Negative Stiffness Induced and Controlled by Constriction

Structures and materials exhibiting negative stiffness are themselves unstable since they release energy during deformation and hence require a stabilizing system to consume the released energy. Constriction that resists the motion in certain directions can provide the stabilizing effect. Furthermore, lateral constriction of a strip (rod) undergoing axial deformation can make the axial modulus negative even if the material of the rod/strip has positive moduli. Another example is sliding over a multitude of rotating particles. In this case, constriction imposed in the direction normal to the sliding makes some groups of particles exhibit negative shear stiffness. This article investigates the stabilizing properties of constriction, in particular marking unrestricted deformation into oscillating. Effects of constriction, inducing bidirectional and unidirectional apparent negative stiffness as well as negative shear stiffness in sliding, are investigated. Constriction also makes possible oscillations of a mass on a negative stiffness spring. The oscillating movement between two limits is modeled, and the difference between bidirectional and unidirectional springs is investigated. The results will contribute to designing new energy realizing structures and metamaterials, as well as explaining the accelerating sliding (e.g., sliding over faults causing seismicity).