论文标题
关于空间均匀位错密度场的应力的评论
A Remark on stress of a spatially uniform dislocation density field
论文作者
论文摘要
在最近的一篇有趣的论文中[1]（A. Acharya，空间均匀的位错密度场的应力，J。弹性137（2019），151--155），Acharya证明，由构成非线性弹性材料的体内空间均匀位错密度场产生的应力可能无法消失。 [1]中构建的反例本质上是$ 2 $ - 二维的：它与子组$ \ Mathcal {O}（2）（2）\ oplus \ langle \ langle {\ bf ID} \ rangle \ rangle \ subset \ subset \ subset \ mathcal \ mathcal {o}（O}（O}（3）$。本说明的目的是将Acharya的结果[1]扩展到$ \ Mathcal {O}（3）$，但要遵守额外的结构假设和较少的规律性要求。
In an interesting recent paper [1] (A. Acharya, Stress of a spatially uniform dislocation density field, J. Elasticity 137 (2019), 151--155), Acharya proved that the stress produced by a spatially uniform dislocation density field in a body comprising a nonlinear elastic material may fail to vanish under no loads. The class of counterexamples constructed in [1] is essentially $2$-dimensional: it works with the subgroup $\mathcal{O}(2) \oplus \langle{\bf Id}\rangle \subset \mathcal{O}(3)$. The objective of this note is to extend Acharya's result in [1] to $\mathcal{O}(3)$, subject to an additional structural assumption and less regularity requirements.
