Modeling, Analysis, and Computation in Nonlinear Elasticity

非线性弹性建模、分析和计算

基本信息

批准号：
2006586
负责人：
Timothy Healey
金额：
$ 32万
依托单位：
Cornell University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-08-01 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2006586&HistoricalAwards=false
关键词：
Modeling Analysis Computation Nonlinear Elasticity

项目摘要

This project is focused on the mathematical prediction of mechanical behavior in highly deformable elastic structures and solids, including both soft elastic systems and brittle materials. Soft structures occur naturally in biological systems such as skin and bio-membranes and are also manufactured as thin films and elastomers. The prediction of their initial instability, such as wrinkling, and post-critical pattern formation under loading and/or growth play a prominent role in this part of the project. For brittle solids (such as ceramics or steels at low temperature), we will use a new approach to fracture, predicting the initiation and formation of cracks under incremental loading. Overall, the project aims to provide new classes of continuum-mechanical models and novel approaches to their analyses, leading to a quantitative understanding of the mechanical behavior of these systems. The work has a range of potential applications – from bio-molecular structures to engineering machines and structures. This project includes opportunities for the research training of graduate students. Classes of nonlinear models of elastic-surface structures, soft elastic solids, and brittle solids will be analyzed. The main goals of the work are: (i) To provide properly formulated mechanics-based models. (ii) To obtain rigorous mathematical results, viz., establish existence theorems – the only true way to “ensure that the mathematical description of a physical phenomenon is meaningful” (R. Courant). (iii) To detect new phenomena. Goals (i) and (ii) inform and enrich each other; goal (iii) is enabled by goals (i) and (ii). This research is highly interdisciplinary, requiring tools and perspectives from several fields, e.g., nonlinear continuum mechanics, elliptic PDE systems, bifurcation theory, calculus of variations, numerical methods, symmetry ideas and biophysics, while providing new links between them. The project will provide new results and insights pertaining to surface-creasing formation in soft elastic solids, fracture of brittle materials, post-critical growth in elastic solids and pattern formation in lipid-bilayer structures or bio-membranes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目的重点是数学T弹性系统和脆性材料。脆性固体（例如陶瓷或低温的钢）的项目，我们将使用新的裂缝启动和形成工作在工程机器和结构上有一系列潜在的应用程序工作的目标是：（i）严格的数学结果（iii）由目标（i）和（ii）启用。项目将在柔软的弹性固体，弹性固体中的POS T临界生长以及脂质双层结构或生物膜中的图案形成中提供新的表面裂隙形成。该奖项反映了NSF'Sf'sf'sf'sf'sf'sf'sf'Sf'story Mission和Sistory Mission and Mission和通过使用Toundation的知识分子优点Meriter影响影响审查标准的评估，人们被认为值得获得支持。