Nonlinear Problems for Thin Elastic Structures

薄弹性结构的非线性问题

• 批准号: 1312377
• 负责人: Timothy Healey
• 金额: $ 33.77万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-10-01 至 2016-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1312377&HistoricalAwards=false
• 关键词: Nonlinear; Problems; Thin; Elastic; Structures

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.

Healey1312377首席研究员及其同事研究了薄结构和固体的非线性弹性问题，并应用于多相脂质双层囊泡，对高度拉伸的床单的皱纹以及固体的损伤/断裂。 工作的主要目标是：（1）提供一类合理，准确的模型，以理解各种负载下此类系统的外来行为； （2）系统地找到其局部稳定的平衡（对应于总势能的局部最小值）作为负载和/或组成参数变化，尤其是较小的参数，例如厚度，近年毛细血管等，渐近地接近零。 目标（2）与（1）密不可分。 研究人员采用以一般本构函数为特征的理性连续体模型来研究存在问题，分叉和不稳定性的阈值以及局部能量最小值的结构。 这项工作是高度跨学科的，需要数学几个领域以及生物物理学和材料科学的工具和观点。 研究者进行了基本的建模和数学分析，从而实现了在施加的负载下对某些结构和固体行为的定量，预测性表征：脂质双层膜囊泡，薄膜以及固体中损伤/裂缝区的成核和成核和进展。 这些中的每一个都与基础科学和技术有直接而重要的联系，尤其是生物技术以及材料和制造业。 例如，脂质双层膜在生物分子系统中无处不在。理解和预测其机械行为对于理解细胞功能至关重要。 该项目的重点是理解在渗透压，温度或成分变化下人造膜或脂质体的行为。 作为药物输送的车辆，脂质体囊泡（闭合膜）的未来希望需要对其在负载和组成变化下的多相机械行为的基本了解。 与此相关的是，薄膜的皱纹也与此相关的是，这也显示在许多薄设备或涂层的设计中，类似织物的结构，人类皮肤的行为等。在高度伸展的环境中，在非常薄的结构中的皱纹发作和发展。 最后，固体的裂缝是结构突然和灾难性失败背后众所周知的罪魁祸首，目前对于收集天然气而言也引起了极大的兴趣。 该项目在该领域尤其缺乏预测模型。 特别是，他研究了损害的发作和发展，导致固体在负载下的骨折。