A relaxation approach to the minimisation of the neo-Hookean energy in 3D
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929347429924864 |
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| author | Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy |
| author_facet | Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy |
| contents | Despite its high significance in nonlinear elasticity, the neo-Hookean energy is still not known to admit minimisers in some appropriate admissible class. Using ideas from relaxation theory, we propose a larger minimisation space and a modified functional that coincides with the neo-Hookean energy on the original space. This modified energy is the sum of the neo-Hookean energy and a term penalising the singularities of the inverse deformation. The new functional attains its minimum in the larger space, so the initial question of existence of minimisers of the neo-Hookean energy is thus transformed into a question of regularity of minimisers of this new energy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_02952 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A relaxation approach to the minimisation of the neo-Hookean energy in 3D Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy Analysis of PDEs 49J45, 49S05, 49Q20, 74B20, 74G65 Despite its high significance in nonlinear elasticity, the neo-Hookean energy is still not known to admit minimisers in some appropriate admissible class. Using ideas from relaxation theory, we propose a larger minimisation space and a modified functional that coincides with the neo-Hookean energy on the original space. This modified energy is the sum of the neo-Hookean energy and a term penalising the singularities of the inverse deformation. The new functional attains its minimum in the larger space, so the initial question of existence of minimisers of the neo-Hookean energy is thus transformed into a question of regularity of minimisers of this new energy. |
| title | A relaxation approach to the minimisation of the neo-Hookean energy in 3D |
| topic | Analysis of PDEs 49J45, 49S05, 49Q20, 74B20, 74G65 |
| url | https://arxiv.org/abs/2311.02952 |