On the estimates for the elastic moduli of random Voronoi triclinic polycrystals

Abstract

Our major new results and the previous ones on the bounds for elastic random polycrystals, and most advanced 3D finite element results for random 3D Voronoi polycrystals are resumed and analysed (together for the first time). Recently obtained numerical Dirichlet and Neumann simulation results for the effective elastic moduli of a large 10000-grain-size random Voronoi polycrystal representative volume element (RVE) for a number of triclinic and monoclinic base crystals (Mursheda and Ranganathan, 2017) are compared critically with the bounds on the moduli. Though major parts within the simulation results fall within the bounds of Pham (2011), some Dirichlet upper estimates still lie outside the bounds. Many more RVEs are needed to represent the Voronoi polycrystal on the same RVE-size-level, and larger RVEs are needed for checking the convergence and comparisons with the bounds.