Simplification of van der Poel's Formula for the Shear Modulus of a Particulate Composite

The coefficients in van der Poel's equation for calculating the shear modulus of a particulate composite have been greatly simplified, making the calculation much less unwieldy. Approximate solutions of van der Poel's equation are also derived, and it is shown that one of the low order approximations is Kernels equation, or Mashin and Shtrikman's equation for the highest lower hound. The Kerner approximation is often too low in value when the volume fraction of filler exceeds 0.2, but it can he used to provide further simplification in van der Poel's equation, or it can be used as a first approximation in a Newton's method of solution.