Triply Periodic Minimal Surfaces

Abstract

With the advent of additive manufacturing, the usage and implementation of lattice-driven designs have increased to a great extent. Due to the nature and geometrical properties of lattices, it becomes a prominent solution for complex problems where compactness and lightweight is desired without compromising the strength. Lattices are of varied types, one such category includes Triply Periodic Minimal Surfaces (TPMS), which have potential applications in various industries ranging from bio-medical to automobile and aerospace. A minimal surface is a geometric concept that refers to a surface with zero mean curvature that is local area minimizing. They are smooth, continuous, and finitely extending curves governed by trigonometric equations with equal periodicity in all three directions. In a nutshell, they locally minimize the area thus sufficing the name and at the same time increasing the overall surface area by keeping the control volume as same. The unit cells within the minimal surface-based designs are well interconnected with each other and share a common boundary between them. Due to its well-structured intrinsic geometry, TPMS is introduced as one of the most promising concepts for providing high stiffness, strength, and energy-absorbing capability. Apart from the structural advantage, they are also viewed as an excellent option for heat transfer applications. They provide an increment in the overall exposed surface area with the heat transfer medium and hence contribute to the advancement of the heat transfer rate. This study gives a brief overview of minimal surfaces and their related properties and potential applications.