Distortion-controlled isotropic swelling: numerical study of free boundary swelling patterns
Distortion-controlled isotropic swelling: numerical study of free boundary swelling patterns
复制标题
变形控制的各向同性膨胀：自由边界膨胀模式的数值研究
DOI：
10.1039/c9sm00392d
复制
发表时间：
2019
期刊：
影响因子：
3.4
通讯作者：
Santangelo, Christian D.
中科院分区：
文献类型：
--
作者：
Duque, Carlos M.;Chen, Bryan Gin-ge;Santangelo, Christian D.
现代制造工具现在已经为设计平板提供了许多平台，这些平板凭借其不均匀的生长，可以弯曲和折叠成目标三维结构。从理论上讲，可以产生相同形状的增长模式有无限种，但从实验的角度来看，几乎没有人知道这多种增长模式中哪种是最优的，甚至几乎没有什么可以实现的。在这里，我们问一个问题：对于给定的目标形状，设计各向同性生长模式的最佳方式是什么？我们提出了一种通过在目标表面引入切割来产生最优生长模式的计算算法。在这个框架内，我们提出需要最少或最短切割的图案在有限厚度下产生与目标形状最接近的图案。在球面上进行了仿真验证，指出了正负高斯曲率曲面所面临的新挑战。
Modern fabrication tools have now provided a number of platforms for designing flat sheets that, by virtue of their nonuniform growth, can buckle and fold into target three-dimensional structures. Theoretically, there is an infinitude of growth patterns that can produce the same shape, yet almost nothing is understood about which of these many growth patterns is optimal from the point of view of experiment, and few can even be realized at all. Here, we ask the question: what is the optimal way to design isotropic growth patterns for a given target shape? We propose a computational algorithm to produce optimal growth patterns by introducing cuts into the target surfaces. Within this framework, we propose that the patterns requiring the fewest or shortest cuts produce the best approximations to the target shape at finite thickness. The results are tested by simulation on spherical surfaces, and new challenges are highlighted for surfaces with both positive and negative Gaussian curvatures.