Calculus of Variations and Geometric Measure Theory

M. Barchiesi - D. Henao - C. Mora-Corral - R. Rodiac

A relaxation approach to the minimisation of the neo-Hookean energy in 3D

created by barchiesi on 01 Nov 2023
modified on 08 Nov 2023


Submitted Paper

Inserted: 1 nov 2023
Last Updated: 8 nov 2023

Year: 2023

ArXiv: 2311.02952 PDF


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.

Keywords: neo-Hookean energy, Relaxation process