Dome-Shape Auxetic Cellular Metamaterials: Manufacturing, Modeling, and Testing

We present in this work the manufacturing, modeling, and testing of dome-shaped cellular structures with auxetic (negative Poisson's ratio) behavior. The auxetic configurations allow the creation of structures with synclastic (i.e., dome-shaped) curvatures, and this feature is used to evaluate the performance of cellular metamaterials under quasi-static indentation conditions. We consider here different cellular geometries (re-entrant, arrow-head, tri-chiral, hexagonal) and the implications of their manufacturing using 3D printing techniques with PLA material. The dome-shaped configurations are modeled using full-scale non-linear quasi-static and explicit dynamic FE models that represent both the geometry and approximate constitutive models of the PLA filament material derived from tensile tests on dogbone specimens. The cellular metamaterials samples are subjected to indentation tests, with maps of strains obtained through DIC measurements. The correlation between experimental and numerical simulations is good, and shows the peculiar indentation behavior of these cellular structures. We also perform a comparative analysis by simulation of the force/displacement, strain and fracture history during quasi-static loading, and discuss the performance of the different cellular topologies for these dome-shape metamaterial designs.