A Relaxation Approach to the Minimization of the Neo-Hookean Energy in 3D
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.
Authors
- Carlos Mora‐Corral (ORCID: https://orcid.org/0000-0002-2412-5508)
- Duvan Henao (ORCID: https://orcid.org/0000-0001-8511-4004)
- Marco Barchiesi (ORCID: https://orcid.org/0000-0001-9161-243X)
- Rémy Rodiac (ORCID: https://orcid.org/0000-0002-1381-3700)
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Trieste (IT)
- Université Paris-Saclay (FR)
- Laboratoire de Mathématiques d'Orsay (FR)
- University of O'Higgins (CL)
- Institute of Mathematical Sciences (ES)
- Universidad Carlos III de Madrid (ES)
- Universidad Autónoma de Madrid (ES)
Publication Details
- Journal
- SIAM Journal on Mathematical Analysis
- Published
- 2024-12-03
- DOI
- https://doi.org/10.1137/23m1614547
- Citations
- 3
- Primary Topic
- Elasticity and Material Modeling
- Type
- article
- Field-Weighted Citation Impact
- 0.55
Funders
- Comunidad de Madrid
- Narodowym Centrum Nauki
- Fondo Nacional de Desarrollo Científico y Tecnológico
- H2020 European Research Council
- H2020 Marie Skłodowska-Curie Actions