Exploring adaptive behaviour of non-linear hexagonal frameworks

Non-linear structural responses offer a rich design space that can be integrated into the development of novel (meta)-materials to enable transformative capabilities. By exploiting robust, repeatable, non-linear elasticity the (meta)-material's performance can be tailored to significantly exceed what has been demonstrated through traditional linear design paradigms. Embracing geometric non-linearity offers the designer the potential for truly bespoke large-range elastic behaviour. Herein we explore the behaviour of bistable elements that can be arranged into a space-filling triangular lattice, constructed in a hierarchical manner. We develop an analysis of the system that can be readily extended to more complex hierarchies, such as the hexagonal arrangement considered herein, whilst retaining physical insight. Specifically, we present the geometric restrictions of lattice elements that govern the existence of stable stress-free states and subsequently characterise the transitions between such states by searching for the minimum energetic transition pathway. Through our approach, we explore how hierarchical multi-stable systems can be analysed, thus contributing to the development of truly bespoke adaptive (meta-)materials.