Geometric Study of Two-Dimension Stellated Reentrant Auxetic Structures to Transformable Architecture

Abstract

Transformable architecture is totally linked to the study and knowledge of geometry. There are some materials in nature, whose geometric invariants establish equivalent structural behavior regarding the scalar transformations, developing different spatial typologies according to dimensional variation. Auxetic materials are characterized by their negative Poisson’s ratio. The can change their geometric configuration from a line to a surface, and from a surface to a volume or spatial framework. This paper is based on establishing and comparing those stellated reentrant auxetic geometries to be able to build new spaces defined by their capacity to architectural transformation, studying analytically geometric properties of stellated reentrant auxetic structures that, from the molecular to the macroscopic level, can be part of the architecture construction. In this investigation a comparative study by means of CAD of stellated reentrant auxetic patterns has been realized. A Computer Aided Design study of stellated reentrant auxetic structures will be realized to use them to architecture. The geometric behavior of the different stellated reentrant auxetic patterns is analyzed from the developed study to generate a systematic comparison, evaluating properties of these forms, such as their maximum achievable area reductions in relation with the total length of bars of the structure, in order to obtain a growth factor.