Microstructure integrated continuum model and numerical scheme for the design and characterization of 2-D microstructured materials

申请人的研究团队目前处于生物相容性复合材料设计和分析的前沿，近年来，由于其在生物力学和纳米力学领域的各种应用而受到越来越多的关注。由于缺乏描述高度非线性和耦合响应的严格预测模型，这类材料的制备和表征主要基于试错法，这严重影响了效率和精度。拟议研究的长期目标是通过开发创新的连续介质模型和稳健的数值技术，为二维微结构材料的设计和表征建立一个合适的分析平台。因此，拟议的研究计划将解决以下两个主要问题：1.纤维增强超弹性材料力学的伪弹性和连续损伤模型。与老龄化有关的健康问题已成为社会和经济负担的重要来源。使用健康监测系统和辅助设备可以是促进受影响群体健康和社会独立的有效手段。然而，仍然存在着巨大的技术挑战，包括开发能够适应各种体内和/或体外环境的生物相容性复合膜。这项研究旨在发展全面的连续介质模型，以方便超弹性复合薄膜的设计和制备。这包括改进一系列基于连续介质的模型，以解释伪弹性和应变硬化/软化响应。增强纤维的运动学和网格取向也将利用它们的位置场和指向场来表示。我们从单向纤维复合材料的情况开始，然后将结果扩展到更一般的多向纤维和初始非正交纤维网状结构的情况。2.表面膨胀、蛋白质扩散和膜内脂质粘度引起的脂质双层膜的形态转变。在拟议的研究中，我们的目标是开发基于连续介质的模型和分子动力学方案来分析类脂膜的形态。通过应用三维液晶理论的降维过程来模拟类脂双层膜的微结构特征，由此可以适应类脂膨胀和倾斜的非标准效应。所获得的模型的一个变体也将被考虑包括与更高梯度效应有关的脂膜的广义毛细管，例如表面扩张、蛋白质扩散和膜内粘性流动。拟议的研究结果可以直接应用于生物传感器和有效的药物输送机制的设计，并最终将增强我们对广泛的基本细胞功能的理解。

The applicant's research team is currently on the forefront of the design and analysis of biocompatible composite materials which have drawn an increasing attention in recent years for their various applications in the fields of biomechanics and nanomechanics. Due to the lack of rigorous prediction models describing highly non-linear and coupled responses, the fabrication and characterization of such materials are mainly based on "trial and error" which significantly compromise the efficiency and precision. The long-term objective of the proposed research is to establish a propound analytical platform for the design and characterization of 2-D microstructured materials by developing innovative continuum models and robust numerical techniques. As such, the proposed research program will address the following two major branches of problems: 1. Pseudo-elastic and continuum damage models for the mechanics of the hyperelastic materials reinforced with fibrous fibers. Aging-related health issues have become a significant source of social and economic burden. The uses of health monitoring systems and assistive devices can be an effective means of promoting health and social independence of impacted groups. However, there exist formidable technical challenges including the developments of biocompatible composite films sustaining various in-vivo and/or in-vitro environments. The proposed research intends to develop comprehensive continuum models that can facilitate the design and fabrication of hyperelastic composite films. This includes the refinement of a series of continuum-based models to account for pseudo-elasticity and strain stiffening/softening responses. The kinematics and mesh orientations of reinforcing fibrous fibers will also be formulated by using their position and director fields. We begin with the case of unidirectional fiber composites and subsequently extend the results to the more general scenarios of multi-directional fibers and initially non-orthogonal fiber meshes. 2. Morphological transitions of lipid bilayer membranes induced by surface dilation, protein diffusion and intra-membrane lipid viscosity. In the proposed research, we aim to develop continuum-based models and molecular dynamics schemes for the analysis of lipid membrane morphology. The microstructure characteristics of lipid bilayer membranes will be modeled via a dimension reduction procedure applied to 3-D liquid crystal theory from which the non-standard effects of lipid distension and tilt can be accommodated. A variant of the obtained model will also be considered to incorporate the generalized capillarity of lipid membranes pertaining to higher gradient effects such as surface dilation, protein diffusion and intramembrane viscous flow. Outcomes from the proposed research can be directly applied to the design of biosensors and effective drug delivery mechanisms and will eventually enhance our understanding of a wide range of essential cellular functions.