bulk modulus κ23, axial shear modulus μ12, longitudinal Young’s modulus E11, major Poisson ratio ν12, of the fiber-reinforced one are derived by the replacement method. The bounds for the effective shear modulus μ and the effective transverse shear modulus μ23 of these two kinds of composite, respectively, are solved with the aid of Christensen and Lo’s (1979) formulations. By considering the six possible geometrical arrangements of the three constituent phases, the values of κ, and of κ23, μ12, E11, and ν12 are found to always lie within the Hashin-Shtrikman (1963) bounds, and the Hashin (1965), Hill (1964), and Walpole (1969) bounds, respectively, but unlike the two-phase composites, none coincides with their bounds. The bounds of μ and μ23 derived here are consistently tighter than their bounds but, as for the two-phase composites, one of the bounds sometimes may fall slightly below or above theirs and therefore it is suggested that these two sets of bounds be used in combination, always choosing the higher for the lower bound and the lower for the upper one.

On the homogenized yield strength of two-phase composites

1992 ◽  
Vol 438 (1903) ◽  
pp. 419-431 ◽  
Keyword(s):  
Yield Strength ◽  
Effective Properties ◽  
Transverse Isotropy ◽  
Two Phase ◽  
Perfectly Plastic ◽  
Plastic Composite ◽  
Plastic Composites ◽  
Effective Yield ◽  
The Individual ◽  
Variational Statement

This paper is concerned with the determination of the effective yield strength of two-phase, rigid-perfectly plastic composite materials. The individual phases are assumed to satisfy, for simplicity, incompressible, isotropic yield criteria of the Mises type. The volume fractions of the constituent phases are prescribed, but their distribution within the composite is otherwise arbitrary. Using the homogenization framework of Suquet (1983) to define the homogenized, or effective, yield strength domain of rigid-perfectly plastic composites, a variational statement is introduced allowing the estimation of the associated effective dissipation functions of plastic composites in terms of the effective dissipation functions of corresponding classes of linearly viscous comparison composites. Thus the variational statement suggests a procedure for generating bounds and estimates for the effective yield strength of rigid-perfectly plastic composites from well-known bounds and estimates for the effective properties of the corresponding linear comparison composites. Sample results are given in the form of upper bounds and lower estimates of the Hashin-Shtrikman type for the effective yield strength of two-phase composites with overall isotropy. Additionally, estimates and bounds are also given for the effective strength domains of two-phase laminated and fibre-reinforced composites, with overall transverse isotropy.

REITERATED HOMOGENIZATION OF INTEGRAL FUNCTIONALS

2000 ◽  
Vol 10 (01) ◽  
pp. 47-71 ◽  
Author(s):  
ANDREA BRAIDES ◽  
DAG LUKKASSEN
Keyword(s):  
Energy Density ◽  
Quadratic Form ◽  
Phase Structure ◽  
Effective Properties ◽  
Effective Property ◽  
Integral Functionals ◽  
Effective Energy ◽  
Two Phase ◽  
Wide Range ◽  
Reiterated Homogenization

We consider the homogenization of sequences of integral functionals defined on media with several length-scales. Our general results connected to the corresponding homogenized functional are used to analyze new types of structures and to illustrate the wide range of effective properties achievable through reiteration. In particular, we consider a two-phase structure which is optimal when the integrand is a quadratic form and point out examples where the macroscopic behavior of this structure underlines an effective energy density which is lower than that of the best possible multirank laminate. We also present some results connected to a reiterated structure where the effective property is extremely sensitive of the growth of the integrand.

On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus

1993 ◽  
Vol 440 (1908) ◽  
pp. 163-188 ◽  
Keyword(s):  
Bulk Modulus ◽  
Complex Dielectric Constant ◽  
Effective Moduli ◽  
Two Phase ◽  
Shear Moduli ◽  
Isotropic Composite ◽  
Effective Bulk Modulus ◽  
Circular Arcs ◽  
Static Regime ◽  
Rigorous Bounds

The dynamic response of isotropic composites of two viscoelastic isotropic phases mixed in fixed proportions is considered in the frequency range where the acoustic wavelength is much larger than the inhomogeneities. The effective bulk-modulus bounds of Hashin-Shtrikman-Walpole are extended to viscoelasticity in this quasi-static régime, where the properties of the isotropic composite can be described by complex bulk and shear moduli. The effective bulk modulus is shown to be constrained to a lens-shaped region of the complex plane bounded by the outermost pair of four circular arcs (three circular arcs in the case of two-dimensional elasticity). This is proved using a new variational principle for viscoelasticity together with two established techniques for deriving bounds on effective moduli, namely the translation method and the Hashin-Shtrikman method. In this application the Hashin-Shtrikman method needs to be generalized to allow the reference tensor to have an associated quasiconvex energy. Microstructures are identified which have bulk-moduli that correspond to various points on each of the circular arcs. Thus these microstructures have extremal viscoelastic behaviour when the associated arc forms one of the outermost pair. The bounds and the extremal microstructures are similar to those obtained for the complex dielectric constant, but the methods used here are entirely different.

Thermal stresses in two‐phase composite media

1995 ◽  
Vol 18 (5) ◽  
pp. 639-653 ◽  
Author(s):  
June‐Liang Chu ◽  
Sanboh Lee
Keyword(s):  
Thermal Stresses ◽  
Composite Media ◽  
Two Phase
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