Kirigami pattern design for buckling-induced assembly 3D structures via topology optimization

Abstract

Complex three-dimensional (3D) mesostructures are attracting an increasing interest due to their wide applications in microelectronics, biomedicine and other fields. A buckling-induced 3D structure can be assembled by buckling of a 2D plane precursor rapidly and precisely at low cost. However, the inverse design problem of finding 2D precursor configurations corresponding to the predetermined 3D mesostructures has not been well solved yet. In the present work, an inverse method is developed for buckling-induced assembly 3D structure design. Unlike the existing methods, the Moving Morphable Void (MMV) -based topology optimization approach is adopted for driving the inverse design. The voids in MMV are defined as kirigami cuts on the 2D precursor with explicit geometry parameters to generate complex buckling deformation. To cope with the costly non-linear optimization, the Equivalent Static Loads (ESL) method is incorporated, with which the non-linear optimization process can be transformed into a linear static optimization process. Therefore, the layout of the pattern of cuts is sought on the 2D precursor with linear sensitivity calculation. Some self-assembly numerical examples demonstrate the effectiveness and efficiency of the proposed approach.