Controlling the Material Width of Equation-Based Lattices for Large-Scale Additive Manufacturing

Additive manufacturing (AM) developments have been strongly driven by the ability of AM to improve the strength-to-weight ratios of structures, in contrast to traditional manufacturing methods, heavily supported by lattice structures. These motivations have persisted with the development of large-scale additively manufactured structures, which can offer more flexibility in manufacturing location and can often be faster than traditional manufacturing. However, current large-scale AM methods are often limited by their precision in order to maintain speed, constraining the method to manufacturing simple structures and often avoiding lattices altogether. This work proposes a mathematical framework for defining an equation-based lattice that splits the lattice into (1) build direction and (2) planar components such that their design can be altered to address AM methods restricted to three degrees of freedom. The framework is applied against a class of lattices called triply periodic minimal surfaces, which are represented using implicit equations, and it is shown that this approach allows for their use in large-scale AM technologies and enables further design control for small-scale AM design.