General method of regularization. III: The unilateral contact problem

Volume 31 / 2004

Jarosław L. Bojarski Applicationes Mathematicae 31 (2004), 473-492 MSC: Primary 49K27; Secondary 49J45, 47N10, 46A20, 26B30, 74C05, 74E05. DOI: 10.4064/am31-4-8

Abstract

The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak$^*$ lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. We deduce that the relaxation of the energy of plastic soil (with the Signorini condition on the boundary) is the weak$^*$ lower semicontinuous regularization of the energy.

Authors

  • Jarosław L. BojarskiWarsaw Agricultural University–SGGW
    Department of Applied Mathematics
    Nowoursynowska 159
    02-787 Warszawa, Poland
    e-mail

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