General method of regularization. III: The unilateral contact problem

Jarosław L. Bojarski¹

¹ Warsaw Agricultural University–SGGW Department of Applied Mathematics Nowoursynowska 159 02-787 Warszawa, Poland

Applicationes Mathematicae, Tome 31 (2004) no. 4, pp. 473-492.

Résumé

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${}^{\ast }$ 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${}^{\ast }$ lower semicontinuous regularization of the energy.

Détail

DOI : 10.4064/am31-4-8

Mots-clés : paper prove relaxation elastic perfectly plastic energy solid made hencky material signorini constraints boundary weak * lower semicontinuous regularization plastic energy consider elastic plastic solid endowed von mises tresca yield condition moreover set solutions relaxed problem equal set solutions relaxed problem proposed suquet deduce relaxation energy plastic soil signorini condition boundary weak * lower semicontinuous regularization energy