Helical Lattice Systems: Bespoke Non-linear Elasticity

Robust non-linear behaviour remains an under-utilised phenomenon in the field of elastic tailoring of structures. This is, in part, due to difficulty in describing the behaviour of non-linear systems in an intuitive way. Herein, we construct a non-linear system that can be tuned to produce robust non-linear responses in a systematic and understandable manner. The system is composed of composite helical lattices that act as effective one-dimensional non-linear springs; we describe the energetic framework for a coupled system of lattices, using either rigid or elastic connections. For each lattice with unique geometry, pre-stress, topology or stiffness added to the system, new global behaviour is observed that cannot be obtained from a single lattice in isolation. We demonstrate the method for tuning the system response to match an arbitrary smooth non-linear function and provide an algorithm for determining the parameters required to obtain the desired behaviour. Examples are provided to show the flexibility of the design space and highlight how the system can exhibit increasingly complex behaviours including bi-stability, multi-stability and bespoke stiffness, through the addition of extra lattices.