Analytical study on growth-induced axisymmetric deformations and shape-control of circular hyperelastic plates
Analytical study on growth-induced axisymmetric deformations and shape-control of circular hyperelastic plates
复制标题
圆形超弹性板生长引起的轴对称变形及形状控制的解析研究
DOI：
10.1016/j.ijengsci.2021.103594
复制
发表时间：
2022-01
影响因子：
6.6
通讯作者：
Jiong Wang
中科院分区：
文献类型：
--
作者：
Zhanfeng Li;Qiongyu Wang;Ping Du;Chennakesava Kadapa;Mokarram Hossain;Jiong Wang
在自然界中，软材料板的生长是常见的现象。然而，生长领域和板样品的形状变化之间的关系仍然知之甚少。本文的目的是推导出超弹性圆板生长诱导轴对称变形的一些解析结果。本文还研究了通过微分生长控制圆板形状的问题。首先，从三维控制系统出发，通过级数展开和截断的方法建立二维矢量板方程组。然后用正则摄动法求解板方程。对板的平面外弯曲和平面内的平板变形分别求出了解析（渐近）解，其结果与数值结果吻合较好。通过能量密度的比较，可以确定任意给定生长函数对应的板的优先变形方式，并在此基础上研究了板的弯曲-平板复合变形。通过求解反问题，得到了超弹性圆薄板形状控制的显式公式。利用该公式，通过选择合适的生长函数，可以生成大部分三维轴对称构型。研究结果不仅可以揭示软材料生长诱导变形的机理，而且在智能软器件的制造中具有广阔的应用前景。
Growth of soft material plates is commonly observed in nature. However, the relations between growth fields and shape changes of the plate samples remain poorly understood. The current work aims to derive some analytical results for the growth-induced axisymmetric deformations of a circular hyperelastic plate. The problem of shape-control of the circular plate through differential growth will also be studied. First, starting from the 3D governing system, we formulate the 2D vector plate equation system through a series expansion and truncation approach. Then, the plate equations are solved by using the regular perturbation method. Some analytical (asymptotic) solutions are derived for both the out-of-plane bending and in-plane flat deformations of the plate, which can fit the numerical results quite well. By comparing the energy densities, the preferred deformation styles of the plate corresponding to any given growth functions can be determined, based on which the combined bending-flat deformation of the plate is also studied. Furthermore, by solving an inverse problem, we derived the explicit formula for shape-control of thin circular hyperelastic plates. With this formula, most of the 3D axisymmetric configurations can be generated by selecting proper growth functions in the plates. The results obtained in the current work can not only reveal the mechanisms of growth-induced deformations of soft material samples, but also have wide potential applications in the manufacture of intelligent soft devices.
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DOI：
10.1103/physreve.103.022412
发表时间：
2021-02
期刊：
Physical review. E
影响因子：
--
作者：
X. Chen;P. Ciarletta;H. Dai
通讯作者：
X. Chen;P. Ciarletta;H. Dai
影响因子：
5.3
作者：
Budday S;Steinmann P;Kuhl E
通讯作者：
Kuhl E
DOI：
10.1016/0021-8928(87)90111-0
发表时间：
1987
期刊：
Journal of Applied Mathematics and Mechanics
影响因子：
--
作者：
V. I. Kondaurov;L. Nikitin
通讯作者：
V. I. Kondaurov;L. Nikitin
DOI：
10.1073/pnas.1116564108
发表时间：
2011-12-20
影响因子：
11.1
作者：
Shepherd, Robert F.;Ilievski, Filip;Whitesides, George M.
通讯作者：
Whitesides, George M.
影响因子：
2.5
作者：
A. Yavari
通讯作者：
A. Yavari