On estimation methods for effective moduli of microcracked solids

Summary  Most of the conventional methods for estimating the overall elastic moduli of microcracked solids are defined based on the concept of effective medium or effective field. The formal similarity of these methods is examined in this paper. A one-to-one correspondence relation exists between the effective medium methods and the effective field methods in the sense that they yield identical results. In addition to the conventional estimation techniques, any other number of such approaches may be constructed by appropriately specifying the effective matrix compliance (or stiffness) tensor and the effective stress (or strain) field which a microcrack is assumed to be subjected to. To generate continuous spectra of new methods for estimating the effective elastic moduli, two simple and straightforward approaches are proposed, which contain one or two adjustable parameters in order to yield results of good accuracy. The discussion in this paper can be extended to other kinds of heterogeneous materials. Received 4 October 2000; accepted for publication 30 January 2001