Locally Varied Auxetic Structures for Doubly-Curved Shapes

In this paper we present a computerized design method which could ultimately serve to greatly simplify the production of free form reinforced concrete components. Using any desired doubly-curved shape as a starting point, we developed a digital workflow in which the spatial information of the shape is processed in such a way that it can be represented in a two-dimensional pattern. This pattern is materialized as an auxetic structure, i.e. a structure with negative transverse stretching or negative Poisson’s ratio (Evans and Alderson in Adv Mater 12(9):617–628, 2000). On a macroscopic scale, auxetic behaviour is obtained by making cuts in sheet materials according to a specific regular pattern. These cuts allow the material to act as a kinematic linkage so that it can be stretched up to a certain point according to the incision pattern (Grima in J Mater Sci 41:3193–3196, 2006, J Mater Sci 43(17):5962–5971, 2008). Our innovative approach is based on the creation of auxetic structures with locally varying maximum extensibilities. By varying the form of the incisions, we introduce local variations in the stretching potential of the structure. Our focus resides on the fully-stretched structure: when all individual facets are maximally stretched, the auxetic structure results in one specific spatial shape. Based on this approach, we have created an iterative simulation process that allows us to easily identify the auxetic structure best approximating an arbitrary given surface (i.e. the target shape). Our algorithm makes it possible to transfer topological and topographical information of a given shape directly onto a specific two dimensional pattern. The expanded auxetic structure forms a matrix resembling the desired shape as closely as possible. Material specific information of the shape is further embedded in the auxetic structure by implementing an FE-analysis into the algorithm. We have thus laid the digital groundwork to produce out of this matrix, in combination with shotcrete, the desired building components as a next step.