Meta-)Materials, e.g. functional or architectured materials that change shape in response to external stimuli, often do so by exploiting solid-solid phase transitions or concerted elastic deformations. For the resulting system to be effective the (meta-)material needs to have desirable and tunable properties at length scales sufficiently small that desirable continuum behaviour of the resulting component is obtained. Developing such (meta-)materials has proven to be an endeavour which requires considerable expertise in science, engineering and mathematics. Here, we pursue an alternative approach where the design for functionality is integrated across multiple length scales in the system. We demonstrate this approach by designing and prototyping helical lattices that act as one-dimensional thermoelastic materials with unusual properties such as negative thermal expansivity-with magnitude far exceeding the most extreme values reported in the literature-and zero-hysteresis shape memory. Our strategy is independent of characteristic length scale, allowing us to design behaviour across a range of dimensions.

Nonlinear structural behaviour offers a richness of response that cannot be replicated within a traditional linear design paradigm. However, designing robust and reliable nonlinearity remains a challenge, in part, due to the difficulty in describing the behaviour of nonlinear systems in an intuitive manner. Here, we present an approach that overcomes this difficulty by constructing an effectively one-dimensional system that can be tuned to produce bespoke nonlinear responses in a systematic and understandable manner. Specifically, given a continuous energy function E and a tolerance ϵ > 0, we construct a system whose energy is approximately E up to an additive constant, with L∞-error no more that ϵ. The system is composed of helical lattices that act as one-dimensional nonlinear springs in parallel. We demonstrate that the energy of the system can approximate any polynomial and, thus, by Weierstrass approximation theorem, any continuous function. We implement an algorithm to tune the geometry, stiffness and pre-strain of each lattice to obtain the desired system behaviour systematically. Examples are provided to show the richness of the design space and highlight how the system can exhibit increasingly complex behaviours including tailored deformation-dependent stiffness, snap-through buckling and multi-stability.

An analytical investigation into the non-linear elastic response of helical lattice structures coupled with an elastic medium is presented. Novel composite templates are then obtained to produce bespoke material characteristics by exploiting tuned hierarchy. System behaviour is approximated as a combination of three non-linear "springs", representing the helical lattice, and the axial and circumferential components of the elastic medium via an energy based approach. Non-dimensional parameters governing each component's non-linear load-displacement behaviour are identified, demonstrating tailoring potential. Further tunable parameters that govern the combined system response, involving form factor, geometric and stiffness ratios are identified. In particular, pseudo-ductile responses are observed. The feasible region of pseudo-ductility, as determined by these non-dimensional parameters, is obtained, allowing discussion of viable materials and geometries. Finally, load-displacement behaviour is utilised to obtain indicative effective stress-strain curves, thus showing promise as a model for future material development.

This paper explores the ability to tailor the mechanical properties of composite compliant shell mechanisms, by exploiting the thermal prestress introduced during the composite laminate cure. An extension of an analytical tape spring model with composite thermal analysis is presented, and the effect of the thermal prestress is studied by means of energy landscapes for the cylindrical composite shells. Tape springs that would otherwise be monostable structures become bistable and exhibit greater ranges of low-energy twisting with thermally induced prestress. Predicted shell geometries are compared with finite element (FE) results and manufactured samples, showing good agreement between all approaches. Wider challenges around the manufacture of prestressed composite compliant mechanisms are discussed.

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