Pyramid Connection Method for Constructing Graded Triply Periodic Minimal Surface Lattices

Abstract

Triply periodic minimal surfaces (TPMSs) use mathematical functions to construct interconnected solid and void regions and are easy to generate gradients. However, present gradient making methods suffer from defects in the transition region when the difference in unit sizes between source structures is large, and the tunable space of elastic modulus is not large with a given volume fraction. Here, we proposed a method to map a standard TPMS structure into a pyramid-shaped space to produce a medium structure connecting two source structures with different geometries. We can obviously increase the elastic modulus by increasing the transition region length or decreasing the layer number in the transition region without changing the volume fraction. The maximum elastic modulus is about 2.34 times of the minimum one constructed using our method, 2.78 times of that using weight function (WF) method, 1.73 times of that using period modification (PM) method, and 1.67 times of that of standard TPMS lattice, with the volume fraction of around 0.29. Moreover, our method can connect two source structures with different volume fractions without defects in transition region. We provide a simple but effective approach to form flawless structural gradients for the composites and additive manufacturing community.

Keywords: Lattice design, Additive Manufacturing, structural composites, gradient construction, elastic modulus