Regularity of solutions in plasticity. I: Continuum

Jarosław L. Bojarski¹

¹ Institute of Fundamental Technological Research Polish Academy of Sciences /Swi/etokrzyska 21 00-049 Warszawa, Poland

Applicationes Mathematicae, Tome 30 (2003) no. 3, pp. 337-364.

Résumé

The aim of this paper is to study the problem of regularity of solutions in Hencky plasticity. We consider a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space $LD({\mit\Omega}) \equiv \{% {\bf u}\in L^{1}({\mit\Omega},{\Bbb R}^{n})\mid\nabla {\bf u}+(\nabla {\bf u})^{T}\in L^{1}({\mit\Omega},{\Bbb R}^{n\times n})\}$ if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.

Détail

DOI : 10.4064/am30-3-8

Keywords: paper study problem regularity solutions hencky plasticity consider non homogeneous material whose elastic plastic properties change discontinuously prove displacement solutions belong space mit omega equiv mit omega bbb mid nabla nabla mit omega bbb times stress solution continuous belongs interior set admissible stresses each point part functional which describes work boundary forces relaxed