A new constitutive framework for arterial wall mechanics and a comparative study of material models
A new constitutive framework for arterial wall mechanics and a comparative study of material models
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DOI：
10.1023/a:1010835316564
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发表时间：
2000-01-01
影响因子：
2
通讯作者：
Ogden, RW
中科院分区：
文献类型：
--
作者：
Holzapfel, GA;Gasser, TC;Ogden, RW
在本文中，我们开发了一个新的本构关系的描述（被动）动脉组织的机械响应。动脉被建模为厚壁非线性弹性圆柱形管，由对应于中膜和外膜（健康组织中的固体机械相关层）的两层组成。每一层都被视为纤维增强材料，纤维对应于材料的胶原成分，并相对于圆柱体轴线对称布置。由此产生的本构关系是正交各向异性的每一层。使用从每个动脉层的组织切片的统计分析中获得的纤维方向。一个特定形式的法律，它只需要三个材料参数的每一层，是用来研究动脉的反应下组合轴向延伸，膨胀和扭转。通过假设材料的自然（无应力和无应变）配置对应于管的开放扇区，然后通过初始弯曲闭合以形成无负载但有应力的圆柱形配置，然后应用延伸、膨胀和扭转，来解释体外动脉中的特征和非常重要的残余应力。残余应力对生理状态下变形动脉壁应力分布的影响进行了研究，该模型适用于动脉的现有数据，并对所考虑的组合载荷进行了评估。它解释了新的模型是如何设计的，以避免某些机械，数学和计算的缺陷，目前可用的唯象模型。这些模型的批判性审查提供了新模式的发展背景。
In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined.The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.