A Remark on stress of a spatially uniform dislocation density field
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866915809876508672 |
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| author | Li, Siran |
| author_facet | Li, Siran |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2003_08065 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Remark on stress of a spatially uniform dislocation density field Li, Siran Classical Physics Mathematical Physics 74B20, 74G25 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. |
| title | A Remark on stress of a spatially uniform dislocation density field |
| topic | Classical Physics Mathematical Physics 74B20, 74G25 |
| url | https://arxiv.org/abs/2003.08065 |