Thermomechanical derivation of noncoaxial plastic constitutive equations considering spins of objective stress Rates

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3 Citations (Scopus)

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 languageEnglish
Pages (from-to)336-342
Number of pages7
JournalJSME International Journal, Series A: Mechanics and Material Engineering
Volume40
Issue number3
Publication statusPublished - 1997 Jul

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Constitutive equations
Plastics
Strain rate
Plastic deformation
Entropy
Thermodynamics

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

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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.",
keywords = "Constitutive Equation, Finite Deformation Theory, Non-coaxiality, Objective Rate, Plasticity, Spin, Thermomechanics",
author = "Kazuyuki Shizawa",
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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.

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KW - Finite Deformation Theory

KW - Non-coaxiality

KW - Objective Rate

KW - Plasticity

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