An existence result for accretive growth in elastic solids
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916158262738944 |
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| author | Davoli, Elisa Nik, Katerina Stefanelli, Ulisse Tomassetti, Giuseppe |
| author_facet | Davoli, Elisa Nik, Katerina Stefanelli, Ulisse Tomassetti, Giuseppe |
| contents | We investigate a model for the accretive growth of an elastic solid. The reference configuration of the body is accreted in its normal direction, with space- and deformation-dependent accretion rate. The time-dependent reference configuration is identified via the level sets of the unique viscosity solution of a suitable generalized eikonal equation. After proving the global-in-time well-posedness of the quasistatic equilibrium under prescribed growth, we prove the existence of a local-in-time solution for the coupled equilibrium-growth problem, where both mechanical displacement and time-evolving set are unknown. A distinctive challenge is the limited regularity of the growing body, which calls for proving a new uniform Korn inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An existence result for accretive growth in elastic solids Davoli, Elisa Nik, Katerina Stefanelli, Ulisse Tomassetti, Giuseppe Analysis of PDEs 74F99, 74B20, 74G22, 49L25 We investigate a model for the accretive growth of an elastic solid. The reference configuration of the body is accreted in its normal direction, with space- and deformation-dependent accretion rate. The time-dependent reference configuration is identified via the level sets of the unique viscosity solution of a suitable generalized eikonal equation. After proving the global-in-time well-posedness of the quasistatic equilibrium under prescribed growth, we prove the existence of a local-in-time solution for the coupled equilibrium-growth problem, where both mechanical displacement and time-evolving set are unknown. A distinctive challenge is the limited regularity of the growing body, which calls for proving a new uniform Korn inequality. |
| title | An existence result for accretive growth in elastic solids |
| topic | Analysis of PDEs 74F99, 74B20, 74G22, 49L25 |
| url | https://arxiv.org/abs/2403.08307 |