Analytic analysis of auxetic metamaterials through analogy with rigid link systems

Reentrant tensegrity: A three-periodic, chiral, tensegrity structure that is auxetic

We present a three-periodic, chiral, tensegrity structure and demonstrate that it is auxetic. Our tensegrity structure is constructed using the chiral symmetry Π⁺ cylinder packing, transforming cylinders to elastic elements and cylinder contacts to incompressible rods. The resulting structure displays local reentrant geometry at its vertices and is shown to be auxetic when modeled as an equilibrium configuration of spatial constraints subject to a quasi-static deformation. When the structure is subsequently modeled as a lattice material with elastic elements, the auxetic behavior is again confirmed through finite element modeling. The cubic symmetry of the original structure means that the auxetic behavior is observed in both perpendicular directions and is close to isotropic in magnitude. This structure could be the simplest three-dimensional analog to the two-dimensional reentrant honeycomb. This, alongside the chirality of the structure, makes it an interesting design target for multifunctional materials.

Self-rotating 3D chiral mechanical metamaterials

In this work, we demonstrate that three-dimensional chiral mechanical metamaterials are able to self-twist and control their global rotation. We also discuss the possibility of adjusting the extent of the global rotation manifested by the system in a programmable manner. In addition, we show that the effect of the global rotation can be observed both for small systems composed of a single structural unit as well as more complex structures incorporating several structural elements connected to each other. Finally, it is discussed that the results presented in this work are very promising from the point of view of potential applications such as satellites or telescopes in space, where appropriately designed mechanical metamaterials could be used for the attitude control as well as other systems where the control of the rotational motion is required.

Design of Pseudo-Mechanisms and Multistable Units for Mechanical Metamaterials

Mechanisms-collections of rigid elements coupled by perfect hinges which exhibit a zero-energy motion-motivate the design of a variety of mechanical metamaterials. We enlarge this design space by considering pseudo-mechanisms, collections of elastically coupled elements that exhibit motions with very low energy costs. We show that their geometric design generally is distinct from those of true mechanisms, thus opening up a large and virtually unexplored design space. We further extend this space by designing building blocks with bistable and tristable energy landscapes, realize these by 3D printing, and show how these form unit cells for multistable metamaterials.

Bulky auxeticity, tensile buckling and deck-of-cards kinematics emerging from structured continua

Complex mechanical behaviours are generally met in macroscopically homogeneous media as effects of inelastic responses or as results of unconventional material properties, which are postulated or due to structural systems at the meso/micro-scale. Examples are strain localization due to plasticity or damage and metamaterials exhibiting negative Poisson’s ratios resulting from special porous, eventually buckling, sub-structures. In this work, through ad hoc conceived mechanical paradigms, we show that several non-standard behaviours can be obtained simultaneously by accounting for kinematical discontinuities, without invoking inelastic laws or initial voids. By allowing mutual sliding among rigid tesserae connected by pre-stressed hyperelastic links, we find several unusual kinematics such as localized shear modes and tensile buckling-induced instabilities, leading to deck-of-cards deformations—uncapturable with classical continuum models—and unprecedented ‘bulky’ auxeticity emerging from a densely packed, geometrically symmetrical ensemble of discrete units that deform in a chiral way. Finally, after providing some analytical solutions and inequalities of mechanical interest, we pass to the limit of an infinite number of tesserae of infinitesimal size, thus transiting from discrete to continuum, without the need to introduce characteristic lengths. In the light of the theory of structured deformations, this result demonstrates that the proposed architectured material is nothing else than the first biaxial paradigm of structured continuum —a body that projects, at the macroscopic scale, geometrical changes and disarrangements occurring at the level of its sub-macroscopic elements.

Corner-Sharing Tetrahedra for Modeling Micro-structure

This paper introduces Corner-Sharing Tetrahedra (CoSTs), a minimalist, constraint-graph representation of micro-structure. CoSTs have built-in structural guarantees, such as connectivity and minimal rigidity. CoSTs form a space, fully accessible via local operations, that is rich enough to design regular or irregular micro-structure at multiple scales within curved objects. All operations are based on efficient local graph manipulation, which also enables efficient analysis and adjustment of static physical properties. Geometric and material detail, parametric or solid splines, can be added locally, on-demand, for example, for printing.

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries

Floppy modes-deformations that cost zero energy-are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in, e.g., mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multibranched. We study the number Δ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that Δ is extensive, peaks at intermediate connection densities, and exhibits mean-field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.

Stiff auxetics: Hierarchy as a route to stiff, strong lattice based auxetic meta-materials

Using a combination of analytic and computational methods, we examine the effect of adding hierarchical substructure to an auxetic lattice. Our novel methodology, involving a coarse grain approach, allows for the analysis of hierarchically sub-structured lattices where direct computation would prove intractable. We show that through hierarchy one can create ultra-lightweight auxetic meta-materials of high strength and stiffness. Through scaling law arguments, we show that the benefits of hierarchical design can also be obtained in the general class of bending-dominated lattices. Furthermore, we show that the hierarchical structures presented show a wide range of tailorability in their mechanical properties, and exhibit increased strength when optimised for buckling resistance. Auxetic materials have a broad range of potential applications, and thus the creation of ultra-light auxetic meta-materials with enhanced stiffness and strength is undoubtedly of practical importance.