A COMPLETE CHARACTERIZATION OF THE POSSIBLE BULK AND SHEAR MODULI OF PLANAR POLYCRYSTALS

This paper investigates the range of possible elastic moduli of two-di mensional isotropic polycrystals. The polycrystals are comprised of gr ains obtained from a single orthotropic material. The overall elastic properties are described by an effective bulk modulus K-0 and an effec tive shear modulus mu(0). The pair (K-0, mu(0)) is shown to be confine d to a rectangle in the (K, mu) plane. Microstructures are identified which correspond to every point within the rectangle, and in particula r to the corner points. Optimal bounds on the effective Poisson's rati o and Young's modulus follow immediately. Under a certain constraint o n the crystal moduli, the rectangle degenerates to a line segment: the effective shear modulus of such a polycrystal is microstructure indep endent. This extends earlier work that established microstructure inde pendence for polycrystals constructed from square symmetric crystals. Copyright (C) 1996 Elsevier Science Ltd