Generating complex fold patterns through stress-free deformation induced by growth
Generating complex fold patterns through stress-free deformation induced by growth
复制标题
通过生长引起的无应力变形生成复杂的折叠图案
DOI：
10.1016/j.jmps.2021.104702
复制
发表时间：
2021-11
影响因子：
5.3
通讯作者：
Jiong Wang
中科院分区：
文献类型：
--
作者：
Xiaoyi Chen;Yi Shen;Zeyu Li;Di;ian Gu;Jiong Wang
本文建立了任意几何形状下曲线坐标下生长引起的无应力变形的二维和三维轴对称模型。在模型的推导过程中，将变形梯度分解为弹性张量和生长张量的乘积，并进一步对生长张量进行极分解，在此基础上在每种构型/状态下适当地选择基矢。推导了增长函数的约束条件以及位置向量和旋转角的控制方程，构成了耦合的非线性偏微分方程组。在一种特殊情况下，得到了该系统的解析解，并在此基础上确定了产生复杂折叠图案的两种机构。一种是在初始构型中引入几何缺陷，另一种是通过转换曲线坐标来产生新的增长张量。应用这两种机制，我们成功地找到了合适的初始几何和生长张量来生成一种特殊类型的折叠图案，该图案在初始环的内外表面具有凸尖或/和凹尖，与脑器官和苦瓜的形态相关。这种类型的模式在弹性不稳定之前似乎还没有报道过。还产生了许多其他复杂的折叠图案，如苔藓樱花、红枫叶、玫瑰、火绒花、原肠胚、单瓣大蒜、肿瘤球体、牵牛花和两种类型的蘑菇。该模型为某些残余应力为零或可忽略的生物组织的形态发生提供了可能的解释。该结果还可以与其他产生残余应力的模型相结合，以给出生物的形态和应力分布的全面描述。得到的变形规律可用于软质材料的4D打印软器件的设计。
The 2D and 3D axisymmetric models for stress-free deformations induced by growth have been established for curvilinear coordinates in arbitrary geometries in the current paper. In the derivation of the models, the deformation gradient is decomposed into the product of an elastic tensor and a growth tensor, and the growth tensor is further polar decomposed, based on which the basis vectors are appropriately chosen in each configuration/state. The constraints for the growth functions are derived together with the governing equations for the position vector and the rotational angle, which constitute coupled nonlinear partial differential equations. Under a special case, the analytical solutions to this system are obtained, based on which two mechanisms for generating complex fold patterns are identified. One is the introduction of geometric imperfection to the initial configuration, and the other is the creation of new growth tensors through the switching of curvilinear coordinates. Applying these two mechanisms, we manage to find a proper initial geometry and growth tensor to generate a special type of fold pattern having convex or/and concave cusps at the inner and outer surfaces of an initial annulus, having relevance with the morphology of a brain organoid and a bitter gourd. It seems this type of pattern has not been reported before by elastic instabilities. Many other complex fold patterns are also generated, like the morphologies of moss sakura, a red maple leaf, a rose, celosia, a gastrula, single clove garlic, a tumor spheroid, morning glory and two types of mushrooms. This model provides possible explanations for the morphogenesis of some biological tissues with zero or negligible residual stress. The results can also be incorporated with other models yielding residual stress to give a comprehensive description of the morphologies and stress distributions of the organisms. And the deformation principles obtained can be used in the design of soft devices through 4D printing of soft material.
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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：
4.1
作者：
Saez, Pablo;Pena, Estefania;Martinez, Miguel Angel;Kuhl, Ellen
通讯作者：
Kuhl, Ellen
影响因子：
5.3
作者：
Budday S;Steinmann P;Kuhl E
通讯作者：
Kuhl E
影响因子：
2.5
作者：
A. Yavari
通讯作者：
A. Yavari
影响因子：
1.9
作者：
R. Skalak;D. A. Farrow;A. Hoger
通讯作者：
R. Skalak;D. A. Farrow;A. Hoger