Shellular Metamaterial Design via Compact Electric Potential Parametrization

Fig. 1. Design of shellular metamaterials. Our structures are represented by an implicit function parameterized by a few dozen electric charges (a). By arranging these charges, we obtain a broad set of geometrically diverse structures (b,c). These structures also exhibit a wide range of properties (d) and remain feasible for fabrication in practical applications (e).

We present a compact yet highly expressive design space for shellular metamaterials that support both interactive exploration and inverse design. With only a few dozen charges, our representation generates a wide family of periodic shells, spanning from simple planar configurations to complex TPMS-like morphologies. To enable rapid evaluation, we introduce an efficient GPU-based homogenization pipeline that computes the effective elastic tensor of a candidate design in near real time (∼ 0.4 s), making interactive shellular design practical. Across a large set of synthesized structures, our design space exhibits geometric diversity and spans a broad spectrum of mechanical responses, covering a wide range of effective material properties. This fast evaluation further enables inverse design for target macroscopic properties. In the low-solid-volume regime, the resulting shellular structures achieve performance competitive with state-of-the-art shell-based metamaterials in multiple material properties. Finally, we validate manufacturability by fabricating tiled prototypes via additive manufacturing, demonstrating the potential of our approach for real-world engineering applications.