## Abstract

In this chapter, the considered issue is presented on the base of two different models of plasticity theory and the detailed derivation of formulae for the average normalised axial stress in the minimal section plane is shown based on different classical approaches. For the sake of fact that all classical derivations are presented in so-called Euler coordinates, the independent variables are coordinates in the current configuration of the point in the space, in which a material particle is located at the considered moment of time. Let us notice that in this coordinate system for the given deformation, an additional problem is the determination of the boundary positions along which the boundary conditions on the neck contour are estimated since they are continuous changing for each stage of deformation. However, this inconvenience can be recompensed by linear equilibrium equations [8].

Original language | English |
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Pages (from-to) | 17-65 |

Number of pages | 49 |

Journal | SpringerBriefs in Applied Sciences and Technology |

Issue number | 9783642221330 |

DOIs | |

Publication status | Published - 2011 |

## Keywords

- Classical and new approaches
- Deformation theory
- Flow theory
- Stress distribution in the sample with neck