On the generalized self-consistent model for elastic wave propagation in composite materials

Abstract

The generalized self-consistent model (GSCM) for the analysis of elastic wave propagation in composite materials is recast. Following the idea of the GSCM in the static problem, elastic wave energy in the model is evaluated by applying the energy theorem for the elastic wave scattering in an absorbing medium. The conditions for dynamic effective medium are then obtained in a self-consistent way as those under which the extinguished wave energy in the model vanishes, thus without relying on the multiple scattering formalism. It is shown that the present dynamic GSCM is equivalent to the models of Yang and Mal [J. Mech. Phys. Solids 42 (1994) 1945] and Yang [J. Appl. Mech. 70 (2003) 575] that have been obtained through the use of the multiple scattering formalism of Waterman and Truell. Numerical results for both fiber-reinforced and particulate composites are presented. Physical realizability of the dynamic GSCM in the low frequency limit is discussed briefly.