建立蜂窝纸板本构模型的方法

Method for Establishing Constitutive Model of Honeycomb Paperboard

目的利用三次贝赛尔曲线建立蜂窝纸板的本构模型。方法利用MATLAB拟合实验曲线,比较拟合曲线和实验曲线的拟合度。结果根据三次贝塞尔曲线的特点,将特征多边形P0P1P2P3首、末两点P0点和P3点作为实验曲线上的点。通过以下判定原则可得到拟合度很好的三次贝塞尔曲线,如果特征多边形P0P1P2P3控制的三次贝塞尔曲线在实验曲线的下方,那么应该将P1点、P2点上移,相反则下移;如果特征多边形P0P1P2P3控制的三次贝塞尔曲线曲线开口比实验曲线大,那么应该将P1点和P2点之间的距离缩小,相反则增大;如果实验曲线有很长一段斜率变化很小,那么与之对应的特征多边形某条边很长,相反则很短。结论利用三次贝塞尔曲线分段拟合蜂窝纸板的应力-应变曲线,拟合曲线和实验曲线有很好的拟合度,用三次贝塞尔曲线参数方程分段表示蜂窝纸板的本构模型是可行的。

The work aims to establish a constitutive model of honeycomb paperboard with the three cubed Bezier curve. The fitting degree of the fitting curve and the experimental curve was compared by fitting the experimental curve with MATLAB. According to characteristics of the three cubed Bezier curve, point P0 and point P3 which were the first and end points of the characteristic polygon P0P1P2P3 were taken as the points in the experimental curve. The three cubed Bezier curve with good fitting degree would be obtained by means of the following principles. Firstly, if the three cubed Bezier curve controlled by the characteristic polygon P0P1P2P3 was below the experimental curve, point P1 and point P2 should be moved upward. Otherwise, it should be moved downward. Secondly, if the opening of the three cubed Bezier curve controlled by the characteristic polygon P0P1P2P3 was larger than that of the experimental curve, the distance between point P1 and point P2 should be reduced. Otherwise, it should be increased. Thirdly, if the experimental curve had a long part with a small change in slope, the edge of the characteristic polygon corresponding to it was very long. Otherwise, it was very short. The stress-strain curve sectional fitted with the three cubed Bezier curve has good fitting degree with the experimental curve. It was feasible to sectional represent the constitutive model of honeycomb paperboard with the three cubed Bezier curve equation.