Effective medium theory for elastic composites

INTRODUCTION

In a series of papers [Berryman (1979,1980a,b)], a variant on effective medium theories for elastic composites was developed by the author. In this paper, I will review the derivation of the effective medium formulas for the elastic constants of composites while elucidating the relationships between my results and the results from effective medium theories proposed by others. These results are then compared to known rigorous bounds on the effective elastic constants.

The general background for theories of elastic composites with special emphasis on earth sciences applications is provided in the review articles by Watt et al. (1976) and Berryman (1995). Another review of effective medium theories with an emphasis on connections to general applied physics applications is given by Elliott et al. (1974). Related work by Willis (1981,1977) is also especially useful for some of the cases not considered here, including anisotropic media and polycrystalline composites.

Effective medium theory for elastic composites