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:----
基利纸艺的加法框架
Translated abstract:
我们提出了一种基于加法的逆向设计方法,用于设计基于基利纸艺的机械元材料,将焦点放在空(负)空间而非实心瓷砖上。通过将每个负空间视为四杆机构,我们确定了相邻机构之间的简单递归关系,得出了一种有效的基利纸艺模式创建方法。这使我们能够使用基本线性代数来解决基利纸艺设计问题,并将兼容性、可重构性和刚性展开能力编码到涉及简单矩阵乘法的迭代过程中。由此产生的线性设计策略规避了求解非凸全局优化问题,并允许我们控制展开角度场、机构偏移和边界条件的自由度。我们通过创建大量刚性展开、紧凑、可重构的基利纸艺模式来证明这一点。随后,我们使用两种简单但有效的材料制作策略在物理上实现了我们的基利纸艺设计。总之,我们的加法方法为基于基利纸艺的机械元材料设计和制造提供了高效的途径。