We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure-valued mappings, which coincides with the original problem under our condition.

Hidden convexity in a problem of nonlinear elasticity

Lavenant, Hugo
;
2021

Abstract

We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure-valued mappings, which coincides with the original problem under our condition.
2021
Ghoussoub, Nassif; Kim, Young-Heon; Lavenant, Hugo; Palmer, Aaron Zeff
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/4036710
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