Negative compressibility, negative Poisson's ratio, and stability

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Mechanical metamaterials: a state of the art (2019, background): “Strong ellipticity means that the following (weaker) conditions must be fulfilled for stability [71]:”
Mechanical metamaterials associated with stiffness, rigidity and compressibility: a brief review (2017, background): “In mechanics, this condition is similar to bistability [302], where energy is stored in [303] or supplied to [304] a deformed object, including post-buckled elements [52,67,69].”
Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs (2016, background): “tropic 3D materials and 1 < < 1 for isotropic 2D materials [3]. This stability condition corresponds to the requirement that the stiness tensor of the solid material must be positive deﬁnite [4]. For most solids, such as metals, polymers and ceramics, varies in a narrow band, i.e. 0:25 < ”