论文标题
从结合高斯曲率中心的发展，复杂的地形
Evolving, complex topography from combining centers of Gaussian curvature
论文作者
论文摘要
液晶弹性体和玻璃可以通过其导演模式确定的显着形状变化。从圆形导演模式变形的锥体具有非平凡的高斯曲率，位于端口的尖端，弯曲界面和交叉点。我们采用广义度量兼容性条件来表征圆形导演模式之间的两个接口家族 - 双曲线和椭圆界面，并发现变形界面在几何上兼容。我们专注于设计复杂的地形和非等法折纸的双曲线界面，包括n折十字，对称和不规则的瓷砖。三倍和四倍平铺的大型设计空间用于定量倒数设计，以显示目标图像。综上所述，我们的发现为执行器，显示器的设计和液晶弹性体和眼镜的软机器人技术提供了全面的设计原理。
Liquid crystal elastomers and glasses can have significant shape change determined by their director patterns. Cones deformed from circular director patterns have non-trivial Gaussian curvature localised at tips, curved interfaces, and intersections of interfaces. We employ a generalised metric compatibility condition to characterize two families of interfaces between circular director patterns -- hyperbolic and elliptical interfaces, and find that the deformed interfaces are geometrically compatible. We focus on hyperbolic interfaces to design complex topographies and non-isometric origami, including n-fold intersections, symmetric and irregular tilings. The large design space of three-fold and four-fold tiling is utilized to quantitatively inverse design an array of pixels to display target images. Taken together, our findings provide comprehensive design principles for the design of actuators, displays, and soft robotics in liquid crystal elastomers and glasses.
