A New Variational Approach to Linearization of Traction Problems in Elasticity

Francesco Maddalena (), Danilo Percivale () and Franco Tomarelli ()
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Francesco Maddalena: Politecnico di Bari
Danilo Percivale: University of Genova
Franco Tomarelli: Politecnico di Milano

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 1, No 16, 383-403

Abstract: Abstract 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.

Keywords: Calculus of variations; Pure traction problems; Linear elasticity; Nonlinear elasticity; Finite elasticity; Critical points; Gamma convergence; Asymptotic analysis; Nonlinear Neumann problems; 49J45; 74K30; 74K35; 74R10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01533-8

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