Large deformation shape optimization of cut-mediated soft mechanical metamaterials

Cutting various patterns in elastomeric sheets has emerged as a simple yet effective way to fabricate soft mechanical metamaterials with unusual or auxetic properties. Upon stretching, the cut ligaments of the metamaterial deform severely and much higher stress is induced around the notch due to stress concentration. This would limit the stretchability or even result in fracture of the cut-mediated metamaterials. Optimization of cut-mediated mechanical materials has been rarely, if at all, been explored, partially due to the difficulty of nonlinear optimization and analysis of materials with large deformation. We present an integrated strategy and a platform based on commercial software to optimize cut-mediated soft mechanical metamaterials. Optimization of the metamaterial is realized by modifying the boundary shape of cut ligaments, which would reduce stress concentration, generate larger negative Poisson's ratio, and allow enhanced stretchability. Our optimization scheme of metamaterials would aid design and fabrication of mechanical metamaterials and transforming structures. (paper)