Invariant formulation for dispersed transverse isotropy in aortic heart valves - An efficient means for modeling fiber splay
Invariant formulation for dispersed transverse isotropy in aortic heart valves - An efficient means for modeling fiber splay
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DOI：
10.1007/s10237-005-0069-8
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发表时间：
2005-11-01
影响因子：
3.5
通讯作者：
Vesely, I
中科院分区：
文献类型：
--
作者：
Freed, AD;Einstein, DR;Vesely, I
大多数软组织具有胶原纤维束的定向结构，赋予其弹性行为各向异性和非线性。通常假设这些组织的子集具有横向各向同性，这些组织具有单一的宏观可识别的首选纤维方向。然而，微观结构研究表明，在一些组织中，胶原纤维围绕平均优选纤维方向近似正态分布。解释纤维这种分散的结构本构方程已被证明可以很好地捕捉这些组织的机械复杂性。然而，对于二维 (2D) 纤维分布来说，这种描述在计算上很麻烦，更不用说对于完全三维 (3D) 纤维群了。在本文中，我们基于分散横向各向同性的新颖不变理论，为此类组织开发了一种新的本构定律。不变量理论源自一种新颖的封闭形式“张开不变量”，可以轻松处理 3D 纤维群，并且在 2D 情况下只需要单个参数。该模型与标准结构模型一样准确地拟合主动脉瓣组织的双轴数据。纤维应力-应变定律的修改不需要重新制定本构切线矩阵，使得模型能够灵活地适应不同类型的软组织。最重要的是，该模型在有限元分析中计算方便，通过对人工心脏瓣膜进行建模证明了这一点。
Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is derived from a novel closed-form 'splay invariant' that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no reformulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis, demonstrated by modeling a bloprosthetic heart valve.