Mechanics of Solids

Potential Fields of Free Energy at the Stages of Hardening and Softening of the Hencky Medium at Nonpositivity of Volume Deformation

K. V. Berdnikov, V. V. Struzhanov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation

Abstract: 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.

UDC: 539.3

MSC: 74C10

Original article submitted 10/IV/2014
revision submitted – 11/V/2014

DOI: 10.14498/vsgtu1307

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