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arXiv · 2311.02952

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

Marco Barchiesi·Duvan Henao·Carlos Mora-Corral·Rémy Rodiac
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Abstract

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.

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Marco Barchiesi, Duvan Henao, Carlos Mora-Corral, Rémy Rodiac. 2023-11-06. A relaxation approach to the minimisation of the neo-Hookean energy in 3D. https://arxiv.org/abs/2311.02952

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