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Stress regularity for a new quasistatic evolution model of perfectly plastic plates

Abstract

We study some properties of solutions to a quasistatic evolution problem for perfectly plastic plates, that has been recently derived from three-dimensional Prandtl–Reuss plasticity. We prove that the stress tensor has locally square-integrable first derivatives with respect to the space variables. We also exhibit an example showing that the model under consideration has in general a genuinely three-dimensional nature and cannot be reduced to a two-dimensional setting.

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Acknowledgments

MGM acknowledges support by GNAMPA–INdAM and by the European Research Council under Grant No. 290888 “Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture”. ED warmly thanks the Center for Nonlinear Analysis (NSF Grant No. DMS-0635983), where part of this research was carried out. The research of ED was funded under a postdoctoral fellowship by the National Science Foundation under Grant No. DMS-0905778. The authors wish to thank Jean-François Babadjian, Kaushik Bhattacharya, and Corrado Maurini for interesting discussions on the plastic plate model derived in [5].

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Correspondence to Maria Giovanna Mora.

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Communicated by L. Ambrosio.

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Davoli, E., Mora, M.G. Stress regularity for a new quasistatic evolution model of perfectly plastic plates. Calc. Var. 54, 2581–2614 (2015). https://doi.org/10.1007/s00526-015-0876-4

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Mathematics Subject Classification

  • 74C05
  • 74G65
  • 74K20
  • 49J45