This article is cited in 7 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.

UDC: 539.3

MSC: 74C10

Original article submitted 13/VI/2012
revision submitted – 11/VIII/2012

DOI: 10.14498/vsgtu1115

Bibliographic databases:

• 
• 
• 
•