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Biot-elastic and Direct Models of Shells and Strips

贝壳和条带的生物弹性和直接模型

基本信息

批准号：
2001262
负责人：
James Hanna
金额：
$ 30.57万
依托单位：
Board of Regents, NSHE, obo University of Nevada, Reno
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-12 至 2025-04-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2001262&HistoricalAwards=false
关键词：
Biot elastic Direct Models Shells

项目摘要

Thin elastic structures such as shells and strips are found in engineering applications across many scales, including aerospace components, soft robots, flexible microelectronic devices, and programmable matter. Despite nearly a century of research on the mechanics of thin structures, questions remain about simple reduced models commonly employed to describe bending and stretching of these bodies in response to pressure or other applied forces. Superficially similar shell models make qualitatively different predictions, such as whether a bent shell will expand or contract under the same conditions. Existing strip models fail to capture experimentally observed shape changes during manipulations. This work will both explain these issues and develop new simple models that will agree with experiments and be useful in a variety of settings, including the design of new flexible and reconfigurable devices, and origami and kirigami structures for engineering applications. Graduate and undergraduate students will be trained as part of this project. The PI and students will develop related laboratory demonstrations and a module for a summer science program for young women in high school. Public outreach efforts will exploit the connections between thin structure mechanics and the behavior of toys such as snap bracelets. This work has two parts. First, an elastic theory will be developed based on systematic expansions in stretch. When applied to shells, this theory will preserve simple relationships between stress and generalized strain and provide the simplest definitions of bending energies. Second, a uniformly valid theory of elastic curves will be developed that interpolates between rod and inextensible wide strip models. This theory will capture bifurcation phenomena of narrow strips and allow numerical integration of strip deformations that create inflection points. More broadly, the work will relate direct and dimensional reduction approaches to thin structures. The new shell theory will be compared with theoretical and numerical results on soft shells from the literature, and the new strip theory will be validated using prior experimental results on bifurcations from the PI?s prior work and the literature. The issues to be addressed in this work are relevant to research areas such as the incompatible elasticity of soft and other materials, design of programmable elastomeric and structured sheets, and instabilities and bifurcations of flexible components.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.

薄的弹性结构，如壳和带，在许多尺度的工程应用中被发现，包括航空航天部件，软机器人，柔性微电子器件和可编程物质。尽管对薄结构力学的研究已经进行了近世纪，但关于通常用于描述这些物体响应于压力或其他作用力的弯曲和拉伸的简单简化模型的问题仍然存在。表面上相似的壳模型做出了性质上不同的预测，例如弯曲的壳在相同条件下是否会膨胀或收缩。现有的条带模型未能捕获实验观察到的形状变化，在操纵。这项工作将既解释这些问题，又开发新的简单模型，这些模型将与实验一致，并在各种环境中有用，包括设计新的灵活和可重构的设备，以及用于工程应用的折纸和kirigami结构。研究生和本科生将作为该项目的一部分接受培训。 PI和学生将开发相关的实验室演示和高中年轻女性暑期科学计划的模块。公众推广工作将利用薄结构力学和玩具（如卡扣手镯）的行为之间的联系。这项工作有两个部分。首先，弹性理论将发展的基础上系统的扩展拉伸。当应用于壳体时，该理论将保持应力和广义应变之间的简单关系，并提供弯曲能的最简单定义。其次，将开发一个统一有效的弹性曲线理论，该理论在杆和不可延伸的宽条模型之间进行插值。该理论将捕获窄条的分叉现象，并允许创建拐点的带变形的数值积分。更广泛地说，这项工作将涉及直接和降维方法薄结构。新的壳理论将与理论和数值计算结果从文献中的软壳进行比较，新的条理论将验证使用以前的实验结果从PI分叉？的前期工作和文献。在这项工作中要解决的问题是相关的研究领域，如不兼容的弹性软材料和其他材料，设计的可编程弹性体和结构片，和不稳定性和分叉的柔性组件。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。