BOUNDS ON THE SHEAR MODULUS OF COMPOSITES BY INTERFACE INTEGRAL METHODS

THE STRUCTURAL parameter eta2 enters into third-order bounds on the ef fective shear modulus of two-component composites. Its definition is o ften given as an integral over correlation functions. We show how to e xpress eta2 as an integral over the component interfaces. This leads t o substantial simplifications from a numerical viewpoint. For the simp le 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 su spensions with thousands of disks per unit cell and for composites wit h arbitrary geometries.