The wedge Topologically Consistent Metamaterial element (wTCM) for the generation of auxetic metamaterials in complex components and its multi-scale numerical calculation with small geometrical and material non-linearities

Metamaterials are gaining importance in different aspects of engineering because their complex capabilities and light weight ensures a key role in critical elements in different fields. But metamaterials have two main drawbacks; a high computational cost at component level, and a lack of adaptability to complex shapes. This latter point is because traditionally the metamaterials have relied on regular or quasi-regular grids, which is not realistic for more of the engineering needs. In this paper we present the wTCM finite element for the generation of auxetic metamaterials and its multiscale calculation accounting forgeometric nonlinear effects (e.g. buckling), and material nonlinear effects (e.g. moderate plasticity and fracture). The proposed element is the opposite the traditional RVE where a large amount of unit cells are assumed to be inside each RVE. In the case of the wTCM only a portion of the unit cell is represented in the element. With this, we gain versatility and precision with a low computational cost, and the capability to generate the metamaterial from the wTCM mesh directly.