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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 3(28), Pages 72–80 (Mi vsgtu1115)  

This article is cited in 6 scientific papers (total in 6 papers)

Mechanics of Solids

On defining relations for the Hencky environment of softening of the material under diagonal stress tensor

V. V. Struzhanov, K. V. Berdnikov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: Medium which strains are described by diagonal components of the strain tensor is considered (in spherical coordinate system). It is assumed that the first invariant of the strain tensor is not positive. Under these restrictions Hencky defining relations with regard to softening of material are written. These defining relations are represented as map of strain space in the stress space. Jacobi matrix of this map is singular in some points in strain space. It is shown that using this map it is possible to find the objective number of deformed states corresponding to a given strain tensor. Also the equations of incremental plasticity law are written. These equations allow us to find the inelastic strain by the total strain.

Keywords: hardening, softening, Hencky enviroment, boundary states, Jacobi matrix and Hesse matrix, non-uniqueness of equilibria, incremental plasticity law

DOI: https://doi.org/10.14498/vsgtu1115

Full text: PDF file (283 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 539.3
MSC: 74C10
Original article submitted 13/VI/2012
revision submitted – 11/VIII/2012

Citation: V. V. Struzhanov, K. V. Berdnikov, “On defining relations for the Hencky environment of softening of the material under diagonal stress tensor”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(28) (2012), 72–80

Citation in format AMSBIB
\Bibitem{StrBer12}
\by V.~V.~Struzhanov, K.~V.~Berdnikov
\paper On defining relations for the Hencky environment of softening of the material under diagonal stress tensor
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 3(28)
\pages 72--80
\mathnet{http://mi.mathnet.ru/vsgtu1115}
\crossref{https://doi.org/10.14498/vsgtu1115}
\zmath{https://zbmath.org/?q=an:1326.74027}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. V. Berdnikov, V. V. Struzhanov, “Ostatochnye napryazheniya v uprugoplasticheskom prostranstve, voznikayuschie posle rasshireniya sfericheskoi polosti”, Vestnik Uralskogo gosudarstvennogo universiteta putei soobscheniya, 2013, no. 2, 18–26  elib
    2. K. V. Berdnikov, V. V. Struzhanov, “Algoritm rascheta napryazhennogo sostoyaniya v uprugoplasticheskom prostranstve so sfericheskoi polostyu pri zadanii peremeschenii tochek ee granitsy”, Matematicheskoe modelirovanie v estestvennykh naukakh, 2013, no. 1, 21–24  elib
    3. K. V. Berdnikov, V. V. Struzhanov, “Ostatochnye napryazheniya v batiskafe posle pogruzheniya na bolshuyu glubinu”, Vestnik Uralskogo gosudarstvennogo universiteta putei soobscheniya, 2013, no. 3 (19), 8–17  elib
    4. K. V. Berdnikov, V. V. Struzhanov, “Potentsialnye polya svobodnoi energii na stadiyakh uprochneniya i razuprochneniya sredy Genki pri nepolozhitelnosti ob'emnoi deformatsii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(35) (2014), 82–88  mathnet  crossref  zmath  elib
    5. V. V. Struzhanov, K. V. Berdnikov, “Ob ustoichivosti protsessa polyarno-simmetrichnogo deformirovaniya tel iz razuprochnyayuschikhsya materialov”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(37) (2014), 111–120  mathnet  crossref  zmath  elib
    6. K. V. Berdnikov, V. V. Struzhanov, “Raschet napryazhenno-deformirovannogo sostoyaniya sfericheskoi polosti v razuprochnyayuschemsya prostranstve pri zadanii peremeschenii tochkam granitsy sfery”, Matematicheskoe modelirovanie v estestvennykh naukakh, 1 (2014), 39–41  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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