We try to make a long way short by proceedingper exemplafrom Kenneth Snelson’s sculptures and Richard Buckminster Fuller’s coinage of the termtensegrityto modern tensegrity metamaterials. We document the passage from initial interest in tensegrity frameworks for their visual impact to today’s interest, driven by their peculiar structural performances. In the past seventy years, the early art pieces and roofing structural complexes have been followed by formalization of the principles governing the form-finding property of ‘pure’ tensegrity structures and by engineering hybridization leading to a host of diverse practical applications, such as variable-geometry civil engineering structures, on-earth and in-orbit deployable structures and robots, and finally to recent and promising studies on tensegrity metamaterials and small-scale tensegrity structures.

A bistable response is an innate feature of tensegrity metamaterials, which is a conundrum to attain in other metamaterials, since it ushers unconventional static and dynamical mechanical behaviors. This paper investigates the design, modeling, fabrication and testing of bistable lattices with tensegrity architecture and nanoscale features. First, a method to design bistable lattices tessellating tensegrity units is formulated. The additive manufacturing of these structures is performed through multiphoton lithography, which enables the fabrication of microscale structures with nanoscale features and extremely high resolution. Different modular lattices, comprised of struts with 250 nm minimum radius, are tested under loading-unloading uniaxial compression nanoindentation tests. The compression tests confirmed the activation of the designed bistable twisting mechanism in the examined lattices, combined with a moderate viscoelastic response. The force-displacement plots of the 3D assemblies of bistable tensegrity prisms reveal a softening behavior during the loading from the primary stable configuration and a subsequent snapping event that drives the structure into a secondary stable configuration. The twisting mechanism that characterizes such a transition is preserved after unloading and during repeated loading-unloading cycles. The results of the present study elucidate that fabrication of multistable tensegrity lattices is highly feasible via multiphoton lithography and promulgates the fabrication of multi-cell tensegrity metamaterials with unprecedented static and dynamic responses.

We give an algorithm for solving the form-finding problem, that is, for finding stable placements of a given tensegrity structure. The method starts with a known stable placement and alters edge lengths in a way that preserves the equilibrium equations. We then characterize the manifold to which classical tensegrity systems belong, which gives insight into the form-finding process. After describing several special cases, we show the results of a successful test of our algorithm on a large system

Tensegrity systems are prestressed frameworks composed of bars and cables. A particular elastic tensegrity system is examined. This system can be bistable in two fundamentally different ways, one depending on its geometric dimensions, and the other one depending on the initial deformation, or prestrain, of the elastic elements. A reduced-order semi-analytical model is derived, and its predictions are verified with a full-order numerical model. In particular, the critical geometry and prestrain at which the system switches from one regime to another are determined. This case study provides a benchmark and new insights on this class of structures.