The Kerner equation was shown to be the same as the lower bound solution for a quasi-isotropic and quasi-homogeneous multiphase material of arbitrary geometry that was developed by Hashin and Shtrikman in. The Hashin and Shtrikman equation, which defined the upper bound solution for the case where the rigid phase was continuous and the lower bound solution where the rigid phase was discontinuous, led to the best possible limits, given only the volume fractions and moduli of the constituent phases.

It was observed that for similar geometry, the relative change of velocity in Newtonian liquids obeys similar rules as the relative change of shear strain in Hookean solids, which is represented by the relationship; (*h _{c}/h_{m}*) = (

*G*). The symbols

_{c}/G_{m}*h*and

_{c}*h*and

_{m}*G*and

_{c}*G*in this equation stand for the viscosity of the particulate composite and matrix, respectively, and the shear modulus of the particulate composite and matrix, respectively. The author further noted that since Newtonian liquids are practically incompressible, the foregoing relationship implies incompressible material behaviour of the Hookean solid matrix. Materials that are incompressible have a Poisson’s ratio of 0.5, which is implied for the matrix by this relationship. It was noted that the shear modulus of particulate composites comprising of rigid particles in rubbery matrices (Poisson’s ratio of 0.5) will increase with increasing content of the rigid particles, in the same way as the viscosity of a liquid with suspended particles in it.

_{m}**Author(s) Details:**

** Maina Maringa, **

Department of Mechanical and Mechatronic Engineering, Central University of Technology, Private Bag X20539, 20 President Brand Street Westdene, Bloemfontein, 9300, Free State, South Africa.