Zhang Wei, Wang Chong, Kassab Ghassan S
Department of Biomedical Engineering, IUPUI, Indianapolis, IN 46202, USA.
Biomaterials. 2007 Aug;28(24):3569-78. doi: 10.1016/j.biomaterials.2007.04.030. Epub 2007 May 3.
It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.
众所周知，血管的应力-应变关系具有高度非线性。为了使该关系线性化，亨奇应变张量被推广为对数-指数（log-exp）应变张量以吸收非线性。通过对该对数-指数应变张量求导，提出了一个二次名义应变势来推导第二皮奥拉-基尔霍夫应力。由此得到的本构方程是广义胡克定律。三维正交各向异性模型需要十个材料常数。对数-指数应变定义中使用的无量纲常数被解释为非线性参数。其他九个常数是相对于对数-指数应变的弹性模量。在本文中，所提出的线性应力-应变关系被证明能很好地表示伪弹性冯模型。
