Regnier C H, Kolsky H, Richardson P D, Ghoniem G M, Susset J G
J Biomech. 1983;16(11):915-22. doi: 10.1016/0021-9290(83)90055-6.
The purpose of this paper is to investigate the theoretical basis for the pressure-distension behavior of the urinary bladder. A finite strain theory is developed for hollow spherical structures and it is shown that the Treloar model is a good prototype only for rubber balloons. The pressure-extension ratio relationship is inverted to lead a general form of strain energy function, and fitted by an empirical relation involving one exponential. The following form of strain energy function is derived: W(lambda, lambda, lambda -2) = C1 (P(1), a) + P(1)C2 (a, lambda)ea(lambda -1). Where C1(P(1), a) is a constant (N m-2), P(1) is the initial pressure, a is the rate of pressure increase and C2 (a, lambda) a third degree polynomial relation. P(1) and a are experimentally determined through volumetric pressure-distension data. It is verified that this type of energy function is also valid for uniaxial loading experiments by testing strips coming from the same bladder for which P(1) and a were computed. There is a good agreement between the experimental points and the theoretical stress-strain relation. Finally, the strain energy function is plotted as a function of the first strain invariant and appears to be of an exponential nature.
本文的目的是研究膀胱压力-扩张行为的理论基础。针对空心球形结构建立了有限应变理论，结果表明，Treloar模型仅对橡胶气球是一个良好的原型。将压力-伸长率关系进行反转，得到应变能函数的一般形式，并通过一个包含指数的经验关系式进行拟合。推导得到如下形式的应变能函数：W(λ, λ, λ -2) = C1 (P(1), a) + P(1)C2 (a, λ)ea(λ -1)。其中C1(P(1), a)是一个常数（N m-2），P(1)是初始压力，a是压力增加率，C2 (a, λ)是一个三次多项式关系。P(1)和a通过体积压力-扩张数据通过实验确定。通过对来自同一膀胱且已计算出P(1)和a的条带进行测试，验证了这种类型的能量函数对于单轴加载实验也是有效的。实验点与理论应力-应变关系之间有良好的一致性。最后，将应变能函数绘制为第一应变不变量的函数，其呈现出指数性质。
