Can tailored non-linearity of hierarchical structures inform future material development?

Abstract

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.

Multiscale tailoring of helical lattice systems for bespoke thermoelasticity

“…For example, at the material level, crystalline lattices with negative thermal expansivities use geometric mechanisms analogous to those of the helical geometry proposed here [7]. More generally, functionality can be designed for from the nano-, to the architectured-and meta-material scale, all the way up to the macro-scale [8][9][10][11][12][13][14][15][16][17]. Tuneable thermal responses have been achieved by tailoring of meta-material lattices [18].…”

“…The lattice is represented schematically in Figure 2 and comprises of N helices of each chirality and 4N unit cells. For simplicity, we consider only lattices with chiral symmetry, since then: (i) the unit cells are rhomboidal, (ii) the lattices elongate/contract without twisting, and (iii) the variable h (see Figure 2) characterises the system uniquely [6,12]. The circumferential and longitudinal diagonals of the unit cell are…”

Bespoke extensional elasticity through helical lattice systems

“…This restriction ensures unit cells are rhombi and prevents the lattice from twisting upon extension [18]. In addition, and conveniently for the current purposes, it creates a bijective correspondence between R and h [18], permitting the lattice extension to be used as the single degree of freedom to characterize the system [23].…”

Exploring Adaptive Behavior of Non-linear Hexagonal Frameworks

“…Instead, using a structural approach, instabilities can be integrated into the design and exploited to obtain a unique richness in system response (Reis, 2015;Bertoldi, 2017). By employing these structural response mechanisms at sufficiently small length scales, a desirable macroscopic continuum response can be achieved (O'Donnell et al, 2016;O'Donnell et al, 2019). Herein, we propose a new approach for creating novel material behavior from a hierarchy of non-linear elements; namely, rather than utilizing complex topologies to achieve the desired non-linear behavior, we can subsume this complexity into well understood non-linear "springs" acting as base-units of a hierarchical design.…”