Modeling of the Pore Shape Effect on the Effective Young's Modulus of Lotus-Type Porous Materials by a Numerical Homogenization Technique

Lotus-type porous materials (LTPMs) are considered as a new category of engineering materials. They are porous materials characterized by long, straight, unidirectional cylindrical pores, and are obtained via unidirectional solidification from a melt under hydrogen and argon atmospheres. The anisotropic pore morphology of lotus-type materials results in the anisotropy of their mechanical and physical properties. This study aims at investigating the effect of cross-sectional pore shapes on the effective Young's modulus (EYM) of LTPMs. The representative volume element-based finite element homogenization method was used to compute the effective bulk and shear moduli. Subsequently, the EYM was deduced from the effective bulk and shear moduli. The numerical results of the circular pores were validated by comparing them with experimental results. Because the results indicated that the EYM is extremely sensitive to the variation in the pore shapes, a formula for estimating the EYM of LTPMs by considering the pore shapes was developed and validated.