Mechanics of disordered auxetic metamaterials

Abstract

Auxetic materials are of great engineering interest not only because of their fascinating negative Poisson's ratio, but also due to the possibility to increase by design the toughness and indentation resistance. The general understanding of auxetic materials comes mostly from ordered or periodic structures, while auxetic materials used in applications are typically strongly disordered. Yet, the effect of disorder in auxetics has rarely been investigated. Here, we provide a systematic theoretical and experimental study of the effect of disorder on the mechanical properties of a paradigmatic two-dimensional auxetic lattice with a re-entrant hexagonal geometry. We show that disorder has a marginal effect on the Poisson's ratio until the point when the lattice topology becomes altered, and in all cases examined the disorder preserves the auxetic characteristics. Depending on the direction of loading applied to these disordered auxetic lattices, either brittle or ductile failure is observed. It is found that brittle failure is associated with a disorder-dependent tensile strength, whereas in ductile failure disorder does not affect strength. Our work thus provides general guidelines to design and optimize elasticity and strength of disordered auxetic metamaterials.

Rigidity percolation control of the brittle-ductile transition in disordered networks

“…This determination is particularly important for a large class of disordered materials: solid lattices or rigid foams composed of disordered beams bonded at their intersections. These materials present an attractive choice for producing lightweight, tunable structures and have recently been developed as (mechanical) metamaterials [11,[15][16][17][18][19]. Furthermore, such discrete structures have been commonly used in statistical models of fracture [20], as a means to conveniently discretize a material.…”

“…For example, the random fuse model (RFM) [7,21,22], fiber bundle model (FBM) [23,24] or elastic springs model [7,9,13,25,26] descriptions rely on such lattices in which material disorder is introduced. Despite a wealth of models, few fracture experiments to discriminate between the various models have been performed on disordered lattices [11,12], in part due to the difficulty of creating samples by hand [22].With the advent of laser-cutting technology, we are able to readily produce samples with precise, reproducible properties and thereby perform controlled experiments on the failure behavior of disordered lattices with various connectivities. We focus on the limiting case where disorder is primarily set via the geometry of the lattice, and material fluctuations are intended to be negligible.…”

Density scaling in the mechanics of a disordered mechanical meta-material

“…Random elastic networks are widely studied [36][37][38] , but there are still large gaps between theoretical investigations and practical purposes such as real solid materials. Mechanical meta-materials with increasing degree of disorder are just emerging [39][40][41][42][43] . Whether disorder is merely the price to pay for self-assembly or whether it provides some advantage is still an open issue.The structural behaviour of lattice based metamaterials, made up of beams with non-hinged nodes, is generally divided into two regimes: stretching-dominated and bending-dominated 44 .…”

Forecasting failure locations in 2-dimensional disordered lattices

“…In each case, one can further idealize the material or structure as a mathematical network of connections between slender beams that intersect at various points within the material. From an engineering perspective, such materials are promising because of their light weights and their tunable, designable properties: a Poisson ratio from the auxetic [4,8,9] to the incompressible limits [4], a targeted local response to a remote perturbation [5], or the ability to change shape [3]. A disadvantage of these materials is that those that are constructed from stiff materials can degrade progressively through successive abrupt failures of the beams during loading [8,10,11].…”

“…Fracture experiments have been conducted previously on printed, disordered auxetic materials [8] and laser-cut, disordered honeycomb two-dimensional (2D) lattices [10]. In these studies, very different fracture behaviors (ductile versus brittle) have been obtained by changing the * ehberthi@ncsu.edu loading direction [8] or tuning the rigidity [10]. In the latter study, a clear change arose in the spatial organization of fractures: they either can be dispersed throughout a system or be localized in the form of a narrow crack.…”