3D analysis of pore effect on composite elasticity by means of the finite-element method

We developed a 3D buffer-layer finite-element method model to investigate the porosity effect on macroscopic elasticity. Using the 3D model, the effect of pores on bulk effective elastic properties was systematically analyzed by changing the degree of porosity, the aspect ratio of the ellipsoidal pore, and the elasticity of the material. The results in 3D space were compared with the previous results in 2D space. Derivatives of normalized elastic stiffness constants with respect to needle-type porosity were integers, if the Poisson ratio of a matrix material was zero; those derivatives of normalized stiffness elastic constants for C-33, C-44, C-11, and C-66 converged to -1, -2, -3, and -4, respectively, at the corresponding condition. We have developed a criterion of R < similar to 1/3, where the mutual interaction between pores became negligible for macroscopic composite elasticity. These derivatives were nearly constant at less than 5% porosity in the case of a spherical pore, suggesting that the interaction between neighboring pores was insignificant if the representative size of the pore was less than one-third of the mean distance between neighboring pores. The relations we obtained in this work were successfully applied to invert the bulk modulus and rigidity of Cmcm-CaIrO3 as a case study; the performance of the inverting scheme was confirmed through this assessment. Thus, our scheme is applicable to predict the macroscopic elasticity of porous object as well.