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A New Variational Approach to Linearization of Traction Problems in Elasticity

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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.

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Acknowledgements

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. Politecnico di Bari, Bari, Italy

    Francesco Maddalena

  2. University of Genova, Genoa, Italy

    Danilo Percivale

  3. Politecnico di Milano, Milan, Italy

    Franco Tomarelli

Authors
  1. Francesco Maddalena
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  2. Danilo Percivale
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  3. Franco Tomarelli
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Correspondence to Franco Tomarelli.

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Dedicated to Alexander Ioffe on the occasion of his 80th Birthday.

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Maddalena, F., Percivale, D. & Tomarelli, F. A New Variational Approach to Linearization of Traction Problems in Elasticity. J Optim Theory Appl 182, 383–403 (2019). https://doi.org/10.1007/s10957-019-01533-8

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  • DOI: https://doi.org/10.1007/s10957-019-01533-8

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