A Relaxation Approach to the Minimization of the Neo-Hookean Energy in 3D
Year: 2024
Type: article
Abstract: . Despite its high significance in nonlinear elasticity, the neo-Hookean energy is still not known to admit minimizers in some appropriate admissible class. Using ideas from relaxation theory, we propose a larger minimization 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 penalizing the singularities of the inverse deformation. The new functional attains its minimum in the larger space, so the initial question of existence of minimizers of the neo-Hookean energy is thus transformed into a question of regularity of minimizers of this new energy.
DOI: 10.1137/23m1614547
Institutions: University of Trieste, University of O'Higgins, Consejo Superior de Investigaciones Científicas, Institute of Mathematical Sciences, Universidad Carlos III de Madrid, Universidad Autónoma de Madrid, Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay, University of Warsaw
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4404976419