Equilibrium of bi-stable flexural-tensegrity segmental beams

One dimensional discrete systems composed of a simple chain of bi-stable springs, with nearest neighbor interaction, have been used to interpret the complex equilibrium states of materials supporting multiple crystallographic phases, foldable macromolecules and biological structures. A discrete system is here proposed for bending within the broad class of flexural-tensegrity beams, which consist of segments in unilateral contact, with tailored-shaped contact surfaces, pre-stressed by an unbonded tendon. Any contact joint shows a bi-stable response to its relative rotation such as a snap-spring hinge, thanks to the internal carving of the segments that increases the mobility of the tendon within them. The constitutive response is nonlocal, because the tendon is free to slide within well lubricated sheaths. The case of pure bending, representing the counterpart of uniaxial tension in the one-dimensional lattice chain, shows that the system can support stable and metastable configurations, possibly containing one snap-spring hinge in the spinodal part of the energy landscape. Remarkably, not only the maximum hysteresis paths, but also the Maxwell paths, are strain-hardening in type. This is due to the nonlocal effect from the unbonded tendon: the rotation of any contact joint stiffens all the other joints, so that the orderly snaps of the spring-hinges occur at an increasing bending moment. An experimental program has been conducted on 3D printed physical models either in a hard or soft device. Symmetric and non-symmetric equilibrium configurations are obtained that are in perfect agreement with the theoretical predictions. Possible applications are envisaged, but they are yet to be fully appreciated.