AI 中文总结
本研究开发了一种考虑几何与材料非线性的连续细观力学理论，揭示纤维网络的诱导向列序与力学响应的关联，通过离散模拟验证理论，明确单轴拉伸下序与致密化的关系及收缩细胞的屈曲传播规律。
AI 中文摘要
收缩细胞和外部载荷会重构纤维状细胞外基质，使纤维在远大于细胞尺寸的距离上排列和致密化，强烈影响伤口愈合、血管生成和肿瘤侵袭等生物过程。我们开发了一种连续细观力学理论，该理论在每个材料点上将载荷诱导的取向序与重新取向后的网络表现出的力学响应关联起来。该网络通过纤维取向的概率密度进行统计描述，并仿射变形，因此单纤维的应力-应变关系可传递到网络应力，变形由力学平衡自洽确定。对于实际生物相关条件，该理论同时考虑几何非线性和材料非线性。将其应用于单轴拉伸下的二维网络，该理论可简化为一个单一的各向异性参数，该参数控制取向分布、向列序、泊松比和纤维致密化。我们的理论表明，诱导序和致密化高度正相关，在单轴拉伸情况下，它们会收敛到一条几乎通用的曲线，与单纤维刚度行为无关。对于收缩细胞，我们发现屈曲控制向列取向序和致密化的传播距离，变形随距离呈代数衰减，并求解了幂律指数对单纤维屈曲缩减刚度的依赖关系。我们通过与非仿射离散纤维网络模拟的比较验证了该理论。
英文摘要
Contractile cells and external loads reorganize the fibrous extracellular matrix, aligning and compacting fibers over distances far exceeding a cell's size, strongly affecting bioprocesses such as wound healing, angiogenesis and tumor invasion. We develop a continuum micromechanical theory that links, at every material point, the load-induced orientational order to the mechanical response that the reoriented network then exhibits. The network is described statistically, by the probability density of fiber orientations, and deforms affinely, so that a single-fiber stress-strain law is carried into the network stress, with the deformation set self-consistently by mechanical equilibrium. Critical to realistic biological relevant conditions, this theory allows both geometrical and material nonlinearities. Applied to a two-dimensional network under uniaxial stretch, the theory collapses onto a single anisotropy parameter that governs the orientation distribution, the nematic order, the Poisson ratio, and the densification of fibers. Our theory reveals that induced order and densification are highly positively correlated, and in the case of uniaxial stretch they collapse onto a nearly universal curve, independent of the single-fiber stiffness behavior. For a contracting cell, we find that buckling controls how far nematic orientational order and densification propagate. We find an algebraic decay of deformations with distance and solve for the dependence of the power-law exponent on the buckled-reduced stiffness of a single fiber. We validate our theory by comparison with non-affine discrete fiber-network simulations.
