### Abstract

Elastoplastic constitutive equations which take into account yield vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In the present paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield vertex can exist on the dissipation surface. Furthermore, the spin used in the objective stress rate is selected by taking into account not only conventional requirements but also thermomechanical ones.

Original language | English |
---|---|

Pages (from-to) | 1649-1655 |

Number of pages | 7 |

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

Volume | 62 |

Issue number | 599 |

Publication status | Published - 1996 Jul |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

**Thermomechanical derivation of noncoaxial plastic constitutive equations considering spins of objective stress rates.** / Shizawa, Kazuyuki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Thermomechanical derivation of noncoaxial plastic constitutive equations considering spins of objective stress rates

AU - Shizawa, Kazuyuki

PY - 1996/7

Y1 - 1996/7

N2 - Elastoplastic constitutive equations which take into account yield vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In the present paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield vertex can exist on the dissipation surface. Furthermore, the spin used in the objective stress rate is selected by taking into account not only conventional requirements but also thermomechanical ones.

AB - Elastoplastic constitutive equations which take into account yield vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In the present paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield vertex can exist on the dissipation surface. Furthermore, the spin used in the objective stress rate is selected by taking into account not only conventional requirements but also thermomechanical ones.

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M3 - Article

VL - 62

SP - 1649

EP - 1655

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 599

ER -