auxetic

Auxetic materials are defined by a negative Poisson's ratio, meaning they become thicker in directions perpendicular to an applied stretch. While ordinary materials contract laterally when stretched, auxetics exhibit lateral expansion. The Poisson ratio ν is given by ν = -ε_perp/ε_axial, and auxetic behavior corresponds to ν < 0.

Auxetic behavior typically arises from specific microstructures, such as re-entrant or hinged cellular networks, rotating units, or chiral lattices. Under load, these geometries unfold or rotate in a way that increases cross-sectional area rather than reduces it.

Materials exhibiting auxetic responses include foams, polymers, metals, ceramics, and composites with engineered porosity. They can be produced by 3D printing, mechanical structuring, or processing foams with tailored cell geometries.

Properties associated with auxetics include enhanced energy absorption, indentation resistance, and shear stiffness, along with tunable stiffness. Applications span protective gear and body armor, packaging, impact damping, biomedical scaffolds, sensors, and aerospace components, where controlled deformation and damage tolerance are valuable.

Origin and terminology: the term auxetic derives from Greek, and negative Poisson's ratio materials were studied in the late 20th century, with notable demonstrations by researchers such as Lakes. Since then, the field has grown into engineered metamaterials.

Characterization typically involves measured Poisson's ratio under standardized loading, noting anisotropy and strain dependence. Some materials show ν that varies with direction, scale, or strain level.