Design of microstructures and structures with negative linear compressibility in certain directions

The linear compressibility of a solid is defined as the relative decrease in length of a line when the solid is subjected to unit hydrostatic pressure. Materials with a negative linear or area compressibility could have interesting technological applications. However, in the case of homogeneous materials only rare crystal phases exhibit this effect. In particular, for isotropic or cubic solids the linear compressibility is known to be isotropic and positive, namely a sphere of a cubic or isotropic crystal under hydrostatic pressure remains a sphere. For less symmetric solids, it generally varies with the direction n. Here we derive explicit expressions of the stationary values (maximum and minimum) of linear compressibility for single phase solids with monoclinic, orthotropic, tetragonal, trigonal, and hexagonal symmetry. A list of crystals that may exhibit negative linear compressibility in certain directions is outlined. Next, by assembling a two-component material, we propose microstructure networks to achieve such a property. Numerical simulations, based on a refined finite element method, are provided.