### Abstract

A thermodynamical theory of elastoplasticity including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.

Original language | English |
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Pages (from-to) | 247-253 |

Number of pages | 7 |

Journal | Journal of Engineering Materials and Technology, Transactions of the ASME |

Volume | 121 |

Issue number | 2 |

Publication status | Published - 1999 Apr |

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### ASJC Scopus subject areas

- Mechanical Engineering
- Materials Science(all)

### Cite this

*Journal of Engineering Materials and Technology, Transactions of the ASME*,

*121*(2), 247-253.

**A thermodynamical theory of plastic spin and internal stress with dislocation density tensor.** / Shizawa, Kazuyuki; Zbib, H. M.

Research output: Contribution to journal › Article

*Journal of Engineering Materials and Technology, Transactions of the ASME*, vol. 121, no. 2, pp. 247-253.

}

TY - JOUR

T1 - A thermodynamical theory of plastic spin and internal stress with dislocation density tensor

AU - Shizawa, Kazuyuki

AU - Zbib, H. M.

PY - 1999/4

Y1 - 1999/4

N2 - A thermodynamical theory of elastoplasticity including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.

AB - A thermodynamical theory of elastoplasticity including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.

UR - http://www.scopus.com/inward/record.url?scp=0033116211&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033116211&partnerID=8YFLogxK

M3 - Article

VL - 121

SP - 247

EP - 253

JO - Journal of Engineering Materials and Technology, Transactions of the ASME

JF - Journal of Engineering Materials and Technology, Transactions of the ASME

SN - 0094-4289

IS - 2

ER -