New families of triply periodic minimal surface-like shell lattices

Triply periodic minimal surface (TPMS)-based shell lattices are increasingly recognized for their exceptional geometric and mechanical attributes. Their open-cell configuration further establishes them as prime candidates for additive manufacturing, especially using liquid-bath or powder-bed techniques. While TPMS can be developed through both implicit and explicit methods, each has its limitations. Implicit methods, commonly adopted, are constrained by a limited set of known functions and a singular level set parameter, narrowing the modeling space. On the other hand, explicit methods, though they aim to minimize the surface area functional, encounter challenges in generating surfaces of high genus due to the complexity in achieving specific topologies. In this paper, we unveil a novel modeling approach for TPMS-like shell lattices. Central to our approach is the creation of periodic boundaries that seamlessly integrate implicitly formed complex surface patches. Our methodology introduces a parametric representation for these boundaries, leveraging a unique search algorithm paired with spline curve parameterization. Following this, we implement a formulation of geometric currents harmonized with boundary periodicity C1 continuity to determine the associated TPMS. This innovation spawns a variety of parametric TPMS-like shell-lattice topologies. Using the homogenization method, we assess the elastic attributes of these diverse families. Our findings reveal that the mechanical property spectrum of our TPMS-like shell lattices surpasses that of conventional TPMS-based counterparts. We spotlight two applications for our modeling technique: designing functionally graded materials and implementing inverse homogenization. Concluding our study, we validate our innovations through a sequence of empirical tests.