Calculus of Variations and Geometric Measure Theory
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F. Maddalena - D. Percivale - F. Tomarelli

A new variational approach to linearization of traction problems in elasticity

created by tomarelli1 on 02 Mar 2019

[BibTeX]

Preprint

Inserted: 2 mar 2019
Last Updated: 2 mar 2019

Pages: 1 - 16
Year: 2018

ArXiv: 1811.11037 PDF
Links: Arxiv

Abstract:

A new energy functional for pure traction problems in elasticity has been deduced in a previous paper as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with respect to the weak convergence of strains when a suitable small parameter tends to zero. This functional exhibits a gap that makes it different from the classical linear elasticity functional. Nevertheless a suitable compatibility condition on the force field ensures coincidence of related minima and minimizers. Here we show some relevant properties of the new functional and prove stronger convergence of minimizing sequences for suitable choices of nonlinear elastic energies.

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