a, b = Radii of particle and concentric matrix
yl), yl(" = Complicated functions of the elastic constants
2.2.1.4 Christensen and Lo's generalized self-consistent scheme
The generalized self-consistent scheme is illustrated in figure 2.2.
b
W SPHERICAL INCLUSION
C MATRIX
EZ3 EFFECTIVE MEDIUM
Figure 2.2 The Generalized Self-Consistent Scheme Model (3)
The shear modulus is given by the following equations:
A:- +2B G + +C= 0 (2.16)
where
A, B, C = Lengthy functions of the elastic constants,.
Up to this point, four micromechanical models have been reviewed. Figure 2.3 (9)
gives a comparison of mixture stiffness calculated from using these four
micromechanical models to measured creep stiffness. The figure shows that the bounds
of Paul are the widest, followed by the arbitrary geometry bounds and the composite
spheres bounds. Paul's model and the arbitrary geometry model cover some measured