Mechanics of surfaces: Continuum-based modeling and analysis for biomembranes and 2D fiber materials

该研究的目标是在表面力学领域建立一个研究项目，专注于开发连续体模型和用于设计和分析先进二维材料的数值技术。特别是，拟开展的研究项目将解决以下两大分支问题，这两大分支问题在生物力学和纳米力学领域的重要应用引起了相当大的关注。脂质膜具有各种有用的医疗和工业应用，包括药物运输和递送，以及基于生物膜的传感器（例如水毒性传感器）。对于这些应用，模拟和预测它们在囊泡形成、融合和膨胀过程中的机械反应是很重要的。脂质双分子层是由含有亲水头基和疏水尾的横向定向脂质分子组成的。这些分子以相反的方向排列成两层，有效地保护了尾部基团不受周围水溶液的影响。事实上，双层结构是所有生物膜（生物膜）的特征。这种排列发生在分子尺度的长度尺度上。因此，脂质双分子层可以看作是一种封闭的膜，其微观取向不同，脂质分子最初与表面法向排列。在本项目中，我们将开发一个完整的连续体模型和数值方法来描述厚度膨胀和非均匀脂质分布下的生物膜形态。更准确地说，我们将通过计算膜相对于平均和高斯曲率、脂质膨胀及其在膜表面的梯度的能量变化来分析建模和检查脂质双分子层。* * * 2。二维纤维复合材料的应变梯度集成建模***本研究旨在建立能够适应纤维抗拉伸、抗弯曲和抗扭转性能的通用二维连续体模型。这将允许更准确地描述二维纤维复合材料在各种外部载荷下的应力场和位移场。特别是，通过提出的研究计划，我们旨在为近年来备受关注的纤维素纳米晶体增强生物复合材料（CNC）的设计和分析奠定坚实的理论和实践基础。通过计算纤维的应变梯度场，将纤维的运动整合到薄膜结构的变形场中。我们从单向纤维复合材料的情况开始，随后将结果扩展到更一般的情况，即薄膜结构由多向纤维和最初的非直纤维支撑

The objective of the proposed research is to establish a research program in the area of the mechanics of surfaces focused on developing continuum models and numerical techniques for the design and analysis of advanced 2D materials. In particular, the proposed research program will address the following two major branches of problems that have drawn a considerable attention due to their important applications in the fields of biomechanics and nanomechanics.***1. Mechanics of biomembranes subjected to thickness distension and non-uniform lipid distribution***Lipid membranes have various useful medical and industrial applications including drug transport and delivery, and biomembrane-based sensors (e.g. water toxicity sensors). For such applications, it is important to simulate and predict their mechanical responses on vesicle formation, fusion and distension involved motions. Lipid bilayers are composed of transversely oriented lipid molecules containing hydrophilic head groups and hydrophobic tails. These molecules arrange themselves into a two layered sheet with opposing orientations that effectively shield the tail groups from the surrounding aqueous solution. In fact, the bilayer structure is characteristic of all biological membranes (biomembranes). The arrangement occurs over length scales on the order of molecular dimensions. Therefore, a lipid bilayer can be regarded as a closed membrane with distinct microscopic orientations of lipid molecules initially aligned with the surface normal. In this project, we will develop a complete continuum model and numerical method in the description of biomembrane morphology under the presence of thickness distension and non-uniform lipid distribution. More precisely, we will analytically model and examine a lipid bilayer by computing the energy variations of the membrane with respect to mean and Gaussian curvatures, lipid distension and its gradient on the membrane surface. ***2. Strain-gradient integrated modeling for 2D fiber composites***The research intends to develop general 2D continuum models that can accommodate fiber's resistance to extension, bending and twist. This will allow more accurate descriptions for stress and displacement fields of 2D fiber composites subjected to various external loadings. In particular, through the proposed research program, we aim to build a strong theoretical and practical foundation in design and analysis of biocomposites reinforced with cellulose nanocrystals (CNC) which has drawn a considerable attention in recent years. By calculating strain-gradient fields of fibers, we will integrate fiber's motions into the deformation fields of the film structure. We begin with the case of unidirectional fiber composites and subsequently extend the results to the more general scenarios where the film structure is supported by multi-directional fibers and initially non-straight fibers.**