We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a simple recursive relationship between adjacent linkages, yielding an efficient method for creating kirigami patterns. This allows us to solve the kirigami design problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into an iterative procedure involving simple matrix multiplications. The resulting linear design strategy circumvents the solution of a non-convex global optimization problem and allows us to control the degrees of freedom in the deployment angle field, linkage offsets and boundary conditions. We demonstrate this by creating a large variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then realize our kirigami designs physically using two simple but effective fabrication strategies with very different materials. All together, our additive approaches present routes for efficient mechanical metamaterial design and fabrication based on ori/kiri-gami art forms.

翻译：我们提出了一种基于剪纸的力学超材料逆向设计的加法方法，该方法聚焦于空白（负空间）而非实体单元。通过将每个负空间视为一个四连杆机构，我们确定了相邻连杆机构之间的简单递归关系，从而建立了一种高效的剪纸图案生成方法。这使得我们能够利用初等线性代数解决剪纸设计问题，将兼容性、可重构性和刚性展开能力编码为一个涉及简单矩阵乘法的迭代过程。所得到的线性设计策略规避了求解非凸全局优化问题，并使我们能够控制展开角度场、连杆偏移量和边界条件中的自由度。我们通过创建大量刚性可展开、紧凑、可重构的剪纸图案来展示这一方法。随后，我们利用两种简单而有效的制备策略（采用截然不同的材料）物理实现了剪纸设计。综合而言，我们的加法方法为基于折/剪纸艺术形式的力学超材料高效设计与制备提供了有效途径。