塑性力学教学中Mises屈服准则几何轨迹证明  

PROVING OF YIELD CRITERION OF MISES GEOMETRIC SHAPE IN PLASTIC MECHANICS TEACHING

作　　者：梅瑞斌[1] 包立[2] 刘相华[1] MEI Ruibin;BAO Li;LIU Xianghua(School of Materials and Engineering,Northeastern University,Shenyang 110819,China;Northeastern University at Qinhuangdao,Qinhuangdao 066004,Hebei,China)

机构地区：[1]东北大学材料与科学工程学院,沈阳110819 [2]东北大学秦皇岛分校,河北秦皇岛066004

出　　处：《力学与实践》2022年第4期955-959,共5页Mechanics in Engineering

基　　金：河北省教育厅精品课程建设项目(2020JPKC061);东北大学课程思政示范课程(2021KCSZ018);东北大学秦皇岛分校教改重点项目(2021JG-A03)资助。

摘　　要：本文针对塑性力学教学中学生难以理解的屈服准则几何轨迹,从教学角度出发,利用坐标变换和空间几何投影关系分析证明了Mises屈服准则的平面椭圆和空间圆柱面轨迹。基于Tresca和Mises屈服准则简化形式,分析了两个准则几何轨迹的内接和外接关系,当用拉伸屈服应力σ表示时,Mises椭圆外接于Tresca六边形,当用剪切屈服强度k表示时,正好相反。It is difficult for students to understand the yield criterion in the plastic mechanics.The plane ellipse and spatial cylindrical trajectory of Mises yield criterion was proved based on the method of coordinate transformation and geometric projection.Furthermore,from the similarities and differences of mathematical expressions,the internal and external relations and geometric shape of Tresca and Mises yield criterions were investigated in the paper.The research is helpful for students to understand the yield criterion.

关 键 词：屈服准则 塑性力学 坐标变换 几何轨迹 

分 类 号：O34[理学—固体力学]