基于自动网格法测量橡胶平面拉伸试验位移场的分区拟合方法

Divided Region Fitting Method for Fitting the Displacement Field of Rubber′s Planar Tension in Post Process of Auto Grid Method

本文提出一种新的分区拟合方法用于拟合橡胶材料非均匀平面拉伸变形的位移场。该方法根据橡胶材料平面拉伸位移场的特点,将其分为均匀区和非均匀区(用分区系数来表征),且分别用不同的多项式来拟合,同时计及区域间位移及其一阶导数的连续条件。与试验结果的对比证实了对于橡胶的平面拉伸试验,采用分区系数f∈[0.2,0.4]、利用不完整二次多项式拟合均匀区和完整四次多项式拟合非均匀区的方案是最佳的。分区拟合方法还可推广至其它非均匀位移场的试验数据后处理中。

A new data fitting method, termed as the divided region fitting method, was introduced in the post process of Auto Grid Method to fit the displacement field of rubber materials＇ planar tension. Based on the features of rubber＇s planar tension, the displacement field was divided into homogeneous and nonhomogeneous fileds （using division coefficient to characterize）. Different polynomial functions were used to fit the two fields, which relevance was characterized by the continuity condition of displacement and its first derivative. By comparing the fitting field with the displacement field obtained by actual planar tension of tire rubber, the Divided Region Fitting Method is proven to be valid. Furthermore when the division coefficient is 0.3, partial quadratic polynomial and the quartic polynomial is introduced to fit the homogeneous and nonhomogeneous fileds respectively and the goodness of fit is the best in this paper. Divided Region fitting method also can be used in post process of other kinds of nonhomogeneous displacement fields.