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

Jarosław L. Bojarski (2011)

Applicationes Mathematicae

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...

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

Jarosław L. Bojarski (2011)

Applicationes Mathematicae

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. ...

Regularity of solutions in plasticity. I: Continuum

Jarosław L. Bojarski (2003)

Applicationes Mathematicae

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 L D ( Ω ) u L ¹ ( Ω , ) | u + ( u ) T L ¹ ( Ω , n × 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.

Regularity of solutions in plasticity. II: Plates

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. We consider a plate made of a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space W 2 , 1 ( Ω ) 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.

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