The elasticity of polycrystals and rocks

We calculate the effective elastic properties of various polycrystals and rocks using a self-consistent integral equation technique developed in the theory of disordered alloys. This technique includes but is more general than the self-consistent approximation developed by Hershey, Kröner (1958), and others. In practice the technique is easily adaptable to computer analysis for modest cost. Our computed results compare well with experimental data. Also we point out that an approximation for the perfectly disordered aggregate developed by Kröner (1967) is not exact as claimed but is an approximation to the selfconsistent approximation.