Biot-elastic and Direct Models of Shells and Strips

薄层弹性结构，如壳和条，在许多尺度的工程应用中都有发现，包括航空航天部件、软机器人、柔性微电子设备和可编程材料。尽管对薄壁结构的力学研究已有近一个世纪的历史，但对于通常用来描述这些物体在压力或其他外力作用下的弯曲和拉伸的简单简化模型，问题仍然存在。表面上相似的壳体模型做出了本质上不同的预测，比如弯曲的壳体在相同条件下会膨胀还是收缩。现有的条带模型无法捕捉到在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，这些模型将符合实验并在各种环境中有用，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Kirigami结构。研究生和本科生将作为该项目的一部分进行培训。PI和学生们将为高中年轻女性的暑期科学项目开发相关的实验室演示和一个模块。公众宣传活动将利用薄壁结构力学和手镯等玩具的行为之间的联系。这项工作由两部分组成。首先，将基于拉伸中的系统展开来发展弹性理论。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，将发展一个统一有效的弹性曲线理论，它在杆和不可扩展的宽条模型之间进行内插。这一理论将捕捉到窄条带的分叉现象，并允许对产生拐点的条带变形进行数值积分。更广泛地说，这项工作将涉及对薄结构的直接降维方法。新的壳体理论将与文献中关于软壳的理论和数值结果进行比较，而新的条形理论将利用之前的PiooS工作和文献中关于分叉的实验结果来验证。这项工作中要解决的问题与研究领域相关，如软材料和其他材料的不相容弹性、可编程弹性体和结构化板材的设计，以及柔性部件的不稳定性和分叉。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。

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.