Modeling the Elastic Properties of Reticulated Porous Ceramics

A model to predict the elastic material properties of reticulated porous ceramics (RPCs) based on the microstructural geometry is presented. The RPC is represented by a repeating unit structure of truncated octahedrons (tetrakaidecahedrons) with the ligaments represented by the cell edges. The deformations of the ligaments in the cellular structure under applied loads are used to determine the effective moduli and Poisson's ratio of the bulk material. The ligament cross section is represented as having a Plateau border exterior surface with a cusp half-angle that is varied between 0 and 90 deg, and a Plateau border interior void with a cusp half-angle of zero, representative of the ranges seen in RPCs. The ligament cross-sectional area is permitted to vary along its length and the distance between internal and external cusps is assumed constant. The relative density of the foam, corresponding to the length, cusp distances, and external-cusp half-angle of the ligaments, is determined using solid geometry. The relative density has the dominant effect on the moduli, while normalized ligament length varies the moduli by 11-49% at a specified relative density. The impact of the external shape of a ligament on the relative moduli is insignificant. The model is validated through comparisons with the measured elastic properties of RPCs in the literature and new data. The model is the first to consider the effect of the microstructural features of ligaments of RPCs on the elastic moduli of the bulk material.