Nonlinear Problems for Thin Elastic Structures

首席研究员和他的同事们研究了薄结构和固体的非线性弹性问题，并将其应用于多相脂质双层囊泡、高拉伸片的起皱和固体的损伤/断裂。这项工作的主要目标是：(1)提供合理的、准确的模型，用于理解这些系统在各种负载下的奇异行为；(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），当载荷和/或组成参数变化时，特别是当厚度、面间毛细等小参数渐近于零时。目标(2)与目标(1)密不可分。研究者采用以一般本构函数为特征的理性连续体模型，研究了局部能量极小值的存在性、分岔和不稳定性阈值以及结构问题。这项工作是高度跨学科的，需要来自数学、生物物理学和材料科学等多个领域的工具和观点。研究者进行基础建模和数学分析，从而对施加载荷下某些结构和固体的行为进行定量、预测性表征：脂质双层膜囊泡、薄膜和固体中损伤/破裂带的成核和进展。这些都与基础科学技术有着直接而重要的联系，尤其是生物技术、材料和制造业。例如，脂质双层膜在生物分子系统中无处不在；了解和预测它们的力学行为对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需要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，也是更普遍的兴趣，是薄膜的起皱，它也出现在许多薄设备或涂层，织物状结构的设计中，在人类皮肤的行为中，等等。研究者研究高度拉伸环境中非常薄的结构中皱纹的发生和发展。最后，众所周知，固体破裂是导致结构突然和灾难性破坏的罪魁祸首，目前也引起了天然气开采的极大兴趣。预测模型是目前该领域所缺乏的。特别是，他研究了固体在载荷作用下导致破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.