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.

诸如壳体和条带之类的薄弹性结构存在于多种规模的工程应用中，包括航空航天部件、软机器人、柔性微电子设备和可编程物质。尽管对薄结构力学的研究已经进行了近一个世纪，但对于通常用于描述这些物体响应压力或其他外力的弯曲和拉伸的简单简化模型，问题仍然存在。表面上相似的壳模型会做出本质上不同的预测，例如弯曲的壳在相同条件下是否会膨胀或收缩。现有的条带模型无法捕捉操作过程中实验观察到的形状变化。这项工作将解释这些问题并开发新的简单模型，这些模型将与实验一致并在各种设置中有用，包括设计新的灵活和可重新配置的设备，以及用于工程应用的折纸和剪纸结构。作为该项目的一部分，研究生和本科生将接受培训。 PI 和学生将为高中年轻女性开发相关的实验室演示和夏季科学项目模块。公共宣传工作将利用薄结构力学与按扣手镯等玩具行为之间的联系。这项工作有两个部分。首先，将基于拉伸的系统扩展来发展弹性理论。当应用于壳时，该理论将保留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，将开发一种统一有效的弹性曲线理论，该理论可以在杆模型和不可延伸的宽带模型之间进行插值。该理论将捕获窄带材的分叉现象，并允许对产生拐点的带材变形进行数值积分。更广泛地说，这项工作将把直接降维方法与薄结构联系起来。新的壳理论将与文献中软壳的理论和数值结果进行比较，并且新的带状理论将使用 PI 先前工作和文献中的分岔实验结果进行验证。这项工作要解决的问题与软质材料和其他材料的不相容弹性、可编程弹性体和结构化片材的设计以及柔性组件的不稳定性和分叉等研究领域相关。该奖项反映了 NSF 的法定使命，并被视为值得通过使用基金会的智力优点和更广泛的影响审查标准进行评估来支持。