Instability-triggered triply negative mechanical metamaterial

We report a three-dimensional instability-triggered mechanical metamaterial that simultaneously possesses negative stiffness, negative bulk modulus, and negative Poisson's ratio. This metamaterial is a periodic arrangement of binder-shell elements. Combining numerical simulation and micromechanics analysis, we show that the thin spherical shells dent inward under compression, which contributes to a negative Poisson's ratio. Snap-through instability is predicted by the Riks method-based simulation, revealing that the metamaterial exhibits negative incremental stiffness. Negative bulk modulus is an outcome of negative stiffness and negative Poisson's ratio. Interestingly, both incremental stiffness and incremental Poisson's ratio approach negative infinity under displacement-controlled loading when snap back takes place. We further show that a triply negative metamaterial can satisfy the strong ellipticity condition, providing a mechanism to prevent the formation of localized deformation bands even when material softening takes place. The proposed triply negative metamaterial can also serve as structural elements for applications such as extreme damping composites, extreme stiff composites, and mechanical actuators.