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 as 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.
Coupled Macroscopic and Microscopic Scale Modeling of Fibrillar Tissues and Tissue Equivalents
Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division March 7, 2000; revised manuscript received March 31, 2001. Associate Editor: G. A. Ateshian.
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Agoram, B., and Barocas, V. H. (March 31, 2001). "Coupled Macroscopic and Microscopic Scale Modeling of Fibrillar Tissues and Tissue Equivalents ." ASME. J Biomech Eng. August 2001; 123(4): 362–369. https://doi.org/10.1115/1.1385843
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