### Abstract

In the previous paper, a strain rate tensor is introduced into free energy and a thermodynamic force conjugate to this rate is newly defined. On the basis of the principle of increase of entropy and one of maximal entropy production rate, a non-coaxial constitutive equation associated with a plastic deformation rate is derived as a flow rule in which a dissipation function plays the role of plastic potential. Material moduli in this equation, however, are still not expressed as functions of hardening law. In this paper, the constitutive equation is newly generalized into corner theory which permits an existence of a vertex on dissipation surface. A non-coaxial angle of a plastic deformation rate is related to the non-coaxial angle of a stress rate by use of strain rate sensitivity. Furthermore, a finite element analysis is carried out for a plane strain tension of homopolymer. Some remarkable numerical results of strain localization for homopolymer are discussed in detail.

Original language | English |
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Pages (from-to) | 682-690 |

Number of pages | 9 |

Journal | Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 68 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2002 Apr |

### Keywords

- Constitutive equation
- Finite element method
- High polymer materials
- Large deformation
- Non-coaxiality
- Plasticity
- Shear band
- Vertex
- Viscoplasticity

### ASJC Scopus subject areas

- Materials Science(all)
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*,

*68*(4), 682-690. https://doi.org/10.1299/kikaia.68.682