### Abstract

Elasto-plastic 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 this 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 the 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 which should be used in the objective stress rate is selected by taking into account not only usual requirements but also thermomechanical ones.

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

Pages (from-to) | 336-342 |

Number of pages | 7 |

Journal | JSME International Journal, Series A: Mechanics and Material Engineering |

Volume | 40 |

Issue number | 3 |

Publication status | Published - 1997 Jul |

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### Keywords

- Constitutive Equation
- Finite Deformation Theory
- Non-coaxiality
- Objective Rate
- Plasticity
- Spin
- Thermomechanics

### ASJC Scopus subject areas

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

### 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 - 1997/7

Y1 - 1997/7

N2 - Elasto-plastic 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 this 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 the 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 which should be used in the objective stress rate is selected by taking into account not only usual requirements but also thermomechanical ones.

AB - Elasto-plastic 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 this 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 the 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 which should be used in the objective stress rate is selected by taking into account not only usual requirements but also thermomechanical ones.

KW - Constitutive Equation

KW - Finite Deformation Theory

KW - Non-coaxiality

KW - Objective Rate

KW - Plasticity

KW - Spin

KW - Thermomechanics

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UR - http://www.scopus.com/inward/citedby.url?scp=0031190064&partnerID=8YFLogxK

M3 - Article

VL - 40

SP - 336

EP - 342

JO - JSME International Journal, Series 1: Solid Mechanics, Strength of Materials

JF - JSME International Journal, Series 1: Solid Mechanics, Strength of Materials

SN - 1340-8046

IS - 3

ER -