Regularity of displacement solutions in Hencky plasticity. I: The extremal relation

• Autorzy: Jarosław L. Bojarski
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. A non-homogeneous material whose elastic-plastic properties change discontinuously is considered. We find (in an explicit form) 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. This extremal relation is used in the proof of the regularity of displacements.
In part II of the paper, we will prove that the displacement solution belongs to the classical Sobolev space (if the stress solution belongs to the interior of a set of admissible stresses, at each point). We will find the regularity theorem for displacement solutions in composite materials whose elastic-plastic properties may change discontinuously.

Kategorie tematyczne

• 49J45: Methods involving semicontinuity and convergence; relaxation
• 49K30: Optimal solutions belonging to restricted classes
• 49N60: Regularity of solutions
• 74C05: Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2011
• Tom: 38
• Numer: 3
• Strony: 259-293

Daty

wydano

2011

Twórcy

autor

Jarosław L. Bojarski

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

Identyfikatory

DOI

10.4064/am38-3-2