Coupled macroscopic and microscopic scale modeling of fibrillar tissues and tissue equivalents
Coupled macroscopic and microscopic scale modeling of fibrillar tissues and tissue equivalents
复制标题
DOI：
10.1115/1.1385843
复制
发表时间：
2001-08-01
影响因子：
1.7
通讯作者：
Barocas, VH
中科院分区：
文献类型：
--
作者：
Agoram, B;Barocas, VH
胶原蛋白力学对许多组织（包括血管、关节软骨以及生物人工组织）的功能和功能失调至关重要。先前基于宏观性质描述来开发胶原组织计算机模拟的尝试，往往因模型过于简单而在应用上受限；相比之下，基于微观描述的模拟则因数学问题的规模而受到数值上的限制。我们提出了一种将宏观方法的易处理性与微观结构方法的灵活性相结合的方法。宏观区域被划分为有限单元（如同标准有限元法那样）。每个单元都包含一个微观尺度的网络。宏观问题不是通过应力本构方程来解决，而是分布在微观尺度网络上，并在每个单元中求解，以满足宏观区域上柯西应力连续性方程的弱形式。这种组合方法的计算量随自由度总数增加约为1.1倍，这使其能够处理比直接微观结构方法更大的问题。模型预测在定性上与各向同性和定向重组的I型胶原凝胶的拉伸试验结果相符。
Collagen mechanics are crucial to the function and dysfunction of many. tissues, including blood vessels and articular cartilage, and bioartificial tissues. Previous attempts to develop computer simulations of collagenous tissue based on macroscopic property descriptions have often been limited in application by, the simplicity of the model; simulations based on microscopic descriptions, in contrast, have numerical limitations imposed by, the size of the mathematical problem. We present a method that combines the tractability of the macroscopic approach with the flexibility of the microstructural approach. The macroscopic domain is divided into finite elements (as in standard FEM). Each element contains a microscopic scale network. Instead of a stress constitutive equation; the macroscopic problem is distributed over the microscopic scale network, and solved in each element to satisfy, the weak formulation of Cauchy's stress continuity equation over the macroscopic domain. The combined method scales by, order 1.1 us the overall number of degrees of freedom is increased, allowing it to handle larger problems than a direct microstructural approach. Model predictions agree qualitatively with tensile tests on isotropic and aligned reconstituted type I collagen gels.