Kirigami pattern design of mechanically driven formation of complex 3D structures through topology optimization

Rapid, precise and controllable assembly of three-dimensional (3D) micro/nanostructures in advanced materials are attracting increasing interest in scientific research and engineering innovation due to its widespread applications. One of the notable approaches that can achieve mechanically driven assembly of 3D mesostructures is realized by applying compressive forces on two-dimensional (2D) micro/nanomembranes with strategically designed geometry and patterns of cuts. This approach is very effective to produce 3D mesostructures for prescribed cutting patterns, however, the inverse problem, that is finding the geometries and patterns of cuts which can lead to predefined desirable 3D morphologies, has not been well addressed yet. In this letter, a systematic approach that can solve the aforementioned inverse design problem is developed under the framework of topology optimization. Design examples provided demonstrate the effectiveness of the proposed approach.