基于超弹性模型的动脉血管数值计算

目的：实验研究表明。血管在周向与轴向两种单轴向拉伸作用下表现出不同的力学特性，本文通过对血管单轴拉伸的数值计算，给出分别适用于周向和轴向荷载的模拟方法。方法：基于超弹性本构模型对轴向和周向两种单轴拉伸作用下血管的应力一应变关系进行数值计算，并结合血管组织结构特点及模型适用范围对结果进行分析，同时通过数值计算对Holzapfel．Gasser-Ogden模型中的各向异性参数对结果的影响展开讨论。结果：计算结果显示单一使用各向同性超弹性应变势函数无法准确完整的模拟两种情况下的单轴拉伸实验，周向拉伸采用各向同性超弹性本构模型的数值结果较好的吻合实验，而轴向拉伸宜采用Holzapfel-Gasser-Ogden模型。Holzapfel。Gasser-Ogden模型中各向异性参数1描述血管中两组增强纤维主方向的分散程度，y值越大即纤维平均主方向与轴向加载方向夹角越小，在外荷载作用下越容易使得纤维旋转到荷载方向；参数K描述血管中每组增强纤维主方向上纤维的分散程度。K值越大，纤维在基体中分散越广泛，材料性子越接近纤维，宏观表现越硬。结论：本文基于超弹性本构模型对轴向和周向两种单轴拉伸作用下血管的应力应变关系进行数值计算，提出分别用多项式形式的各向同性超弹性本构模型数值计算周向荷载作用下应力应变关系、Holzapfel-Gasser-Ogden各向异性超弹性本构模型数值模拟轴向荷载下力学性质，数值结果与实验吻合较好，为心血管系统的数值模拟提供指导，对血管系统的力学机制和临床研究具有重要意义。

Numerical Calculation of Arterial Layers With Hyperelastic Model

Objective： The experiment results show that blood vessels performance different mechanical properties under axial and circumferential this two kinds of uniaxial tensile loading. An applicative simulation method for the circumferential and axial loading is given through numerical calculation of uniaxial tensile experiment of blood vessels in this paper. Methods ： The stress - strain relation of blood vessels under axial and circumferential loading this two kinds ofuniaxial tensile loading are calculated which is based on the hyperelastic constitutive model, the analysis of the results are gave combining with the orga- nization structure characteristics of vessels and applicable scope of models, meanwhile the influences of anisotropic parame- ters in Holzapfel-Gasser-Ogden model to the results is discussed through the numerical calculation. Results： It is shown that only using isotropic hyperelastic strain potential function can not accuratly completely simulate two cases of uniaxial tensile experiments, the isotropic hyperelastic model of the numerical result is in good agreement with the experiment under circum- ferential tensile loading, while Holzapfel-Gasser-Ogden model should be used under axial tensile loading. Anisotropic param- eters 7 of Holzapfel - Gasser - Ogden model describe the dispersion degree of two fiber principal direction the greater of the y value is, which means the angle between average principal direction of fiber and axial loading direction is smaller, the easier to make fiber rotation to loading direction under the action of outer loading; The parameter k describes the fiber dispersion de- gree of blood vessels in each group of reinforcing fiber, the greater of the k value is,which means the fiber： in the matrix is more widely scattered, the closer to fiber of material characteristics are and the stiffer macroscopic view performance. Conclusions： The stress - strain relation of blood vessels under axial and circumferential loading this two kinds of uniaxial tensile load- ing are calculated which is based on the hyperelastic model. A new method for calculating stress - strain relation of blood ves- sels is put forward, which is using polynomial forms of isotropic hyperelastic constitutive model simulates stress - strain relation under circumferential load applied and using Holzapfel - Gasser - Ogden anisotropic hyperelastic constitutive model numerical calculates mechanical properties under axial load applied. The numerical results are in good agreement with the experiment, which provides guidance for the cardiovascular system of numerical simulation.This work has important significance for the me- chanical system of the vascular system and clinical research.