Abstract. Particular expressions of upper and lower estimates for the macroscopic elastic bulk modulus of random cell tetragonal polycrystalline materials are derived and computed for a number of practical crystals. The cell-shape-unspecified bounds, based on minimum energy principles and generalized polarization trial fields, appear close to the simple bounds for specific spherical cell polycrystals.

Numerical finite element simulations on the homogenization problem for large random-aggregate samples of a particular 2D hexagonal-shape-geometry random polycrystals from the base crystals of orthorhombic symmetry have been performed. At sufficiently large random-aggregate samples, the scatter intervals converge toward the Voigt-Reuss-Hill bounds, and then our recently constructed bounds, which have been specified for the aggregates.