ITO for Auxetic Metamaterials

Abstract

In the above chapter, the ITO method is applied to address the design of micro unit cells in architected materials and intends to find a series of novel and interesting microstructures. In the current chapter, the ITO method is applied to study the design of auxetic metamaterials, and the main intention is to seek for a family of new and interesting micro unit cells but with the auxetic behavior. Comparatively speaking, the design of auxetic metamaterials and the design of architected materials can be putted in a same category of topology optimization problem. The main cause is that auxetic metamaterials can be also viewed as a subtype of architected materials but with a special property, namely the negative Poisson ratio (NPR). In the design of auxetic metamaterials using topology optimization, the whole process is similar to the design of architected materials, and a critical difference lies in the objective function. In Chap. 6, the objective function in the design of architected materials refers to extreme elastic moduli. In the current work, the corresponding objective function is also defined by the homogenized elastic tensor, but it can effectively push the optimizer can find micro unit cells with the NPR, namely the auxetic behavior. Hence, in the design of auxetic metamaterials using the ITO method, material description model to present structural topology using the DDF and the IGA-based energy-based homogenization method should be required in the development of the ITO formulation for the design of auxetic metamaterials, and the details for the development of these two components can be referred to Chaps. 2 and 6, respectively.