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• Elastic behavior of isotropic discrete models with an arbitrary geometry is analyzed. • An analytical estimation of the macroscopic elastic characteristics is derived. • It is shown that the widest limits of the Poisson's ratio are obtained for Voronoi and Power tessellation. • The Poisson's ratio limits cannot be further extended by manipulations with the model geometry. The use of discrete material representation in numerical models is advantageous due to the straightforward way it takes into account material heterogeneity and randomness, and the discrete and orientated nature of cracks. Unfortunately, it also restricts the macroscopic Poisson's ratio and therefore narrows its applicability. The paper studies the Poisson's ratio of a discrete model analytically. It derives theoretical limits for cases where the geometry of the model is completely arbitrary, but isotropic in the statistical sense. It is shown that the widest limits are obtained for models where normal directions of contacts between discrete units are parallel with the vectors connecting these units. Any deviation from parallelism causes the Poisson's ratio limits to shrink. A comparison of the derived equations to the results of the actual numerical model is presented. It shows relatively large deviations from the theory because the fundamental assumptions behind the theoretical derivations are largely violated in systems with complex geometry. The real shrinking of the Poisson's ratio limit is less severe compared to that which is theoretically derived. [ABSTRACT FROM AUTHOR]

Discrete models of solids have been motivated, in large part, by the discontinuous and heterogeneous nature of material structure and its breakdown under loading. The capabilities of discrete models have evolved over the past several decades, offering novel means for investigating material structure–property relationships. However, lack of understanding of both the utilities and disadvantages of discrete models limits their further development and applications. This paper reviews relevant features of discrete approaches applied to modeling the mechanical behavior of geomaterials, concrete materials in particular. The discrete models are classified according to their form and abilities to represent elastic and fracture behaviors in the presence of large-scale material heterogeneity. Discretization of the material domain plays a large role in this respect. Emphasis is placed on particle-based lattice models. The relative merits of various strategies for introducing reinforcing components, which are essential for many applications, are outlined. Recent advances are highlighted, including the use of discrete models for coupled, multi-field analysis. The merits of discrete approaches are summarized in the conclusions. • Discrete methods for simulating concrete fracture are critiqued. • Model capabilities depend on the choice of physical or non-physical forms of discretization. • The topics of stress oscillation, Poisson's ratio and volumetric effects are examined. • Dual-lattice models are suited to modeling hygro-mechanical couplings in cracked media. • Application examples demonstrate the utilities and expanding use of discrete methods. [ABSTRACT FROM AUTHOR]