Constitutive modeling of crimped collagen fibrils in soft tissues
Constitutive modeling of crimped collagen fibrils in soft tissues
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DOI：
10.1016/j.jmbbm.2008.12.009
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发表时间：
2009-10-01
影响因子：
3.9
通讯作者：
Meschke, Guenther
中科院分区：
文献类型：
--
作者：
Grytz, Rafael;Meschke, Guenther
针对软结缔组织中存在的卷曲胶原纤维的超弹性响应，提出了一种面向微结构的本构公式。该模型是基于观察到嵌入在软基质中的胶原纤维在卸载时卷曲成平滑的三维图案。遵循Beskos和Jenkins提出的观点[Beskos，D.，Jenkins，J.，1975]。哺乳动物肌腱的力学模型。应用力学杂志42,755-758]和Freed and Doehring[Freed，A.，Doehring，T.，2005]。卷曲的胶原纤维的弹性模型。生物力学工程杂志127,587-593]胶原原纤维卷曲由圆柱形螺旋近似，以表示生物组织在纤维水平上的分级组织亚结构的本构行为。该模型从可伸缩螺旋弹簧的非线性轴向力-拉伸关系出发，以弹簧的完全伸长为极限情况。用迭代法求解了可伸缩螺旋弹簧的几何非线性问题。该模型只需要一个材料参数和两个几何参数由实验确定。所提出的模型能够再现纤维组织的生物力学反应的能力被证明为来自大鼠尾肌腱的束、猪角膜条和牛跟腱。(C)2009爱思唯尔有限公司。保留所有权利。
A microstructurally oriented constitutive formulation for the hyperelastic response of crimped Collagen fibrils existing in soft connective tissues is proposed. The model is based on observations that Collagen fibrils embedded in a soft matrix crimp into a smooth three-dimensional pattern when unloaded. Following ideas presented by Beskos and Jenkins [Beskos, D., Jenkins, J., 1975. A mechanical model for mammalian tendon. ASME journal of Applied Mechanics 42, 755-758] and Freed and Doehring [Freed, A., Doehring, T., 2005. Elastic model for crimped Collagen fibrils. journal of Biomechanical Engineering 127, 587-593] the Collagen fibril crimp is approximated by a cylindrical helix to represent the constitutive behavior of the hierarchical organized substructure of biological tissues at the fibrillar level. The model is derived from the nonlinear axial force-stretch relationship of an extensible helical spring, including the full extension of the spring as a limit case. The geometrically nonlinear solution of the extensible helical spring is carried out by an iterative procedure. The model only requires one material parameter and two geometrical parameters to be determined from experiments. The ability of the proposed model to reproduce the biomechanical response of fibrous tissues is demonstrated for fascicles from rat tail tendons, for porcine cornea strips, and for bovine Achilles tendons. (C) 2009 Elsevier Ltd. All rights reserved.