CAREER: Statistical Mechanics of Slender Structures

该职业奖支持理论和计算研究和教育，以促进对力学的理解，即机械装置如何在微观长度范围内工作到纳米结构的规模。大自然制造能够感知环境并对其做出反应的纳米机器的迷人能力，促使研究人员探索不同的小型化功能设备的方法。成功采用的策略之一是制作图案化/复合原子层，它可以在平面状态下制备，并且随后可以根据外部刺激改变其形状。通过利用折纸的折叠原理，研究人员已经制造出了功能性的自折叠折纸微型装置，它可以进行活组织检查和输送药物。类似地，来自纸基里伽米和弹出式卡片的想法已经引导研究人员设计出微型可伸缩电子设备和极其敏感的力传感器。功能性微型火箭已被用于操纵和分离细胞以及各种环境应用，包括水监测、修复和解毒。随着设备变得越来越小，它们的机制将对来自环境的缺陷和随机波动变得越来越敏感。例如，随机缺陷将平坦的原子层转变成让人想起皱巴巴的纸的形状，而随机的热搅拌可以在某个临界温度以上自发地粉碎球形壳。这些效应可能违背基于宏观结构力学的直觉。这使得设计功能性的微纳米结构具有挑战性。PI旨在开发一个理论和计算框架，以研究存在缺陷和随机波动的复杂微观细长结构的力学。这项研究将阐明生物结构的功能，设计可以机械调节的新型电子结构，以及在平面状态下制备的微观结构的设计，这些结构随后可以自我折叠成所需的形状，具有生物医学设备和各种环境和工业应用的潜力。这里提出的研究将有助于教育下一代跨学科的科学家，他们的专业知识驻留在连续介质力学，统计力学和生物学的交叉点。此外，连续介质力学的课程通常是从工程角度教授的，很少有对生物学和统计力学感兴趣的学生参加。为了解决这个问题，PI已经开发了一门新的研究生课程，名为“工程微型设备的生物学课程”，并将在二年级必修的连续介质力学工程课程中添加新的主题。该奖项还支持教育、激励和指导新泽西州特伦顿市未被充分代表和社会经济弱势群体的高中生。公众将获得一个新的教育博客，该博客将涵盖生物学，物理学，力学和工程学的界面主题。本职业奖支持一项理论和计算研究，并结合热波动、非平衡波动和无序如何影响微观细长结构的力学。研究议程的动机是生物微观外壳的重要性和最近的实验发展，其中各种形状和成分的原子薄层材料现在经常生产。实验人员可以制造出高度可拉伸的石墨烯基里米装置和复合/图案原子层，它们可以根据外部刺激改变形状。然而，理论无法描述热化或无序平板的力学，超出了它们对外力的线性响应。人们对壳的统计力学知之甚少。这个项目的目标是弥合理论与实验之间的差距。该项目将开发一个理论框架和模拟工具，以便在热波动、非平衡波动和淬火缺陷存在的情况下研究具有复杂几何形状的结构的力学。发展粗粒度有限元分子动力学模拟的基础，将是对三种不同类型的小元素的研究：平片，弯曲壳和受挫片。在存在波动的情况下，由于弯曲、拉伸、剪切等载荷组合，将通过开发新的重整化群计算来研究此类斑块的有效静态和动态应力-应变响应，并使用复制方法处理缺陷。PI将寻求缺陷和热非平衡波动作用之间的定量差异，这可以反映在静态应力-应变曲线非线性体系中的不同通用指数中，以及对动态载荷的不同速率相关响应中。机械性能主要取决于几何形状，三种不同类型的贴片——平片、弯曲壳和受挫片——预计会表现出不同性质的行为，例如，波动可以稳定平片，但它们会降低壳的稳定性。基于这些研究，PI将开发粗粒度模拟工具，用于研究具有复杂几何形状的结构的统计力学。该奖项将对生物结构的力学、可机械调谐的新型电子结构的设计以及在平面状态下制备的微观结构的设计产生直接影响，这些微观结构随后可以自我折叠成所需的形状，具有生物医学设备和各种环境和工业应用的潜力。这里提出的研究将有助于教育下一代跨学科的科学家，他们的专业知识驻留在连续介质力学，统计力学和生物学的交叉点。此外，连续介质力学的课程通常是从工程角度教授的，很少有对生物学和统计力学感兴趣的学生参加。为了解决这个问题，PI已经开发了一门新的研究生课程，名为“工程微型设备的生物学课程”，并将在二年级必修的连续介质力学工程课程中添加新的主题。该奖项还支持教育、激励和指导新泽西州特伦顿市未被充分代表和社会经济弱势群体的高中生。公众将获得一个新的教育博客，该博客将涵盖生物学，物理学，力学和工程学的界面主题。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical and computational research and education to advance understanding of mechanics how mechanical devices work at microscopic length scales down to the scale of nanostructures. Nature's fascinating ability to make nanomachines that can sense and respond to their environment has motivated researchers to explore different ways of miniaturizing functional devices. One of the strategies that was successfully employed is to make patterned /composite atomic layers, which can be prepared in a flat state and can subsequently transform their shapes in response to external stimuli. By using ideas from the folding of paper origami, researchers have produced functional self-folding origami micro-devices, which can perform biopsies and deliver drugs. Similarly, the ideas from paper kirigami and pop-up cards have led researchers to design micro-scale stretchable electronics and extremely sensitive force sensors. Functional micro-rockets have been employed for manipulation and isolation of cells and for diverse environmental applications, including water monitoring, remediation and detoxification.As devices are made smaller and smaller, their mechanics will become increasingly sensitive to imperfections and random fluctuations coming from the environment. For example, random imperfections transform flat atomic layers into shapes reminiscent of crumpled paper, while random thermal agitations can spontaneously crush spherical shells above some critical temperature. These effects can defy intuition based on the mechanics of macroscopic structures. This makes it challenging to design functional micro- and nano-structures. The PI aims to develop a theoretical and computational framework to investigate the mechanics of complex microscopic slender structures in the presence of defects and random fluctuations. The research will illuminate how biological structures function, to design novel electronic structures that can be tuned mechanically, and the design of microscopic structures that are prepared in a flat state and can subsequently self-fold to desired shapes with potential for biomedical devices and diverse environmental and industrial applications.The research proposed here will help educate the next generation of interdisciplinary scientists whose expertise resides at the intersection of continuum mechanics, statistical mechanics, and biology. Moreover, courses in continuum mechanics are typically taught from an engineering perspective and are very rarely attended by students with interests in biology and statistical mechanics. To address this issue, the PI has developed a new graduate course titled "Lessons from Biology for Engineering Tiny Devices" and will add new topics to the required sophomore engineering course on continuum mechanics. This award also supports educating, inspiring and mentoring high school students from underrepresented and socioeconomically disadvantaged populations in Trenton, NJ. The public will be reached with a new educational blog that will cover topics at the interface of biology, physics, mechanics and engineering.TECHNICAL SUMMARYThis CAREER award supports a theoretical and computational study integrated with education of how thermal fluctuations, nonequilibrium fluctuations, and disorder affect the mechanics of microscopic slender structures. The research agenda is motivated by the importance of biological microscopic shells and by recent experimental developments, where atomically thin layers of materials of various shapes and compositions are now routinely produced. Experimentalists can make highly stretchable graphene kirigami devices and composite/patterned atomic layers which can transform their shapes in response to external stimuli. However,, theory cannot describe the mechanics of thermalized or disordered flat sheets beyond their linear response to external forces. Less is known about the statistical mechanics of shells. The goal of this project is to bridge the gap between theory and experiments.This project will develop a theoretical framework and simulation tools that will enable studies of the mechanics of structures with complex geometries in the presence of thermal fluctuations, nonequilibrium fluctuations, and quenched defects. The basis for the development of coarse-grained finite-element molecular dynamics simulations, will be studies of small elements of three different types: flat sheets, curved shells and frustrated sheets. The effective static and dynamic stress-strain responses for such patches due to combination of loading, such as bending, stretching, shearing, in the presence of fluctuations will be studied by developing new renormalization group calculations, with defects treated using the replica approach. The PI will seek quantitative differences between the role of defects and of thermal and nonequilibrium fluctuations, which could be reflected in different universal exponents in the nonlinear regime of static stress-strain curves, as well as in different rate-dependent responses to dynamic loads. Mechanical properties are expected to depend critically on geometry, and three different types of patches - flat sheets, curved shells, and frustrated sheets - are expected to exhibit qualitatively different behaviors, for example fluctuations can stabilize flat sheets, but they reduce the stability of shells. Based on these studies the PI will develop coarse-grained simulation tools that will enable studies of the statistical mechanics of structures with complex geometries. The award will have direct implication for the mechanics of biological structures, for the design of novel electronic structures that can be tuned mechanically, and for the design of microscopic structures that are prepared in a flat state and can subsequently self-fold to desired shapes with potential for biomedical devices and diverse environmental and industrial applications.The research proposed here will help educate the next generation of interdisciplinary scientists whose expertise resides at the intersection of continuum mechanics, statistical mechanics, and biology. Moreover, courses in continuum mechanics are typically taught from an engineering perspective and are very rarely attended by students with interests in biology and statistical mechanics. To address this issue, the PI has developed a new graduate course titled "Lessons from Biology for Engineering Tiny Devices" and will add new topics to the required sophomore engineering course on continuum mechanics. This award also supports educating, inspiring and mentoring high school students from underrepresented and socioeconomically disadvantaged populations in Trenton, NJ. The public will be reached with a new educational blog that will cover topics at the interface of biology, physics, mechanics and engineering.