scholarly journals EFFECTIVE-MEDIUM THEORY FOR ELECTRICAL CONDUC-TANCE OF A TWO-PHASE COMPOSITE MEDIUM WITH ELLIPSOIDAL-INCLUSIONS

1992 ◽  
Vol 41 (5) ◽  
pp. 833
Author(s):  
BAO KE-DA
Keyword(s):  
Effective Medium Theory ◽  
Effective Medium ◽  
Composite Medium ◽  
Two Phase ◽  
Medium Theory

Ultrasonic velocity‐porosity relationships for sandstone analogs made from fused glass beads

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 108-119 ◽  
Author(s):  
Patricia A. Berge ◽  
Brian P. Bonner ◽  
James G. Berryman
Keyword(s):  
Upper Bound ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Glass Beads ◽  
Composite Medium ◽  
Host Material ◽  
Consistent Theory ◽  
Medium Theory ◽  
Wide Range ◽  
Self Consistent

Using fused glass beads, we have constructed a suite of clean sandstone analogs, with porosities ranging from about 1 to 43 percent, to test the applicability of various composite medium theories that model elastic properties. We measured P‐ and S‐wave velocities in dry and saturated cases for our synthetic sandstones and compared the observations to theoretical predictions of the Hashin‐Shtrikman bounds, a differential effective medium approach, and a self‐consistent theory known as the coherent potential approximation. The self‐consistent theory fits the observed velocities in these sandstone analogs because it allows both grains and pores to remain connected over a wide range of porosities. This behavior occurs because this theory treats grains and pores symmetrically without requiring a single background (host) material, and it also allows the composite medium to become disconnected at a finite porosity. In contrast, the differential effective medium theory and the Hashin‐Shtrikman upper bound overestimate the observed velocities of the sandstone analogs because these theories assume the microgeometry is represented by isolated pores embedded in a host material that remains continuous even for high porosities. We also demonstrate that the differential effective medium theory and the Hashin‐Shtrikman upper bound correctly estimate bulk moduli of porous glass foams, again because the microstructure of the samples is consistent with the implicit assumptions of these two theoretical approaches.

scholarly journals Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

Materials ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1243 ◽  
Author(s):  
Andrei A. Snarskii ◽  
Mikhail Shamonin ◽  
Pavel Yuskevich
Keyword(s):  
Composite Materials ◽  
Elastic Properties ◽  
Effective Conductivity ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Effective Parameters ◽  
Two Phase ◽  
Medium Theory ◽  
Percolation Thresholds ◽  
Conductive Properties

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.

Sign in / Sign up

Export Citation Format

Share Document