Young's modulus of isotropic porous materials with spheroidal pores

Based on the Eshelby solution for the single-inclusion problem and Wu's specification of this solution to spheroidal pores, we show that the Eshelby–Wu coefficients for Young's modulus, in contrast to their counterparts for the bulk and shear moduli, are quite insensitive to changes of the Poisson ratio. Therefore the Eshelby–Wu coefficients of Young's modulus can be described (to a very good approximation) by a unique function of the aspect ratio, which is calculated in this paper and for which a master curve is obtained by segment-wise fitting. Also the implementation of the Eshelby–Wu coefficients into the well-known effective medium approximations (Maxwell, self-consistent, differential) and our exponential relation is discussed. Irrespective of the model into which the Eshelby–Wu coefficients are implemented, prolate pore shape affects the porosity dependence of Young's modulus only very weakly, whereas oblate pore shape can lead to an arbitrary reduction of Young's modulus.