稳定材料在应力π平面上屈服曲线的特性

The property of the yield curves of the stable material on the stress π plane

对稳定材料来说，在应力π平面上，双剪应力屈服准则［１］为所有屈服准则的外包络线，Ｍｏｈｒ－Ｃｏｕｌｏｍｂ屈服准则为所有屈服准则的内包络线（当材料的单向拉伸强度与单向压缩强度相等时，Ｍｏｈｒ－Ｃｏｕｌｏｍｂ屈服准则退化为广义Ｔｒｅｓｃａ屈服准则）．但关于此问题的严格数学证明却还是空白．本文作者通过引入凸集概念，对上述问题做出了数学上的严格证明．

Twin shear stress,yield criterion is the exterior envelope and Mohr-Coulomb yield criterion is the interior envelope of all the yield criteria of the stable material on the stress π plane (if the strength of simple extension test equals that of simple compression test,Mohr-Coulomb yield criterion degenerates into extensive Tresca criterion). But there is still a blank in the area of the strict mathematical proof of this problem.In this paper,the authors solve the problem by citing the mathematical concept of convex set.