SGER: Formation and Evolution of Localized Structures

壳结构的许多现象学方面还远未被理解，并对力学在纳米结构和生物学等新领域的应用提出了根本性的挑战。一个这样的特殊和未探索的现象，这是由高度非线性机制驱动的，是存在和演化的稳定的局部结构的压缩壳。本研究的主要目的是揭示弹性壳中稳定局域结构的存在、形成和演化。这项工作需要开发一个理论模型，探讨这种现象的定性方面，并构建详细的计算模型，以数值模拟的响应压缩弹性壳横向扰动高保真。此外，薄壳上的实验将进行解开这些相互作用的局部化结构的形成和演化的物理机制。智力优势。这项研究的智力价值是巨大的：我们的计算模拟将提供对弹性壳中一种新现象的洞察，这种现象可以影响固体和材料力学以外的几个科学领域。我们的计算模型，它模拟了系统的准静态和动态响应，将几何非线性效应，使详细的建模壳的结构行为，可以提供有价值的洞察驱动大变形和不稳定的壳和板结构的机制。此外，严格的实验研究将有助于验证我们的计算模拟，并揭示相互作用局域结构形成和演化的物理机制。这个项目是重要的，不仅在其直接目标方面的理解局部结构和模式在弹性壳的形成和演变，而且在更广泛的背景下的力学高度变形结构。首先，本研究的结果将扩大我们的基本知识的行为，壳结构的变形在非线性制度和他们的不稳定性。虽然我们的研究的更广泛的影响将是阐明壳结构中的一种新现象，这不仅可以影响几个科学领域，而且通过为弹性壳的受控图案化提供新的途径，具有潜在的技术和商业应用。将特别强调该主题的跨学科方面，并确定了学术合作者，以增加视角和传播信息，以探索该项目的跨学科应用。

Many phenomenological aspects of shell structures are far from being understood and pose fundamental challenges for applications of mechanics in new areas such as nanostructures and biology. One such peculiar and unexplored phenomenon, which is driven by highly-nonlinear mechanisms, is the existence and evolution of stable localized structures in compressed shells. The main goal of this proposed study is to shed light into existence, formation and evolution of stable localized structures in elastic shells. The work entails developing a theoretical model to explore the qualitative aspects of this phenomenon and constructing detailed computational models to numerically simulate the response of compressed elastic shells subject to lateral perturbation with high fidelity. Furthermore, experimentation on thin shells will be conducted to unravel the physical mechanisms of formation and evolution of these interacting localized structures. Intellectual Merit. The intellectual merits of this research are vast: Our computational simulation will provide insight into a new phenomenon in elastic shells which can impact several scientific fields other than the Mechanics of Solids and Materials. Our computational model, which simulates quasi-static and dynamic response of the system incorporating the geometrical nonlinearity effect, enables detailed modeling of the structural behavior of shells and can provide valuable insight into the mechanisms driving large deformation and instability of shell and plate structures. In addition, rigorous experimental investigations will help validating our computational simulations and revealing physical mechanisms of formation and evolution of interacting localized structures.Broader Impacts. This project is important not only in terms of its immediate goals with respect to understanding the formation and evolution of localized structures and patterns in elastic shells, but also in the broader context of Mechanics of Highly-Deformed Structures. First, the results of this research will expand our fundamental knowledge on the behavior of shell structures deformed deeply in the nonlinear regime and their instability. While the broader impact of our research will be in elucidating a novel phenomenon in shell structures which not only can impact several scientific fields, but also has potential technical and commercial applications by providing new avenues for controlled patterning of elastic shells. Particular emphasis will be given to the interdisciplinary aspects of the subject and academic collaborators have been identified to add perspective and disseminate information to explore the interdisciplinary applications of this project.