Abstract
Minimum energy principles and generalized polarization trial fields are used to derive bounds on the effective elastic moduli of d-dimensional random cell polycrystals, which are extensions of our earlier 3D (3-dimensional) results. The bounds are specialized to the 2D random aggregates of square-symmetric crystals, with numerical results for a number of particular crystals. Numerical finite element simulations for sufficiently large random aggregate samples of a particular 2D random polycrystal model show convergence toward the possible scatter interval for the effective elastic moduli enveloped by the new bounds, which are tighter than the classical Voigt–Reuss–Hill and Hashin–Shtrikman ones.
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