SGER: Formation and Evolution of Localized Structures

壳结构的许多现象学方面还远未被理解，这对力学在纳米结构和生物学等新领域的应用构成了根本挑战。压缩壳体中稳定局域结构的存在和演化是一种由高度非线性机制驱动的奇特而未被探索的现象。这项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。这项工作需要建立一个理论模型来探索这一现象的定性方面，并构建详细的计算模型来高保真地数值模拟受横向摄动的压缩弹性壳的响应。此外，还将进行薄壳实验，以揭示这些相互作用的局域结构形成和演化的物理机制。智力上的功绩。这项研究的学术价值是巨大的：我们的计算模拟将提供对弹性壳中的一种新现象的洞察，该现象可以影响固体和材料力学以外的几个科学领域。我们的计算模型模拟了考虑几何非线性效应的系统的准静态和动态响应，能够对壳的结构行为进行详细的建模，并可以为驱动壳和板结构的大变形和失稳的机理提供有价值的见解。此外，严格的实验研究将有助于验证我们的计算模拟，并揭示相互作用的局域结构形成和演化的物理机制。该项目的重要意义不仅在于它的近期目标是理解弹性壳中局部结构和模式的形成和演变，而且还在于高度变形结构的力学的更广泛的背景。首先，本文的研究成果将拓展我们对壳体结构在非线性区域内的深度变形及其失稳行为的基本认识。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，该现象不仅可以影响几个科学领域，而且通过为弹性壳的可控模式提供新的途径而具有潜在的技术和商业应用。将特别重视这一主题的跨学科方面，并已确定学术合作者，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.