Coupling of helical lattice structures for tunable non-linear elasticity

Helical lattice structures as investigated by Pirrera et al. [1] possess non-linear elastic responses that may be tuned to offer various distinct behaviours such as zero stiffness and multi-stability. Potential applications of such helices were explored in further detail by O'Donnell et al. [2] by combining the lattice with an elastic medium permitting the system to display pseudo-ductility, thus highlighting one of many possible applications. Other such applications include, for example, adaptive and deployable structures, robotics, and vibration isolators. By coupling the helical lattice with a secondary system, additional response characteristics, that cannot be achieved by the lattice alone, can be obtained. A natural extension of [1,2], explored in this paper, is to consider the effects of combining multiple concentric lattice structures, coupled through radial springs, resulting in a design space that offers significant potential for non-linear elastic tailoring.

As is often observed in biological systems, structural hierarchy offers mechanisms through which novel response characteristics may be observed [3-6]. The helices in this investigation were inspired by the virus bacteriophage T4 [1]. The composite behaviour of the system under investigation exploits such hierarchy in order to obtain highly tuned nonlinear force displacement behaviour. The helices in each lattice are formed from pre-stressed composite strips, the lattices are then combined concentrically via elastic springs to form a composite helical system. An outline of the analytical modelling framework developed to capture this behaviour is now discussed.