free surface modle

Free surface model is a type of computational fluid dynamics (CFD) model that simulates the behavior of fluids with a free surface, such as waves on the ocean or ripples on a pond. It is commonly used in marine engineering, naval architecture, and offshore engineering to study the behavior of ships and offshore structures in waves.

The free surface model solves the Navier-Stokes equations for fluid flow, but also includes an additional equation to track the position of the free surface. This equation takes into account the effects of surface tension, gravity, and other forces that act on the fluid surface.

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翻译This SiO2 shell is a key component in the mechanism for reversible actuation, as illustrated by finite element analysis (FEA) in Fig. 1C. An increase in temperature transforms the SMA (nitinol) from the martensitic to the austenitic phase, causing the 3D structure to flatten into a 2D shape. The responses of the SMA elements at the joints act as driving forces to deform the PI skeleton. This process also elastically deforms the SiO2 shell, resulting in a counter force that limits the magnitude of the deformation. The change in shape ceases when the forces from the shell balance those from the joints (right frame in Fig. 1C). Upon a reduction in temperature, the SMA changes from the austenitic back to the martensitic phase, thereby reducing the force produced by the SMA at the joints to zero. The elastic forces associated with the shell then push the entire system back to the original 3D geometry (left frame in Fig. 1C). Figure S3A simulates the moments generated by the SMA and the SiO2 shell. In the FEA model, the SiO2 shell appears on both the outer and inner surfaces of the 3D robot, consistent with experiments (fig. S3B). Although a single layer of the SiO2 shell at the outer or inner surface can also provide restoring force, the double-layer shell structure follows naturally from the conformal deposition process. This actuation scheme allows for reversible shape transformations using a one-way shape memory material. Without the shell, the structure only supports a single change in shape, from 3D to 2D, as illustrated in fig. S3C. Figure 1D shows optical images of a freestanding 3D peekytoe crab on the edge of a coin, highlighting the preserved 3D geometry enabled by the SiO2 shell after release from the elastomer substrate. Other 3D structures in geometries that resemble baskets, circular helices, and double-floor helices also exhibit high shape storage ratios (>85%) after cycles of heating and cooling (fig. S4). This ratio (s) is defined as s = 1 − |L1 − L0|/L0 × 100%, where L0 and L1 are the distances between the bonding sites at both ends at the initial stage and subsequent stages, respectively

这个SiO2壳是可逆作用机制的关键组成部分，如图1C所示的有限元分析所示。温度的升高将SMA（尼钛）从马氏体相转变为奥氏体相，导致3D结构变成2D形状。连接处SMA元件的响应作为变形PI骨架的驱动力。这个过程也会弹性变形SiO2壳，产生抵消变形幅度的对抗力。当壳体受力平衡连接处的力时，形状的变化停止（图1C右侧）。温度降低时，SMA从奥氏体相变回马氏体相，因此连接处由SMA产生的力减少到零。与壳体相关的弹性力将整个系统推回原始的3D几何形状（图1C左侧）。图S3A模拟了SMA和SiO2壳体产生的力矩。在有限元分析模型中，SiO2壳体出现在3D机器人的外表面和内表面，与实验结果一致（图S3B）。虽然在外表面或内表面只有一个SiO2壳层也可以提供恢复力，但双层壳体结构自然地遵循共形沉积过程。这种作用机制使用单向形状记忆材料实现可逆形状转换。没有壳体，结构只支持从3D到2D的单次形状变化，如图S3C所示。图1D显示了一只自由站立的3D Peekytoe蟹在硬币边缘的光学图像，突出了SiO2壳在从弹性体基底释放后保留的3D几何形状。几何形状类似于篮子、圆螺旋和双层螺旋的其他3D结构在加热和冷却循环后也表现出高形状存储比率（>85%）（图S4）。这个比率（εs）定义为εs = 1-|L1-L0|/L0×100%，其中L0和L1分别是初始阶段和随后阶段两端结合点之间的距离。