LONGWAVE SPEEDS IN MATERIALS WITH CRACKS AND CAVITIES OF VARIOUS SHAPES Boris Shafiro Mechanical Engineering Department Tufts University Medford, MA 02155 Mark Kachanov Mechanical Engineering Department Tufts University Medford, MA 02155 INTRODUCTION Propagation of plane elastic waves in materials with cavities of various shapes and cracks (or mixtures of cavities of diverse shapes) is discussed in the longwave limit. In this limit, the wavespeeds are determined by the effective elastostatic moduli, i.e. the material is modeled by the homogeneous elastic solid having effective elastic constants. A particular attention is paid to anisotropies due to preferential orientations of cavities of various shapes and to the number of independent constants and wavespeeds. The analysis is based on recently obtained results of Kachanov [1] and Kachanov et al [2] for the effective elastic properties of materials with cavities of various shapes. GENERAL RELATIONS FOR THE EFFECTIVE PROPERTIES This section briefly overviews the general approach to the problem of effective moduli of solids with cavities and cracks. For details, see [1], [2]. An Infinite Solid with One Cavity The starting point is the observation that the total strain in a solid subjected to a remotely applied stress u and containing a cavity is given by a sum (1) where MO is the compliance tensor of the matrix; a colon denotes contraction over two indices. The additional strain due to introduction of a cavity is .1c=--l-f (un+nu)dT 2V r Review of Progress in Quantitative Nondestructive Evaluation. Vol. 14 Edited by D.O. Thompson and D.E. Chimenti. Plenum Press. New York. 1995 (2) 1955