Title: 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 their increased toughness
and indentation resistance. These materials are typically synthesized polyester
foams with a very heterogeneous structure, but the role of disorder in auxetic
behavior is not fully understood. Here, we provide a systematic theoretical and
experimental investigation in to the effect of disorder on the mechanical
properties of a paradigmatic auxetic lattice with a re-entrant hexagonal
geometry. We show that disorder has a marginal effect on the Poisson's ratio
unless the lattice topology is 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 optimize
elasticity and strength of disordered auxetic metamaterials.