Poroelastic metamaterials with negative effective static compressibility

We suggest a three-dimensional metamaterial structure exhibiting an isotropic expansion in response to an increased hydrostatic pressure imposed by a surrounding gas or liquid. We show that this behavior corresponds to a negative absolute (rather than only differential) effective compressibility under truly static and stable conditions. The poroelastic metamaterial is composed of only a single ordinary constituent solid. By detailed numerical parameter studies, we find that a pressure increase of merely one bar can lead to a relative increase in the effective volume exceeding one percent for geometrical structure parameters that should be accessible to fabrication by 3D printing.