Aperiodic minimal surfaces for high toughness metamaterials

Architected materials based on triply periodic minimal surfaces (TPMS) offer excellent stiffness–weight efficiency but often suffer from anisotropic behaviour and preferential crack paths imposed by their underlying symmetry. This work introduces a new class of aperiodic minimal surface metamaterials constructed through a boundary method-based minimal surface formulation. These geometries preserve continuous curvature while embedding long-range structural disorder, enabling manufacturable three-dimensional metamaterials without repeating units or inter-cell discontinuities. Using a combination of additive manufacturing, mechanical testing, and continuum damage finite element analysis, it is shown that the aperiodic Vertices and Edges-connected topologies achieve 40–80% higher stiffness, 30–40% greater strength, and up to 50% higher toughness. Toughness improvements are driven by the designs’ inherently irregular curvature networks that suppress aligned weakness planes and promote highly tortuous crack paths. Unlike TPMS, which display strong orientation-dependent response, the aperiodic architectures show near-isotropic behaviour under 0° and 45° domain rotations. The results demonstrate that geometric aperiodicity provides an effective route to improving flaw tolerance, delaying catastrophic crack propagation, and achieving superior toughness in minimal surface-based metamaterials. This establishes a design framework for next-generation tough, lightweight structures leveraging aperiodic minimal geometry. • Aperiodic minimal surfaces created using the boundary-method • Continuously smooth aperiodic shells avoid symmetry-driven crack paths • Aperiodic minimal surfaces achieve higher stiffness, strength, and toughness • Aperiodic architectures show reduced orientation-dependent mechanical response • Experiments and FEA reveal tortuous crack growth and enhanced defect tolerance