Vaishnav R N, Young J T, Janicki J S, Patel D J
Biophys J. 1972 Aug;12(8):1008-27. doi: 10.1016/S0006-3495(72)86140-X.
A nonlinear theory of large elastic deformations of the aortic tissue has been developed. The wall tissue has been considered to be incompressible and curvilinearly orthotropic. The strain energy density function for the tissue is expressed as a polynomial in the circumferential and longitudinal Green-St. Venant strains. Limiting application to states of strains wherein the geometric axes are the principal axes and truncating the energy expression to include terms with highest degrees 2, 3, and 4, three expressions with 3, 7, and 12 constitutive constants are obtained. Results of application of these expressions to data from three series of in vitro and in vivo experiments involving 31 dogs have been presented. Whereas all the three expressions are found to be applicable to various degrees, the third-degree expression for the strain energy density function with seven constitutive constants is particularly recommended for general use.
已建立了主动脉组织大弹性变形的非线性理论。壁组织被视为不可压缩且曲线正交各向异性的。组织的应变能密度函数表示为周向和纵向格林-圣维南应变的多项式。将应用限制在几何轴为主轴的应变状态，并将能量表达式截断以包括最高次数为2、3和4的项，得到了具有3、7和12个本构常数的三个表达式。给出了将这些表达式应用于涉及31只狗的三个系列体外和体内实验数据的结果。虽然发现所有三个表达式都在不同程度上适用，但特别推荐使用具有七个本构常数的应变能密度函数的三次表达式以供一般使用。
