Collaborative Research: Strain-limiting Cosserat Rods with Applications to Modeling Biological Fibers

合作研究：应变限制 Cosserat 棒在生物纤维建模中的应用

• 批准号: 2307563
• 负责人: Kumbakonam Rajagopal
• 金额: $ 9.69万
• 依托单位: Texas A&M Engineering Experiment Station
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307563&HistoricalAwards=false
• 关键词: Collaborative; Research; Strain; limiting; Cosserat

A vast array of objects encountered throughout science, engineering, and everyday life have two physical dimensions that are much smaller than a third. Examples include collagen fibers, DNA, RNA, beams, pipelines, pencils, and cellphone charger cords. This research project concerns the theory of Cosserat rods: bodies that are parameterized by a curve with two perpendicular directions, the two smaller physical dimensions, specified at each point. This theory models the bodies response to applied forces using partial differential equations, expressing balance of linear momentum, angular momentum, energy, and entropy. The research will investigate and validate a new class of Cosserat rod models, describing the stretch-limiting behavior of biological fibers, including DNA and RNA. Apart from determining the models’ fundamental properties from the mathematical physics point of view, the results of the research will contribute to the understanding and prediction of how fibers bend, twist, and stretch during biological processes. The project will provide research training opportunities for graduate students. The research project will focus on new nonlinear, thermodynamically consistent, strain-limiting constitutive relations between the bending, twisting, and stretching strains and the contact couples and forces in a Cosserat rod. In the static Green elastic setting, the research will include establishing energetic stability and bifurcation results for helical equilibrium states, and the quantitative comparison of predictions to the associated, available, experimental data. In the dynamic viscoelastic setting, the balance equations are a system of parabolic partial differential equations with different field equations, resulting from specifying different dissipation rates. The investigators will focus on obtaining global well-posedness, Lyapunov stability and long-time asymptotic results for solutions to such nonlinear field equations with experimentally natural boundary conditions.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.

在科学、工程和日常生活中遇到的大量物体都有两个物理维度，远小于三分之一。例子包括胶原纤维、DNA、RNA、光束、管道、铅笔和手机充电线。这个研究项目涉及到Cosserat棒的理论：由两个垂直方向的曲线参数化的物体，两个较小的物理尺寸，在每个点指定。这个理论用偏微分方程来模拟物体对外力的反应，表达线性动量、角动量、能量和熵的平衡。该研究将调查并验证一类新的Cosserat棒模型，描述生物纤维（包括DNA和RNA）的拉伸限制行为。除了从数学物理的角度确定模型的基本特性外，研究结果将有助于理解和预测纤维在生物过程中如何弯曲、扭曲和拉伸。该项目将为研究生提供研究培训机会。该研究项目将重点研究coserat杆中弯曲、扭转和拉伸应变与接触偶和力之间新的非线性、热力学一致、应变极限的本构关系。在静态格林弹性环境下，研究将包括建立螺旋平衡态的能量稳定性和分岔结果，并将预测结果与相关的、可用的实验数据进行定量比较。在动态粘弹性条件下，平衡方程是一个具有不同场方程的抛物型偏微分方程组，这是由于指定了不同的耗散率而产生的。研究人员将重点关注具有实验自然边界条件的非线性场方程解的全局适定性、Lyapunov稳定性和长时间渐近结果。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。