A Low-Parametric Rhombic Microstructure Family for Irregular Lattices
A Low-Parametric Rhombic Microstructure Family for Irregular Lattices
复制标题
不规则晶格的低参数菱形微结构族
DOI：
10.1145/3386569.3392451
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发表时间：
2020
影响因子：
6.2
通讯作者：
Zorin, Denis
中科院分区：
文献类型：
--
作者：
Tozoni, Davi Colli;Dumas, Jeremie;Jiang, Zhongshi;Panetta, Julian;Panozzo, Daniele;Zorin, Denis
新的制造技术大大降低了具有高度复杂几何结构的形状的制造成本。复杂精细几何结构的一个重要应用是在由单一材料制造的形状中创建可变的有效弹性材料属性。材料性能的改变有多种用途，从航空航天应用到软机器人和假肢设备。由于其可扩展性和有效性，一种越来越常见的创建空间变化材料的方法是将形状划分为单元，并使用具有已知有效性质的小规模几何结构族来填充单元。我们提出了一种新的方法来解决挤压平面微结构的这一问题。与已有的基于正方形周期单元的规则网格不能满足任意边界的两尺度优化方法不同，我们引入了由(近)菱形单元组成的单元分解。这些网格在逼近任意形状方面比正方形网格具有更大的灵活性，同时具有许多简化小规模结构构造的性质。我们的主要贡献包括一族新的2D晶胞几何结构，由它们的有效杨氏模E、泊松比v和菱形角度α显式参数化，几何参数直接表示为E、v和α的光滑样条函数。这一族导致了瓷砖之间的平滑过渡，并可以处理广泛的菱形晶胞形状。我们介绍了一套完整的基于该微结构族的材料设计流水线，包括从四边形网格生成菱形网格的算法和微结构几何综合的算法。我们制作了许多模型，并通过实验演示了我们的方法如何与材料优化相结合来实现所需的变形行为。
New fabrication technologies have significantly decreased the cost of fabrication of shapes with highly complex geometric structure. One important application of complex fine-scale geometric structures is to create variable effective elastic material properties in shapes manufactured from a single material. Modification of material properties has a variety of uses, from aerospace applications to soft robotics and prosthetic devices. Due to its scalability and effectiveness, an increasingly common approach to creating spatially varying materials is to partition a shape into cells and use a parametric family of small-scale geometric structures with known effective properties to fill the cells.We propose a new approach to solving this problem for extruded, planar microstructures. Differently from existing methods for two-scale optimization based on regular grids with square periodic cells, which cannot conform to an arbitrary boundary, we introduce cell decompositions consisting of (nearly) rhombic cells. These meshes have far greater flexibility than those with square cells in terms of approximating arbitrary shapes, and, at the same time, have a number of properties simplifying small-scale structure construction. Our main contributions include a new family of 2D cell geometry structures, explicitly parameterized by their effective Young's moduliE, Poisson's ratiosv, and rhombic angleαwith the geometry parameters expressed directly as smooth spline functions ofE, v, andα.This family leads to smooth transitions between the tiles and can handle a broad range of rhombic cell shapes. We introduce a complete material design pipeline based on this microstructure family, composed of an algorithm to generate rhombic tessellation from quadrilateral meshes and an algorithm to synthesize the microstructure geometry. We fabricated a number of models and experimentally demonstrated how our method, in combination with material optimization, can be used to achieve the desired deformation behavior.