| CPC F01D 5/147 (2013.01) [B22F 5/04 (2013.01); B22F 10/28 (2021.01); B29C 64/40 (2017.08); B33Y 10/00 (2014.12); B33Y 80/00 (2014.12); F01D 5/28 (2013.01); B22F 2301/15 (2013.01); F05D 2220/32 (2013.01); F05D 2250/184 (2013.01); F05D 2300/17 (2013.01)] | 17 Claims | 

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               1. An auxetic (NPR) structure, comprising: 
            a three-dimensional unit cell, the unit cell including a plurality of vertical intersecting dimpled sheets, each dimpled sheet exhibiting a negative Poisson's ratio, 
                wherein each dimpled sheet is sinusoidally-shaped to define a saddle, 
                wherein each dimpled sheet intersects two adjacent dimpled sheets at the saddle points of the sinusoidal waves to create a rectangular tubular structure, and wherein a portion of each dimpled sheet projects outward from its intersection with an adjacent dimpled sheet, 
                wherein the amplitude of each dimple on the plurality of dimpled sheets is such that no overhanging surface of the dimpled sheet exceeds an angle threshold for three-dimensional printability of the auxetic (NPR) structure, wherein the auxetic (NPR) structure itself provides support to the forming layers of the auxetic (NPR) structure as the auxetic (NPR) structure is additively manufactured without involving an external support structure. 
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