In this investigation, mechanical behavior of periodic cellular solids with diamond-shaped inclusions connected via wavy network were explored. Two families of cellular solids within this category were designed based on two different geometric constraints. Auxetic effects and snap-through instability were observed for each family, respectively. The mechanical properties, including the stress-strain behavior, stiffness and Poisson’s ratio, were systematically quantified via finite element (FE) simulations. The parametric space for auxetic effects and snap-through instability was numerically identified. This study demonstrates the connection and transition between mechanical auxeticity and snap-through instability. The materials designed have potential engineering applications, such as lightweight supporting and protective foams, biomedical devices, smart composites or fabrics with switchable properties responsive to external environments.

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