A Remark on stress of a spatially uniform dislocation density field

Abstract

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 $\mathcal{O}(2)\oplus ⟨\mathbf{Id}⟩\subset \mathcal{O}(3)$. 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.

5 pages

References in corpus (1)

• On Local Strong Solutions to the Cauchy Problem of Two-Dimensional Density-Dependent Magnetohydrodynamic Equations with Vacuum