Nonlinear Problems for Thin Elastic Structures

中国人1312377 主要研究者和他的同事们研究了薄结构和固体的非线性弹性的几个问题，并应用于多相脂质双层囊泡，高度拉伸的片材的拉伸和固体的损伤/断裂。 工作的主要目标是：（1）提供合理的，准确的模型来理解这些系统在各种载荷下的奇异行为;（2）系统地找到它们的局部稳定平衡（对应于总势能的局部最小值），因为载荷和/或组成参数变化，特别是像厚度，界面毛细作用等小参数，渐近地接近零。 目标（2）与目标（1）密不可分。 研究人员采用合理的连续模型，其特征在于一般的本构函数，研究问题的存在，阈值的分歧和不稳定性，以及结构的局部能量极小值。 这项工作是高度跨学科的，需要从数学以及生物物理学和材料科学的几个领域的工具和观点。 研究人员进行基本建模和数学分析，能够定量，预测表征某些结构和固体在施加载荷下的行为：脂质双层膜囊泡，薄膜和固体中损伤/断裂区的成核和进展。 其中每一个都与基础科学和技术-特别是生物技术、材料和制造业-有着直接和重要的联系。 例如，脂质双层膜在生物分子系统中无处不在;理解和预测它们的机械行为对于理解细胞功能至关重要。 该项目的重点是了解人造膜或脂质体在渗透压，温度或成分变化下的行为。 脂质体囊泡（封闭膜）作为药物递送载体的未来前景要求对其在负载和组成变化下的多相力学行为有基本的了解。 与此相关的，但也更普遍的兴趣，是薄膜的褶皱，这也出现在许多薄设备或涂层，织物状结构的设计，在人类皮肤的行为等研究人员研究的发病和高度拉伸环境中非常薄的结构皱纹的发展。 最后，固体的断裂，结构中突然和灾难性故障背后的众所周知的罪魁祸首，目前也是出于采集天然气的目的而引起极大兴趣的。 预测模型，这是特别缺乏在这一领域，在这个项目中得到解决。 特别是，他研究了在载荷作用下导致固体断裂的损伤的发生和发展。

Healey1312377 The principal investigator and his colleagues study several problems of nonlinear elasticity for thin structures and solids, with applications to multi-phase lipid bilayer vesicles, wrinkling of highly stretched sheets and damage/fracture of solids. The main goals of the work are: (1) provide classes of rational, accurate models for understanding the often exotic behavior of such systems under various loadings; (2) systematically find their locally stable equilibria (corresponding to local minima of the total potential energy) as loading and/or composition parameters vary, particularly as small parameters like thickness, inter-facial capillarity, etc., asymptotically approach zero. Goal (2) is inextricably linked to (1). The investigator employs rational continuum models, characterized by general constitutive functions, to study questions of existence, thresholds of bifurcation and instability, and the structure of local energy minima. The work is highly interdisciplinary, requiring tools and perspectives from several areas of mathematics as well as biophysics and materials science. The investigator undertakes fundamental modeling and mathematical analysis enabling a quantitative, predictive characterization of the behavior of certain structures and solids under applied loading: lipid-bilayer membrane vesicles, thin films and the nucleation and progression of damage/fracture zones in solids. Each of these has direct and important connections to basic science and technology -- especially biotechnology and materials and manufacturing. For example, lipid-bilayer membranes are ubiquitous in bio-molecular systems; understanding and predicting their mechanical behavior is crucial for understanding cell function. The project focuses on understanding the behavior of man-made membranes or liposomes under changes in osmotic pressure, temperature, or composition. The future promise of liposome vesicles (closed membranes) as vehicles for drug delivery demands a fundamental understanding of their multi-phase mechanical behavior under loading and change of composition. Associated with this, but also of more general interest, is the wrinkling of thin films, which also shows up in the design of many thin devices or coatings, fabric-like structures, in the behavior of human skin, etc. The investigator studies the onset and development of wrinkles in very thin structures in highly stretched environments. Finally, the fracture of solids, a well-known culprit behind sudden and catastrophic failures in structures, is also currently of great interest for purposes of harvesting natural gas. Predictive models, which are especially lacking in this field, are addressed in this project. In particular, he studies the onset and development of damage leading to fracture of solids under loading.