CAREER: Finite Elasticity of Morphing Metamaterials. Theory and Applications

职业：变形超材料的有限弹性。

• 批准号: 2045881
• 负责人: Hussein Nassar
• 金额: $ 60.96万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-04-01 至 2026-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2045881&HistoricalAwards=false
• 关键词: CAREER; Finite; Elasticity; Morphing; Metamaterials.

This Faculty Early Career Development (CAREER) grant will investigate the elastic behavior of structures that can unfold and deploy from compact configurations into useful 3D geometries. Deployable structures are used in several areas pertaining to robotics (e.g., soft robots used in minimally invasive surgeries and in search-and-rescue), to aeronautics and astronautics (e.g., smart airfoils, deployable mirrors and solar panels and sails in space missions) and to smart structures (e.g., deployable shelters and rooftops). The relationships that exist between the global behavior of a deployable structure and the local behavior of its elementary constituents (bars, plates and membranes) are governed by a mixture of geometrical and mechanical laws. The research aims to establish a fundamental understanding of such local-to-global relationships and of the way they dictate how a deployable structure changes shape under external loads so as to improve current modeling, design and control paradigms. The theme of geometry provides aesthetic and appealing connections with several areas of artistic and fashion design and will be leveraged to increase public engagement with science and technology through outreach activities which, with the help of an institutional center, will particularly target K-12 and underrepresented minorities.The main purpose of the project is to initiate a theory of the finite, geometrically non-linear, elastic deformations of deployable structures that are tailored on small space scales as in architected materials and metamaterials. The technical objectives of the research efforts are to (i) characterize the macroscopic deformation paths compatible with the small-scale kinematics of a deployable structure composed of rigid or inextensible elements; to (ii) compute the generalized, strain-gradient or enriched, elasticity functionals that govern the equilibrium geometries of a deployable structure and particularly so in cases where standard Strength of Materials theories break down; (iii) formulate conceptual control problems and solve them for actuation parameters understood as the boundary data that deform the deployable structure into a target shape; and (iv) establish inverse design paradigms that allow us to find deployable structures with pre-programmed deformation paths. To do so, the project will develop analysis methods marrying differential geometry, asymptotics and homogenization theory. This project will allow the PI to advance the knowledge base in solid mechanics and to support his long-term career within that field.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.

这个教师早期职业发展（CAREER）补助金将调查结构的弹性行为，这些结构可以从紧凑的配置展开和部署到有用的3D几何形状。可展开结构用于与机器人技术有关的若干领域（例如，用于微创手术和搜索和救援的软机器人），用于航空和航天学（例如，智能机翼、可展开镜子、太阳能电池板和太空任务中的帆）和智能结构（例如，可展开的遮蔽物和屋顶）。可展开结构的整体行为与其基本组成部分（杆、板和膜）的局部行为之间的关系受几何和力学定律的混合支配。该研究的目的是建立一个基本的理解，这种局部到全局的关系，以及它们如何决定一个可展开的结构如何在外部负载下改变形状，以改善当前的建模，设计和控制模式。几何主题提供了与艺术和时装设计的几个领域的美学和吸引力的联系，并将通过推广活动，特别是针对K-12和代表性不足的少数民族，利用几何来增加公众对科学和技术的参与。可展开结构的弹性变形，如建筑材料和超材料中的小空间尺度。研究工作的技术目标是（i）表征与由刚性或不可伸展元件组成的可展开结构的小尺度运动学相容的宏观变形路径;（ii）计算控制可展开结构的平衡几何形状的广义应变梯度或富集弹性泛函，特别是在标准材料强度理论失效的情况下;（iii）制定概念控制问题，并解决它们的驱动参数理解为边界数据，变形的可展开结构到目标形状;和（iv）建立逆设计范式，使我们能够找到可展开结构与预先编程的变形路径。为此，该项目将开发结合微分几何、渐近和均匀化理论的分析方法。该项目将使PI能够推进固体力学的知识基础，并支持他在该领域的长期职业生涯。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Effective isometries of periodic shells

周期壳的有效等距

• DOI: 10.1016/j.jmps.2024.105553
• 发表时间: 2024
• 期刊: Journal of the Mechanics and Physics of Solids
• 影响因子: 5.3
• 作者: Nassar, Hussein;Weber, Andrew
• 通讯作者: Weber, Andrew

Willis elasticity from microcontinuum field theories: Asymptotics, microstructure-property relationships, and cloaking

微连续场理论中的威利斯弹性：渐近、微观结构-性质关系和隐身

• DOI: 10.1016/j.wavemoti.2023.103206
• 发表时间: 2023
• 期刊: Wave Motion
• 影响因子: 2.4
• 作者: Nassar, H.;Brucks, P.
• 通讯作者: Brucks, P.

Frustration propagation in tubular foldable mechanisms

管状可折叠机构中的挫败传播

• DOI: 10.3389/fphy.2023.1296661
• 发表时间: 2023
• 期刊: Frontiers in Physics
• 影响因子: 3.1
• 作者: Reddy, A.;Karami, A.;Nassar, H.
• 通讯作者: Nassar, H.

Isometric deformations of surfaces of translation

平移面的等距变形

• DOI: 10.2140/memocs.2024.12.1
• 发表时间: 2023
• 期刊: Mathematics and Mechanics of Complex Systems
• 影响因子: 1.9
• 作者: Nassar, Hussein

Strain compatibility and gradient elasticity in morphing origami metamaterials

变形折纸超材料中的应变相容性和梯度弹性

• DOI: 10.1016/j.eml.2022.101722
• 发表时间: 2022
• 期刊: Extreme Mechanics Letters
• 影响因子: 4.7
• 作者: Nassar, Hussein;Lebée, Arthur;Werner, Emily
• 通讯作者: Werner, Emily