Investigation of the compressive properties of three-dimensional Voronoi reticula

With the rise of additive manufacturing technologies, artificial production of stochastic cellular materials is becoming increasingly more feasible and convenient, exposing the need of accurate models able to predict their mechanical properties. However, the construction of generalized predictive models for stochastic structures is non-trivial: on the one hand, this is due to the several potential base materials, and on the other it is because of the difficulty in implementing geometrically accurate numerical models. In light of these considerations, the present work presents a systematic analysis of one the most known – and commonly used – stochastic cellular structure, the Voronoi three-dimensional lattices; the aim is providing simple empirical relations between the main properties of a generic base material and the compressive properties of the related additively manufactured stochastic Voronoi reticulum as a function of its geometry. The investigation provides novel insights on the mechanical properties of Voronoi reticula, highlighting superior efficiency with respect to their natural counterpart, the open-cell foams, and exposing unsuitability of classical equations for accurate prediction of their mechanical properties.