Negative stiffness behaviors emerging in elastic instabilities of prismatic tensegrities under torsional loading

• Prismatic tensegrity can have two stable states and one unstable state without load.
• The tensegrity exhibits negative structural stiffness behavior under torsion.
• Critical conditions are established for the occurrence of structural instability.
• These conditions help to design tensegrities showing specific negative stiffness.

Tensegrities with elastic instabilities hold potential applications in advanced sensors and actuators, energy storage/adsorption equipments, and folding/unfolding devices. In this paper, we explore the negative stiffness behaviors of prismatic tensegrities emerging in their instability responses under torsion. The explicit conditions for the occurrence of negative structural stiffness in specific deformation regimes are established in terms of three dimensionless parameters. Several representative tensegrities are designed based on the obtained conditions, and their mechanical responses are calculated to validate the predicted negative stiffness properties. This work is helpful for the design of prismatic tensegrities to exhibit featured instabilities with particular functions.