School of Civil Engineering and Transportation, South China University of Technology, 510640 Guangzhou, Guangdong, China.
Soft Matter. 2019 Mar 13;15(11):2391-2399. doi: 10.1039/c9sm00160c.
In this work, we study the plane-strain deformations of hyperelastic plates induced by differential growth, aiming to derive some analytical formulas for 2D shape-programming of hyperelastic plates. First, we present a plate equation system with the growth functions incorporated, which is derived from the 3D governing system through a series expansion and truncation approach. By proposing a novel analytical method, the plate equation system is solved explicitly. The obtained solutions can reveal the dependence of the current configurations of the hyperelastic plates on the differential growth fields. By solving an inverse problem, some analytical formulas are obtained, which can be used to identify the growth functions for generating arbitrary 2D geometrical shapes of the hyperelastic plates. To demonstrate the efficiency of these formulas, some representative examples are studied, which show good consistency with the numerical simulations. The obtained analytical formulas have wide potential applications in the design of intelligent soft devices.
在这项工作中，我们研究了由差异生长引起的超弹性板的平面应变变形，旨在为超弹性板的 2D 形状编程推导一些解析公式。首先，我们提出了一个包含生长函数的板方程系统，该系统是通过级数展开和截断方法从 3D 控制方程推导出来的。通过提出一种新的解析方法，我们可以显式地求解板方程系统。得到的解可以揭示超弹性板的当前构型对差异生长场的依赖关系。通过求解逆问题，我们得到了一些解析公式，这些公式可以用于识别生成超弹性板任意 2D 几何形状的生长函数。为了验证这些公式的有效性，我们研究了一些代表性的例子，结果与数值模拟具有很好的一致性。所得到的解析公式在智能软设备的设计中有广泛的潜在应用。
