A Numerical Framework to Study and Design the Mechanical Response of Configurable Elastic Rod Networks

这笔赠款支持开发一种高效和易于实施的数字框架的研究，该框架允许对弹性杆网络的力学进行参数研究，并促进具有目标几何形状和机械性能的新型弹性网络的设计。由于其重量轻、灵活性高，由细长弹性杆或条组成的网络可以通过对其关节和杆的定制设计来变形为三维表面结构。它们可以在不同的规模上找到广泛的应用，从超材料、软机器人和可展开的空间天线，到大跨度可展开的掩体。由于它们的大变形、多稳定性和复杂的分叉，理解和设计它们的力学行为是具有挑战性的。这项研究项目将开发一个描述它们的静态平衡和分叉的数值框架和一种设计方法，将网络细胞组装成机械、土木、生物医学工程和建筑应用的功能变形系统，促进科学进步、国民健康、繁荣和福利。该项目还将通过暑期项目和一名研究生的研究培训为高中生和本科生提供研究经验，并通过科学博览会和展览向K-12社区推广。研究的目标是设计能够通过定制弹性网络的拓扑、连接和杆设计来控制其形状和机械性能的材料和结构。研究子任务包括：(A)推导用于对弹性杆网络的力学进行参数研究的一般数值框架；(B)开发确定(A)中所得平衡点稳定性的共轭点检验；以及(C)利用弹性多边形单元作为构件来构造泛函弹性网络。这项工作涉及软物质和非线性力学的研究课题，包括可展开的轻质建筑和空间结构、灵活的软机械臂和机械可变形超材料的数值建模和设计。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 grant supports research to develop an efficient and easy-to-implement numerical framework that allows for parametric studies of the mechanics of elastic rod networks and promotes the design of novel elastic networks with target geometries and mechanical properties. Due to their light weight and high flexibility, networks consisting of thin elastic rods or strips can morph into 3D surface structures through customized design of their joints and rods. They can find wide applications at different scales, ranging from metamaterials, soft robots and deployable space antennas, to long-span deployable shelters. Understanding and designing their mechanical behavior is challenging due to their large deformations, multi stability, and intricate bifurcations. This research project will develop a numerical framework that describes their static equilibria and bifurcations and a design method that assembles network cells into functional morphing systems for mechanical, civil, and biomedical engineering as well as architectural applications, promoting the advancement of science, national health, prosperity, and welfare. The project will also provide research experiences for high school and undergraduate students through summer programs and research training for one graduate student, and outreach to the K-12 community through a science fair and exhibition.The goal of the research is to design materials and structures capable of controlling their shapes and mechanical properties by tailoring the topology, connections, and rod design of elastic networks. The research sub-tasks include: (a) derivation of a general numerical framework for conducting parametric studies of the mechanics of elastic rod networks, (b) development of a conjugate point test that determines the stability of the equilibria obtained in (a), and (c) construction of functional elastic networks from elastic polygonal cells used as building blocks. This work relates to research topics in soft matter and nonlinear mechanics, including the numerical modeling and design of deployable lightweight architectural and space structures, flexible soft robotic arms, and mechanical morphable metamaterials.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.