Bistability and thermal coupling in elastic metamaterials with negative compressibility

When elastic metamaterials are subjected to tension they may respond by undergoing contraction instead of expansion as an ordinary material would (and vice versa). This negative compressibility behavior can only occur if the system moves from one stable state to a different stable state as the force is applied, i.e., displays bistability. With a simple model potential, we demonstrate that this negative behavior leading to a pinched hysteresis on the stress cycle diagram is a solid-to-solid condensation-type phase transformation. In addition, we show that the negative compressibility may disappear in realistic dynamical systems, unless coupling with an external heat sink is strong enough to stabilize the newly formed phase. Such a material is an open thermodynamical system where the condensation process is accompanied by a fast return of the released heat into the ambient. Molecular dynamics with Verlet integration is used to study the dynamics of this behavior.