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

Jarosław L. Bojarski. "Regularity of displacement solutions in Hencky plasticity. I: The extremal relation." Applicationes Mathematicae 38.3 (2011): 259-293. <http://eudml.org/doc/279892>.

@article{JarosławL2011,
abstract = { 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. },
author = {Jarosław L. Bojarski},
journal = {Applicationes Mathematicae},
keywords = {duality in convex optimization for hencky plasticity; bounded deformation; boundary transmission problems in plasticity; composite materials},
language = {eng},
number = {3},
pages = {259-293},
title = {Regularity of displacement solutions in Hencky plasticity. I: The extremal relation},
url = {http://eudml.org/doc/279892},
volume = {38},
year = {2011},
}

TY - JOUR
AU - Jarosław L. Bojarski
TI - Regularity of displacement solutions in Hencky plasticity. I: The extremal relation
JO - Applicationes Mathematicae
PY - 2011
VL - 38
IS - 3
SP - 259
EP - 293
AB - 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.
LA - eng
KW - duality in convex optimization for hencky plasticity; bounded deformation; boundary transmission problems in plasticity; composite materials
UR - http://eudml.org/doc/279892
ER -