两个方向应力之和为定值问题

ssw001

如下图,弹性力学两个方向应力之和为定值(弹性),在塑性性时成立吗,为什么,谢谢

tonnyw

You need to explain a little bit more. Seems like the stresses are measured in polar coordinates.

ssw001

就是一般应力矩阵对角线之和为定值,在塑性时不成立,原因是什么,谢谢

tonnyw

ssw001 发表于 2011-11-24 21:42
就是一般应力矩阵对角线之和为定值,在塑性时不成立,原因是什么,谢谢

This is something related to the invariant of stress tensor.

Assume you have a stress tensor in the following form:
|s_xx, s_xy, s_xz |
|s_yx, s_yy, s_yz |
|s_zx, s_zy, s_zz  |
The trace is the invariant, namely, s_xx + s_yy + s_zz = s_1 + s_2 + s_3
where s_1, s_2, s_3 are principal stresses.

This also holds for plasticity.

zhangxd1985

楼主应该是问的应力张量的第一不变量，这对任何情况下都成立。只不管在考虑塑性时，如果不是考虑土体等剪力会引起体积变形的情况，都认为塑性变形只与应力偏量有关，而对于应力偏量张量的第一不变量为零。