CAREER: Finite Elasticity of Morphing Metamaterials. Theory and Applications

该学院早期职业发展（Career）基金将研究结构的弹性行为，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。可展开结构被用于机器人技术（例如，用于微创手术和搜救的软机器人）、航空航天（例如，智能机翼、可展开的镜子和太阳能电池板以及太空任务中的帆）和智能结构（例如，可展开的庇护所和屋顶）等多个领域。可展开结构的整体行为与其基本组成部分（杆、板和膜）的局部行为之间存在的关系受几何和力学规律的混合支配。该研究旨在建立对这种局部到全局关系的基本理解，以及它们决定可部署结构如何在外部负载下改变形状的方式，从而改进当前的建模、设计和控制范例。几何主题为艺术和时尚设计的几个领域提供了美学和吸引人的联系，并将通过外展活动来增加公众对科学和技术的参与，在机构中心的帮助下，这些活动将特别针对K-12和代表性不足的少数民族。该项目的主要目的是提出一种有限的、几何非线性的、弹性变形的可展开结构的理论，这些结构可以在小空间尺度上定制，如建筑材料和超材料。研究工作的技术目标是：(i)描述与由刚性或不可扩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丰富弹性泛函，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，并解决驱动参数的问题，驱动参数被理解为使可展开结构变形为目标形状的边界数据；（iv）建立反设计范式，使我们能够找到具有预编程变形路径的可展开结构。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。该项目将允许PI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。该奖项反映了美国国家科学基金会的法定使命，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。

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.