Abstract: A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the directional orthogonal to the direction under tension. The articles of footwear have soles that have at least one layer made of a material that has a pattern of sole elements with apertures. The sole elements have may 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. One or more auxetic or flat liners may be used to prevent entry of debris into the apertures.

Abstract: 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.

Abstract: A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the direction orthogonal to the direction under tension. The articles of footwear have soles that have at least one layer made of a material that has a pattern of apertures to provide the auxetic structure. The apertures are surrounded by sole portions that can rotate or pivot to change the size of the apertures. An outer covering can be mated with an outsole structure formed by the auxetic structure. The outer covering includes features that mate with the apertures in the outsole structure. The outer covering is elastic and can stretch to accommodate expansion of the auxetic structure.

Abstract: A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the directional orthogonal to the direction under tension. The articles of footwear have soles that have at least one layer made of a material that has a pattern of geometrical patterns with polygonal apertures. The geometrical patterns have hinged polygons 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.

Abstract: A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the directional orthogonal to the direction under tension. 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. In some cases the recesses may extend through the entire sole component layer.

Abstract: A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the directional orthogonal to the direction under tension. The articles of footwear have soles that have at least one layer made of a material that has a pattern of sole elements with apertures. The sole elements have may 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. One or more auxetic or flat liners may be used to prevent entry of debris into the apertures.

Abstract: A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the directional orthogonal to the direction under tension. The articles of footwear have soles that have at least one layer made of a material that has a pattern of apertures to provide the auxetic structure. The apertures are surrounded by sole portions that can rotate or pivot to change the size of the apertures.

Abstract: A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the directional orthogonal to the direction under tension. The articles of footwear have soles that have at least one layer made of a material that has a pattern of geometrical patterns with polygonal apertures. The geometrical patterns have hinged polygons 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.