Abstract of the paper ``Variational bounds on elastic constants for the
penetrable sphere model''
Since analytical results are known for the two-point and three-point
spatial correlation functions of the penetrable sphere model, Milton's
geometric parameters zeta and eta may be computed numerically as accurately
as desired. Once tabulated these geometric parameters may be then used to provide
variational bounds on elastic constants for a wide variety of two-phase composite materials assuming
that the geometrical distribution of constituents is similar to that of
the penetrable sphere model. The present paper develops the required
numerical methods for calculating the Milton numbers, provides a table of
results, and demonstrates the application to variational bounds in a few cases.
In those cases considered, the bounds of McCoy and of Milton and Phan-Thien
on the shear modulus are found to be virtually indistinguishable for the
penetrable sphere model.
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