Geodesic
Potential Fields of Free Energy at the Stages of Hardening and Softening of the Hencky Medium at Nonpositivity of Volume Deformation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2014), pp. 82-88

Voir la notice de l'article provenant de la source Math-Net.Ru

The Hencky medium with softening under isothermal and quasistatic deformation is considered. It is believed that volume deformation is not positive. In this case softening is characterized by the part of union curve with negative slope. For aforementioned conditions function of free energy is presented. For all stages of deformation in the space “volume deformation – intensity of shear's deformation” level lines of the free energy are constructed. It is established that level lines are ellipses in hardening and function of free energy increases with distance from their centers, while in softening hyperbolas are level lines and function of free energy decreases with distance from their centers. Obtained results indirectly confirm the change in type of boundary value problem from elliptic to hyperbolic under material transition to the softening.
Keywords: Hencky medium, free energy, potential fields, level lines, hardening, softening. 
@article{VSGTU_2014_2_a6,
     author = {K. V. Berdnikov and V. V. Struzhanov},
     title = {Potential {Fields} of {Free} {Energy} at the {Stages} of {Hardening} and {Softening} of the {Hencky} {Medium} at {Nonpositivity} of {Volume} {Deformation}},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {82--88},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2014_2_a6/}
}
TY  - JOUR
AU  - K. V. Berdnikov
AU  - V. V. Struzhanov
TI  - Potential Fields of Free Energy at the Stages of Hardening and Softening of the Hencky Medium at Nonpositivity of Volume Deformation
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2014
SP  - 82
EP  - 88
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2014_2_a6/
LA  - ru
ID  - VSGTU_2014_2_a6
ER  - 
%0 Journal Article
%A K. V. Berdnikov
%A V. V. Struzhanov
%T Potential Fields of Free Energy at the Stages of Hardening and Softening of the Hencky Medium at Nonpositivity of Volume Deformation
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2014
%P 82-88
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2014_2_a6/
%G ru
%F VSGTU_2014_2_a6
K. V. Berdnikov; V. V. Struzhanov. Potential Fields of Free Energy at the Stages of Hardening and Softening of the Hencky Medium at Nonpositivity of Volume Deformation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2014), pp. 82-88. http://geodesic.mathdoc.fr/item/VSGTU_2014_2_a6/