Geodesic
On defining relations for the Hencky environment of softening of the material under diagonal stress tensor
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 72-80

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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, boundary states, non-uniqueness of equilibria, incremental plasticity law.
Mots-clés : Hencky enviroment, Jacobi matrix and Hesse matrix 
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     title = {On defining relations for the {Hencky} environment of softening of the material under diagonal stress tensor},
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     pages = {72--80},
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V. V. Struzhanov; K. V. Berdnikov. On defining relations for the Hencky environment of softening of the material under diagonal stress tensor. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 72-80. http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a6/