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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.13746 |
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| _version_ | 1866917671235223552 |
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| author | Akramov, Ibrokhimbek Knüpfer, Hans Kružík, Martin Rüland, Angkana |
| author_facet | Akramov, Ibrokhimbek Knüpfer, Hans Kružík, Martin Rüland, Angkana |
| contents | We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from \cite{CS} and \cite{KnuepferKohn-2011}, we derive the lower scaling bound by invoking a two-well rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13746 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Minimal Energy for Geometrically Nonlinear Elastic Inclusions in Two Dimensions Akramov, Ibrokhimbek Knüpfer, Hans Kružík, Martin Rüland, Angkana Analysis of PDEs We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from \cite{CS} and \cite{KnuepferKohn-2011}, we derive the lower scaling bound by invoking a two-well rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion. |
| title | Minimal Energy for Geometrically Nonlinear Elastic Inclusions in Two Dimensions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2207.13746 |