Deterministic material-based averaging theory model of collagen gel micromechanics
Deterministic material-based averaging theory model of collagen gel micromechanics
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DOI：
10.1115/1.2472369
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发表时间：
2007-04-01
影响因子：
1.7
通讯作者：
Barocas, Victor H.
中科院分区：
文献类型：
--
作者：
Chandran, Preethi L.;Barocas, Victor H.
像许多组织一样，胶原蛋白凝胶的力学是由在比材料的功能尺度小得多的长度尺度上发生的事件所控制的。为了应对将确定性微观力学纳入连续宏观模型的挑战，我们开发了一个基于平均理论的胶原蛋白凝胶建模框架。假设宏观有限元模型中各积分点周围的平均体积经历与宏观变形场均匀的边界变形，并求解积分点处的平均应力的微观力学问题。二维模型将微观结构建模为非线性弹簧网络，发现500个节段足以实现统计均匀性。然后将该方法用于模拟Tower等人的实验。生物医学。Eng。， 30, pp. 1221-1233)，她进行了预排列胶原蛋白凝胶的单轴延伸。模拟捕获了许多实验的定性特征，包括脚趾区域和伸展过程中纤维网络的重新排列。最后，将该方法应用于基于Bowes等人（wound Repair Regen）的表征测量的理想伤口模型。，第7页，179-186页)。该模型由一个强烈对齐的“伤口”区域由一个不太强烈对齐的“健康”区域包围。创面区原纤维的排列导致轴向应变降低，健康区原纤维的排列，加上创面区更大的有效刚度，导致创面区在单轴拉伸时发生旋转。虽然本研究的微观模型相对粗糙，但多尺度框架具有通用性，可以与任何微观结构模型结合使用。
Mechanics of collagen gels, like that of many tissues, is governed by events occurring on a length scale much smaller than the functional scale of the material. To deal with the challenge of incorporating deterministic micromechanics into a continuous macroscopic model, we have developed an averaging-theory-based modeling framework for collagen gels. The averaging volume, which is constructed around each integration point in a macroscopic finite-element model, is assumed to experience boundary deformations homogeneous with the macroscopic deformation field, and a micromechanical problem is solved to determine the average stress at the integration point. A two-dimensional version was implemented with the microstructure modeled as a network of nonlinear springs, and 500 segments were found to be sufficient to achieve statistical homogeneity. The method was then used to simulate the experiments of Tower et al. (Ann. Biomed. Eng., 30, pp. 1221-1233) who performed uniaxial extension of prealigned collagen gels. The simulation captured many qualitative features of the experiments, including a toe region and the realignment of the fibril network during extension. Finally, the method was applied to an idealized wound model based on the characterization measurements of Bowes et al. (Wound Repair Regen., 7, pp. 179-186). The model consisted of a strongly aligned '' wound '' region surrounded by a less strongly aligned '' healthy '' region. The alignment of the fibrils in the wound region led to reduced axial strains, and the alignment of the fibrils in the healthy region, combined with the greater effective stiffness of the wound region, caused rotation of the wound region during uniaxial stretch. Although-the microscopic model in this study was relatively crude, the multiscale framework is general and could be employed in conjunction with any microstructural model.