Triply periodic minimal surfaces (TPMSs) constitute a type of metamaterial, deriving their unique characteristics from their microstructure topology. They exhibit wide parameterization possibilities, but their behavior is hard to predict. This study focuses on using an implicit modeling method that can effectively generate novel thin-walled metamaterials, proposing eight shell-based TPMS topologies and one stochastic structure, along with the gyroid acting as a reference. After insights into the printability and design parameters of the proposed samples are presented, a cell homogeneity analysis is conducted, indicating the level of anisotropy of each cellular structure. For each of the designed metamaterials, multiple samples were printed using a stereolithography (SLA) method, using a constant 0.3 relative density and 50 µm resolution. To provide an understanding of their behavior, compression tests of sandwich-type specimens were performed and specific deformation modes were identified. Furthermore, the study estimates the general mechanical behavior of the novel TPMS cores at different relative densities using an open cell mathematical model. Alterations of the uniform topologies are then suggested and the way these modifications affect the compressive response are presented. Thus, this paper demonstrates that an implicit modeling method could easily generate novel thin-walled TPMSs and stochastic structures, which led to identifying an artificially designed structure with superior properties to already mature topologies, such as the gyroid.
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