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: 2307562
• 负责人: Casey Rodriguez
• 金额: $ 23万
• 依托单位: University of North Carolina at Chapel Hill
• 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=2307562&HistoricalAwards=false
• 关键词: Collaborative; Research; Strain; limiting; Cosserat; 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.

在整个科学，工程和日常生活中遇到的各种物体都有两个物理维度，这些维度远小于三分之一。例如，胶原蛋白纤维，DNA，RNA，梁，管道，铅笔和手机充电器线。该研究项目涉及Cosserat杆的理论：由两个垂直方向的曲线参数化的物体，即每个点指定的两个较小的物理维度。该理论使用部分微分方程对身体对施加力的响应进行了建模，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杆模型，描述包括DNA和RNA在内的生物纤维的拉伸行为。除了从数学物理学的角度确定模型的基本属性外，研究结果还将有助于理解和预测纤维如何在生物过程中弯曲，扭曲和伸展。该项目将为研究生提供研究培训机会。该研究项目将集中于弯曲，扭曲和拉伸菌株之间的新的非线性，热力学一致，限制应变的本构关系，以及在Cosserat杆上的接触夫妇和力量。在静态绿色弹性环境中，该研究将包括建立螺旋平衡状态的能量稳定性和分叉结果，以及对相关，可用的实验数据的预测进行定量比较。在动态粘弹性设置中，平衡方程是一个具有不同场方程的抛物线偏微分方程系统，这是由于指定不同的耗散率而产生的。研究人员将专注于获得具有实验自然边界条件的这种非线性场方程的解决方案解决方案的解决方案的全球良好套索，lyapunov稳定性和长期不对称结果。这项奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响审查标准来通过评估来诚实地支持。