BOUNDS ON THE SHEAR MODULUS OF COMPOSITES BY INTERFACE INTEGRAL METHODS

THE STRUCTURAL parameter eta2 enters into third-order bounds on the effective shear modulus of two-component composites. Its definition is often given as an integral over correlation functions. We show how to express eta2 as an integral over the component interfaces. This leads to substantial simplifications from a numerical viewpoint. For the simple hexagonal array of disks we give eta2 to double precision accuracy for any volume fraction. In the past only one accurate digit, or less, has been achieved for this geometry. We also discuss how to apply the fast multipole method to make possible the calculation of eta2 for suspensions with thousands of disks per unit cell and for composites with arbitrary geometries.