Shellular Metamaterial Design via Compact Electric Potential Parametrization

TL;DR

The paper presents a compact, expressive design space for shellular metamaterials parameterized by a small set of charges, enabling a wide range of geometries including TPMS. A GPU-accelerated, energy-based homogenization workflow computes the effective tensor $C^H$ in near real-time, enabling rapid forward evaluations and gradient-free inverse design to target mechanical properties. Key contributions include a reduced-dimensional implicit-surface representation, an efficient GPU-based homogenization pipeline, and an optimization framework (CMA-ES) for property-driven structure synthesis, validated by random, existing, and fabricated TPMS-like shells. The work demonstrates high design freedom, fast exploration, and manufacturability, with results approaching theoretical bounds and practical viability for additively manufactured infills and lightweight components.

Abstract

We introduce a compact yet highly expressive design space for shellular metamaterials. By employing only a few dozen degrees of freedom, this design space represents geometries ranging from simple planar configurations to complex triply periodic minimal surfaces. Coupled with this representation, we develop an efficient GPU-based homogenization pipeline that evaluates the structure in under 20 ms and computes the corresponding effective elastic tensor in near-real-time (0.5 s). The high speed of this evaluation facilitates an exhaustive exploration of the design space and supports an inverse-design scheme that tailors the shellular structure to specific macroscopic target property. Structures derived through this approach exhibit not only geometric diversity but also a wide spectrum of mechanical responses, covering a broad range of material properties. Moreover, they achieve up to 91.86% of theoretical upper bounds, a level of performance comparable to state-of-the-art shellular structures with low solid volume. Finally, our prototypes, fabricated via additive manufacturing, confirm the practical manufacturability of these designs, underscoring their potential for real-world engineering applications.

Figures (8)

• Figure 1: The electric charge potential behaves similarly to the signed distance function. Only two charges are necessary to represent a plane (black solid vertical line).
• Figure 2: Different numbers of bases lead to distinct surface. Here, we assume that $\alpha_{hkl}=1$.
• Figure 3: Plot of $h(\cdot)$ as a function of $k$ and $v_0$. A larger value of $k$ sharpens the function, resulting in a thinner shellular structure. Meanwhile, the parameter $v_0$ helps alleviate numerical issues by preventing $K_e$ from reaching zero.
• Figure 4: Energy plot of each optimization method. We compare multiple gradient-free and gradient-based optimization methods in terms of their effectiveness at lowering the energy. Our findings indicate that the gradient-free methods outperform the gradient-based method in both problems.
• Figure 5: Our design space can cover a large set of structures with diverse geoemtry. Here we show three type of structures, structures constructed without symmetric, structures built from cubic FBV, and structure built from tetrahedron FBV.