Micromechanical modeling of 3D printable interpenetrating phase composites with tailorable effective elastic properties including negative Poisson's ratio

Abstract

3D printable two-phase interpenetrating phase composites (IPCs) are designed by embedding a 3D periodic re-entrant lattice structure (as the reinforcing phase) in a matrix phase. These IPCs display the cubic or tetragonal symmetry. A micromechanical model is developed to evaluate effective elastic properties of the IPCs. Effective Young's moduli, shear moduli and Poisson's ratios (PRs) of each IPC are determined from the effective stiffness and compliance matrices of the composite, which are obtained through a homogenization analysis using a unit cell-based finite element (FE) model incorporating periodic boundary conditions. The FE simulation results are also compared with those based on various analytical bounding techniques in micromechanics, including the Voigt–Reuss, Hashin–Shtrikman, and Tuchinskii bounds. The effective properties of the IPC can be tailored by adjusting five geometrical parameters, including two strut lengths, two re-entrant angles and one strut diameter, and elastic properties of the two constituent materials. The numerical results reveal that IPCs with a negative PR can be generated by using a compliant matrix material and large re-entrant angles. In addition, it is found that the two re-entrant angles can greatly affect other effective elastic properties of the IPC: the effective shear modulus can be enhanced, while the effective Young's modulus can be enhanced or compromised with the increase of the re-entrant angles. Furthermore, it is seen that by adjusting one of the two re-entrant angles or one of the two strut lengths, the material symmetry exhibited by the IPC can be changed from cubic to tetragonal.