Evaluation of effective elastic properties of 3D printable interpenetrating phase composites using the meshfree radial point interpolation method

摘要

Interpenetrating phase composites (IPCs) have recently been fabricated using three-dimensional (3D) printing methods. In a two-phase IPC, the two phases are topologically interconnected and mutually reinforced in the three dimensions. As a result, such IPCs exhibit higher stiffness, strength, and toughness than particle- or fiber-reinforced composites. In the current study, three unit cell models for the IPCs with the simple cubic (SC), face-centered cubic (FCC), and body-centered cubic (BCC) microstructures are developed using the meshfree radial point interpolation method. Radial basis functions with polynomial reproduction are applied to construct shape functions, and the Galerkin method is employed to formulate discretized equations. These unit cell-based meshfree models are used to evaluate effective elastic properties of 3D printable IPCs. The simulation results are compared with those based on the finite element (FE) method and various analytical bounding techniques in micromechanics, including the Voigt-Reuss, Hashin-Shtrikman, and Tuchinskii bounds. It is found that all of the simulation results for the effective Young's modulus and shear modulus fall between the Voigt-Reuss upper and lower bounds for each IPC considered, with the FE models predicting higher values than the meshfree models. In addition, it is seen that the SC microstructure leads to higher effective Young's modulus than the BCC and FCC microstructures. Furthermore, the numerical results reveal that the IPCs with the SC, BCC, and FCC microstructures can be approximated as isotropic materials (with the Zener anisotropic ratio varying between 0.9 and 1.0), with the BCC IPC being the most isotropic one, and the SC IPC being the least isotropic one among the three types of IPCs.