Regularity of displacement solutions in Hencky plasticity. II: The main result

Jarosław L. Bojarski¹

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

Applicationes Mathematicae, Tome 38 (2011) no. 4, pp. 413-434

Résumé

The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. Here, a non-homogeneous material is considered, where the elastic-plastic properties change discontinuously. In the first part, we have found the extremal relation between the displacement formulation defined on the space of bounded deformation and the stress formulation of the variational problem in Hencky plasticity. In the second part, we prove that the displacement solution belongs to the appropriate Sobolev space (if the stress solution belongs to the interior of a set of admissible stresses, at each point). Then we deduce a regularity theorem for displacement solutions in composite materials.

Détail

DOI : 10.4064/am38-4-2

Keywords: paper study problem regularity displacement solutions hencky plasticity here non homogeneous material considered where elastic plastic properties change discontinuously first part have found extremal relation between displacement formulation defined space bounded deformation stress formulation variational problem hencky plasticity second part prove displacement solution belongs appropriate sobolev space stress solution belongs interior set admissible stresses each point deduce regularity theorem displacement solutions composite materials