Calculus of Variations and Geometric Measure Theory

F. Maddalena - D. Percivale - F. Tomarelli

A new variational approach to linearization of traction problems in elasticity

created by tomarelli1 on 02 Mar 2019
modified on 21 Jun 2019


Published Paper

Inserted: 2 mar 2019
Last Updated: 21 jun 2019

Pages: 1 - 16
Year: 2019
Doi: 10.1007/s10957-019-01533-8
Links: J. Optim. Theory Appl (2019) 182, 383-403.


In a recent paper, we deduced a new energy functional for pure traction problems in elasticity, as the variational limit of nonlinear elastic energy functional related to a material body subject to an equilibrated force field: a kind 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.