The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-02-22 , DOI: 10.1140/epje/s10189-021-00012-1 Andrea Pedrini , Epifanio G. Virga
Abstract
Minimizing the elastic free energy of a thin sheet of nematic polymer network among smooth isometric immersions is the strategy purported by the mainstream theory. In this paper, we broaden the class of admissible spontaneous deformations: we consider ridged isometric immersions, which can cause a sharp ridge in the immersed surfaces. We propose a model to compute the extra energy distributed along such ridges. This energy comes from bending; it is shown under what circumstances it scales quadratically with the sheet’s thickness, falling just in between stretching and bending energies. We put our theory to the test by studying the spontaneous deformation of a disk on which a radial hedgehog was imprinted at the time of crosslinking. We predict the number of folds that develop in terms of the degree of order induced in the material by external agents (such as heat and illumination).
Graphic Abstract
中文翻译:
薄向列型聚合物网络的脊能量
摘要
主流理论所主张的策略是在光滑的等距浸入中使向列型聚合物网络薄片的弹性自由能最小化。在本文中,我们拓宽了允许的自发形变的类别:我们认为是脊形的等距浸没,可能会在浸没表面形成尖锐的脊。我们提出了一个模型来计算沿这些脊分布的额外能量。这种能量来自弯曲。它显示了在什么情况下,它随板材的厚度呈二次方缩放,恰好介于拉伸和弯曲能量之间。通过研究在交联时刻有径向刺猬的圆盘的自发变形,我们对理论进行了检验。我们根据外部因素(例如热量和光照)在材料中诱导的有序度来预测折叠的数量。