Rigorous estimation of effective elastic properties of heterogeneous random materials requires a “statistical approach” [1], which, due to its complexity, is invariably restricted to the generation of “bounds”, by consideration of limited statistical information [2]. Alternatively, an “intuitive approach” [1] based on the notion of an RVE subjected to a homogeneous boundary condition [3] may be employed. In this context, use of “Eshelby-like” solutions [4] enables, by means of intuitive procedures such as the (classical) self-consistent scheme (SCS) or the Mori-Tanaka scheme (MTS), actual estimation (rather than bounding) of effective elastic properties of polycrystals or composites, respectively. However, only exceptionally [1], do we know how reliable such SCS- and MTS-based estimates are, with for instance, available bounds for assessing SCS-based estimates for porous polycrystals, being still only up to second order and restricted to the nonporous polycrystal case [5]. This symposium aims at bringing together scientists and engineers involved in cutting-edge theoretical, computational, and experimental research on rigorous statistical estimation of effective elastic properties of heterogeneous materials. Submitted contributions should address recent theoretical advances in this area (including experimental determination of second, third, or higher order correlation functions) and comparison of corresponding estimates with SCS- and/ or MTS-based estimates. REFERENCES [1] J.E. Gubernatis and J.A. Krumhansl, Macroscopic engineering properties of polycrystalline materials: Elastic properties, Journal of Applied Physics 46 (1975) 1875-1883. [2] M.J. Beran, T.A. Mason, B.L. Adams and T. Olsen, Bounding elastic constants of an orthotropic polycrystal using measurements of the microstructure, Journal of the Mechanics and Physics of Solids 44 (1996) 1543-1563. [3] R. Hill, The essential structure of constitutive laws for metal composites and polycrystals, Journal of the Mechanics and Physics of Solids 15 (1967) 79-95. [4] J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London A 241 (1957) 376-396. [5] M. Lobos Fernández and T. Böhlke, Representation of Hashin–Shtrikman bounds in terms of texture coefficients for arbitrarily anisotropic polycrystalline materials, Journal of Elasticity 134 (2019) 1-38.