A semi-analytical equation for the Young’s modulus of isotropic ceramic materials

This paper proposes a new relation between the Young’s modulus of ceramics and the volume fraction of porosity. The relation is obtained by upscaling (coarse-graining) the fluctuations of the microstructure. The microstructure is modeled in terms of phase random fields, which upon upscaling lead to elastic coefficients described by continuous spatial random fields. The effective (macroscopic) elastic modulus is then obtained by averaging over the continuum-scale disorder. Using physically motivated arguments, an explicit expression between the Young’s modulus and the porosity is proposed. This expression involves three empirical parameters, i.e. the solid-phase modulus and two perturbation coefficients. The parametric expression is shown to fit well experimental measurements from the literature. Empirical “bounds” for the Young’s modulus are also formulated. These bounds account for variations due to microstructural properties that are not explicitly calculated in the upscaling.