A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals

Kazuyuki Shizawa, H. M. Zbib

Research output: Contribution to journalArticle

108 Citations (Scopus)

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 languageEnglish
Pages (from-to)899-938
Number of pages40
JournalInternational Journal of Plasticity
Volume15
Issue number9
Publication statusPublished - 1999

Fingerprint

Elastoplasticity
Tensors
Plastics
Constitutive equations
Entropy
Stretching
Hardening
Residual stresses
Kinematics

Keywords

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

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

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

In: International Journal of Plasticity, Vol. 15, No. 9, 1999, p. 899-938.

Research output: Contribution to journalArticle

@article{f09fb259dd944c85b39fa23d529f8cfa,
title = "A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals",
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.",
keywords = "Constitutive behavior, Dislocation density tensor, Elastic-plastic material, Finite strain, Thermomechanical processes",
author = "Kazuyuki Shizawa and Zbib, {H. M.}",
year = "1999",
language = "English",
volume = "15",
pages = "899--938",
journal = "International Journal of Plasticity",
issn = "0749-6419",
publisher = "Elsevier Limited",
number = "9",

}

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 -