A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. The articles of footwear have sole components that have at least one layer made of a material that has a pattern of geometrical patterns. The geometrical patterns have hinged portions that rotate with respect to each other when the sole is under lateral or longitudinal tension, thus increasing the lateral and longitudinal dimensions of the sole. The sole component may include a pattern of recesses with varying depths, sizes, and shapes disposed along the inner surface as well as the outer surface of the sole component.

A structured porous metamaterial includes a three-dimensional matrix of at least one repeating base unit. The matrix is formed from an array of at least eight base units, each base unit including a platonic solid including at least one shaped void, wherein each base unit has void geometry tailored to provide a porosity of between 0.3 and 0.97, and to provide the metamaterial with a response that includes a Poisson's ratio of 0 to 0.5 when under tension and compression, or negative linear compression (NLC), negative area compression (NAC), zero linear compression (ZLC), or zero area compression (ZAC) behaviour when under pressure.

A novel material for producing auxetic foams is disclosed. The material comprises a multiphase, multicomponent polymer foam with a filler polymer having a carefully selected glass transition temperature. Novel methods for producing auxetic foams from the material are also disclosed that consistently, reliably and quickly produce auxetic polyurethane foam at about room temperature (25 C.). This technology overcomes challenging issues in the large-scale production of auxetic PU foams, such as unfavorable heat-transmission problem and harmful organic solvents.

Disclosed herein is a method of manufacturing an auxetic stretchable substrate with a flexible joint structure. The method includes preparing a substrate made of an elastic material, forming an auxetic to form a plurality of first regions on the substrate, and forming flexible joints in each of the plurality of first regions, wherein each of the plurality of first regions is a region in which a material constituting the auxetic is not printed, and at least some of the flexible joints formed in each of the plurality of first regions have different Young's moduli.