Spatial regularity for general yield criteria in dynamic and quasi-static perfect plasticity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929575132397568 |
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| author | Babadjian, Jean-François Giacomini, Alessandro Mora, Maria Giovanna |
| author_facet | Babadjian, Jean-François Giacomini, Alessandro Mora, Maria Giovanna |
| contents | This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$ boundary and positive definite second fundamental form, it is proved that the Cauchy stress admits spatial partial derivatives that are locally square integrable. In the dynamic case, a similar regularity result is established for the velocity as well. In the latter case, one-dimensional counterexamples show that, although solutions are Sobolev in the interior of the domain, singularities may appear at the boundary and the Dirichlet condition may fail to be attained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_02167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatial regularity for general yield criteria in dynamic and quasi-static perfect plasticity Babadjian, Jean-François Giacomini, Alessandro Mora, Maria Giovanna Analysis of PDEs This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$ boundary and positive definite second fundamental form, it is proved that the Cauchy stress admits spatial partial derivatives that are locally square integrable. In the dynamic case, a similar regularity result is established for the velocity as well. In the latter case, one-dimensional counterexamples show that, although solutions are Sobolev in the interior of the domain, singularities may appear at the boundary and the Dirichlet condition may fail to be attained. |
| title | Spatial regularity for general yield criteria in dynamic and quasi-static perfect plasticity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.02167 |