Regularity of solutions in plasticity. I: Continuum

Volume 30 / 2003

Jarosław L. Bojarski Applicationes Mathematicae 30 (2003), 337-364 MSC: Primary 49N60; Secondary 49J45, 49K30, 74C05. DOI: 10.4064/am30-3-8


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.


  • Jarosław L. BojarskiInstitute of Fundamental Technological Research
    Polish Academy of Sciences
    /Swi/etokrzyska 21
    00-049 Warszawa, Poland

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