A New Variational Approach to Linearization of Traction Problems in Elasticity

  • Francesco Maddalena
  • Danilo Percivale
  • Franco TomarelliEmail author


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.


Calculus of variations Pure traction problems Linear elasticity Nonlinear elasticity Finite elasticity Critical points Gamma convergence Asymptotic analysis Nonlinear Neumann problems 

Mathematics Subject Classification

49J45 74K30 74K35 74R10 



The research was partially supported by C.N.R. INDAM Project 2018: G.N.A.M.P.A.—Problemi asintotici ed evolutivi con applicazioni a metamateriali e reti.


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Authors and Affiliations

  1. 1.Politecnico di BariBariItaly
  2. 2.University of GenovaGenoaItaly
  3. 3.Politecnico di MilanoMilanItaly

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