CAREER: Effective Continuum Modeling of Mechanism-Based Metamaterials

这一学院早期职业发展(Career)奖将支持对一系列变形超材料的机械响应的基础研究，这些超材料的灵感来自于流行的艺术形式，如折纸和Kirigami。变形超材料是基于细胞的刚性面板图案，连接在灵活的铰链或折叠上，旨在实现大的整体形状变化，而总体应力很小。它们是许多应用的很有前途的材料，包括软机器人的移动以及医疗设备和卫星的部署。然而，它们的力学行为是由多尺度耦合引起的，建模具有挑战性：集体胞状弹性相互作用、大的面板旋转以及铰链或折叠处的局部变形。这项研究的目的是开发能够有效地导航这些材料的设计空间并预测其在大范围载荷和刺激下的响应的建模工具。该奖项还将研究纳入教育和外联工作，拥抱洛杉矶社区的多样性。外展工作包括为加州州立大学的本科生提供暑期研究机会，以及通过南加州大学维特比的暑期高中下一代工程强化(SINE)计划为当地高中生提供暑期研究机会。该研究项目旨在为基于机制的变形超材料的有效连续介质建模奠定理论基础。其关键目标是用有效的(细胞平均的)连续变形和辅助场来代替超材料构建块的复杂的微运动，目标是在工程尺度上粗粒化材料的集体弹性相互作用。这项研究远不是本构选择，而是使用严格的渐近分析方法、变分法和几何刚性来证明有效的连续统理论是一系列变形超材料力学的基础。这一理论发展将使实用的连续体本构模型成为可能，这些模型将超材料的几何设计直接连接到可有效模拟和预测的广义弹性连续体模型。所获得的知识将导致广泛适用的工具来探索变形超材料的设计-性能关系，以及对其在负载下的行为的新见解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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) award will support fundamental research on the mechanical response of a wide range of morphing metamaterials that take inspiration from popular artforms like origami and kirigami. Morphing metamaterials are cell-based patterns of stiff panels, connected at flexible hinges or folds, designed to achieve large overall shape-change at little overall stress. They are promising materials for many applications, including for locomotion in soft robotics and for deployment of medical devices and satellites. However, their mechanical behavior arises from a multiscale coupling that is challenging to model: collective cellwise elastic interactions, large panel rotations, and localized distortion at the hinges or folds. This study aims to develop modeling tools capable of efficiently navigating the design space of these materials and predicting their response under a broad range of loads and stimuli. The award also integrates research into educational and outreach efforts that embrace the diversity of the Los Angeles community. The outreach effort includes summer research opportunities for undergraduate students from Cal State LA, a minority serving regional university, and for local high school students through USC Viterbi’s Summer High School Intensive in Next Generation Engineering (SHINE) program.This research project seeks to lay a theoretical foundation to effective continuum modeling of mechanism-based morphing metamaterials. The key objective is to replace the complex micro-motions of the metamaterials building blocks by an effective (cell-averaged) continuum deformation and auxiliary fields, with the goal of coarse graining the material’s collective elastic interactions at the engineering scale. Far from being a constitutive choice, this study will employ rigorous asymptotic analysis methods, calculus of variations, and geometric rigidity to demonstrate that effective continuum theories underlie the mechanics of a host of morphing metamaterials. This theoretical development will enable practical continuum constitutive models that link the geometric design of the metamaterial directly to models of generalized elastic continua that are efficient to simulate and predictive. The knowledge gained will lead to broadly applicable tools to explore the design-property relationship of morphing metamaterials, as well as novel insight into their behavior under loads.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.