Calculus of Variations and Geometric Measure Theory

M. G. Mora - F. Riva

Pressure live loads and the variational derivation of linear elasticity

created by riva on 21 Mar 2022
modified on 07 Dec 2023


Published Paper

Inserted: 21 mar 2022
Last Updated: 7 dec 2023

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Volume: 153
Number: 6
Pages: 1929-1964
Year: 2022

ArXiv: 2203.04078v2 PDF


The rigorous derivation of linear elasticity from finite elasticity by means of Gamma-convergence is a well-known result, which has been extended to different models also beyond the elastic regime. However, in these results the applied forces are usually assumed to be dead loads, that is, their density in the reference configuration is independent of the actual deformation. In this paper we begin a study of the variational derivation of linear elasticity in the presence of live loads. We consider a pure traction problem for a nonlinearly elastic body subject to a pressure live load and we compute its linearization for small pressure by Gamma-convergence. We allow for a weakly coercive elastic energy density and we prove strong convergence of minimizers.

Keywords: Gamma-convergence, nonlinear elasticity, linear elasticity, live loads, pressure loads