Fig. 2: The 3 steps recipe.
From: A three step recipe for designing auxetic materials on demand
a Step 1, we start with a bipartite network, the blue and red colours stand for the A and B sets respectively. We showcase a random bipartite network to demonstrate the versatility of this recipe. b Step 2, every node of the graph becomes the position of each polygon and we place each polygon’s vertex on top of each corresponding segment of the network. At rest the polygon’s position is collinear with its neighbour’s position and the vertex between them. c Step 3, each polygon vertex is positioned such that the ratio C = bji/aij remains constant along the network. aij is the distance from the node to each vertex in the A set polygons, bji is the analogue for the B set. d The resulting polygon network after performing the 3 steps. e A section of the final random auxetic design printed in 3D. As every section of the model is inherently a perfect auxetic, the printed material keeps being auxetic. f A compression shows that the polygon network is a perfect auxetic. In the zoom in we see how each polygon counter rotates with respect to its neighbours. θi and θj show the rotation of the A and B set respectively.
