多元线性回归法确定橡胶Mooney-Rivlin模型常数  

Determination of mechanics constants of Mooney-Rivlin model by using multilinear regression method

作　　者：王智宇[1] 王安稳[1] 

机构地区：[1]海军工程大学理学院,武汉430033

出　　处：《海军工程大学学报》2011年第2期18-21,共4页Journal of Naval University of Engineering

基　　金：国家自然科学基金资助项目(10572150)

摘　　要：根据丁苯橡胶试样在单轴拉伸实验中得到的拉力和变形值等实验数据,运用多元线性回归法求得橡胶材料Mooney-Rivlin模型三项式的模型常数。为检验计算结果的准确性,将常数用于对试样进行有限元计算并与实验结果对比分析,计算采用有限元软件ANSYS11.0,得到的计算结果与实验结果较为吻合。对比分析结果表明:随着形变量的增加,变形增量的有限元计算值对于实验值的相对误差逐渐减小并趋于稳定,说明采用多元线性回归法求解Mooney-Rivlin模型的常数是可行的。该方法也可推广至五项式和九项式Mooney-Rivlin模型常数的求解。Based on the experimental results of pulls and deformations of uniaxially loaded SBR samples, the material constants of the three-parameter Mooney-Rivlin model of SBR were gained by using the multilinear regression method. In order to test the correctness of the computed results, the constants were employed to compute the samples with the finite element method, and then the computed results were compared and analyzed with the experimental ones. When the finite element software ANSYS 11.0 was used to compute, the results basically coincided with the experimental ones. The results of analysis show that with an increase in the deformations, the corresponding errors between the computed results and the experimental ones decrease and tend to stabilization. So it is feasible to determine the constants of Mooney-Rivlin model by using multilinear regression method. The method can also be introduced to solve the material constants of five-parameter Mooney-Rivlin model and nineparameter Mooney-Rivlin model.

关 键 词：超弹性 橡胶 Mooney-Rivlin模型 多元线性回归 有限元 

分 类 号：O34[理学—固体力学]