论文标题
可变形环中柔性纤维的生长
Growth of a flexible fibre in a deformable ring
论文作者
论文摘要
我们研究与弹性柔性环中弹性纤维生长有关的平衡构型。该系统代表了各种生物，医学和工程问题的范式。我们认为一种简化的几何形状，其中最初是一个半径$ r $的圆形环。然后，随着纤维长度$ l $的增加，从$ l = 2r $开始，通过求解平衡方程来研究准静态增长。将纤维和环视为不可延迟的和无法理解的，我们发现超出了临界长度，这取决于相对弯曲刚度，纤维扣。此外，随着纤维的进一步折叠，扭曲了环，直到它在$ l>2πr$下诱导镜子对称性中断。我们知道平衡形状仅取决于二小无参数：长度比$μ= l/r $和弯曲刚度比$κ$。这些发现也得到了有限元模拟的支持。最后，我们通过实验验证理论结果，显示了可变几何参数下观察到的屈曲和折叠状态的良好定量预测。
We study the equilibrium configurations related to the growth of an elastic fibre in a confining flexible ring. This system represents a paradigm for a variety of biological, medical, and engineering problems. We consider a simplified geometry in which initially the container is a circular ring of radius $R$. Quasi-static growth is then studied by solving the equilibrium equations as the fibre length $l$ increases, starting from $l = 2R$. Considering both the fibre and the ring as inextensible and unshearable, we find that beyond a critical length, which depends on the relative bending stiffness, the fibre buckles. Furthermore, as the fibre grows further it folds, distorting the ring until it induces a break in mirror symmetry at $l>2 πR$. We get that the equilibrium shapes depend only on two dimensionless parameters: the length ratio $μ= l/R$ and the bending stiffnesses ratio $κ$. These findings are also supported by finite element simulation. Finally we experimentally validate the theoretical results showing a very good quantitative prediction of the observed buckling and folding regimes at variable geometrical parameters.
