空间均匀位错密度场的应力
Stress of a spatially uniform dislocation density field
摘要：
可以表明，在没有载荷的情况下，由包括线性弹性材料的主体中的空间均匀位错密度场产生的应力为零。我们证明了在几何非线性情况下，同样的结果一般不成立。这个力学问题建立了一个纯粹的几何结果，即一个足够光滑的二维旋转场的$\curl$不可能是域上的非零常数。
英文摘要：
It can be shown that the stress produced by a spatially uniform dislocation density field in a body comprising a linear elastic material under no loads vanishes. We prove that the same result does not hold in general in the geometrically nonlinear case. This problem of mechanics establishes the purely geometrical result that the $\curl$ of a sufficiently smooth two-dimensional rotation field cannot be a non-vanishing constant on a domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
