### Abstract

A thermodynamical theory of gradient elastoplasticity, including kinematic hardening, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. Thermodynamically consistent constitutive equations for plastic stretching, plastic spin and back stress are rigorously derived. Also, an expression for the plastic spin is obtained from the constitutive equation of dislocation drift rate and an expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present gradient theory yields a symmetric stress tensor. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given.

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

Pages (from-to) | 899-938 |

Number of pages | 40 |

Journal | International Journal of Plasticity |

Volume | 15 |

Issue number | 9 |

Publication status | Published - 1999 |

### Fingerprint

### Keywords

- Constitutive behavior
- Dislocation density tensor
- Elastic-plastic material
- Finite strain
- Thermomechanical processes

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*International Journal of Plasticity*,

*15*(9), 899-938.

**A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I : Fundamentals.** / Shizawa, Kazuyuki; Zbib, H. M.

Research output: Contribution to journal › Article

*International Journal of Plasticity*, vol. 15, no. 9, pp. 899-938.

}

TY - JOUR

T1 - A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I

T2 - Fundamentals

AU - Shizawa, Kazuyuki

AU - Zbib, H. M.

PY - 1999

Y1 - 1999

N2 - A thermodynamical theory of gradient elastoplasticity, including kinematic hardening, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. Thermodynamically consistent constitutive equations for plastic stretching, plastic spin and back stress are rigorously derived. Also, an expression for the plastic spin is obtained from the constitutive equation of dislocation drift rate and an expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present gradient theory yields a symmetric stress tensor. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given.

AB - A thermodynamical theory of gradient elastoplasticity, including kinematic hardening, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. Thermodynamically consistent constitutive equations for plastic stretching, plastic spin and back stress are rigorously derived. Also, an expression for the plastic spin is obtained from the constitutive equation of dislocation drift rate and an expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present gradient theory yields a symmetric stress tensor. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given.

KW - Constitutive behavior

KW - Dislocation density tensor

KW - Elastic-plastic material

KW - Finite strain

KW - Thermomechanical processes

UR - http://www.scopus.com/inward/record.url?scp=0001275882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001275882&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001275882

VL - 15

SP - 899

EP - 938

JO - International Journal of Plasticity

JF - International Journal of Plasticity

SN - 0749-6419

IS - 9

ER -