A comprehensive investigation of the lattice structure mechanical properties based on Schwarz Primitive triply periodic minimal surface: Elastic modulus, yield strength, and maximum bearing force in the elastic region

Abstract

Due to ongoing investigations, the potential for using triply periodic minimal surface (TPMS) lattice structures in various industries has been increased. The analytical relationships that determine the mechanical properties of these structures make cost-effective designs achievable for designers. In this study, a comprehensive investigation that includes analytical, numerical, and experimental approaches to determine the mechanical properties of the Primitive triply periodic minimal surface (P-TPMS) lattice structure under unidirectional loading was performed. The innovation of this paper is the derivation of analytical relationships of mechanical properties, including elastic modulus, yield strength, and maximum load-bearing force in the elastic region in terms of geometrical parameters of Primitive unit cell and properties of the constituent materials. These mechanical properties were obtained using the energy method and Euler-Bernoulli beam theory for relative densities in the range of 0.24–0.76. Relative density was determined based on the geometric parameter of the surface size (m). In addition, the lattice structures were fabricated additively manufactured, and compressive test experiments were conducted. The mechanical properties of P-TPMS lattice structures vary dramatically with varying surface size values, according to the study's findings. The P-TPMS lattice structure's elastic modulus and yield strength at m=0.35 are more than 11 and 32 times larger, respectively than the yield stress and elastic modulus at m=0.65. The unit cell's length has no bearing on the elastic modulus or yield strength.