A study on the conventional theory of mechanism-based strain gradient plasticity for mixed hardening by the method of characteristics

Jiang Qin, Keh Chih Hwang*, Yonggang Huang

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The Conventional Theory of Mechanism-based Strain Gradient Plasticity (CMSG) is of lower-order strain gradient that retains the essential structure of classical plasticity theory. It does not require additional non-classical boundary conditions, thus it can be easily applied in numerical analysis. The constitutive relations of CMSG theory for mixed hardening are established, and its well-posedness is studied by the method of characteristics. For an infinite layer in shear, the "domain of determinacy" for CMSG theory at different mixed hardening states is determined. Within the "domain of determinacy", the presented results agree well with the numerical solution obtained by the finite difference method. Outside the "domain of determinacy", the solution may not be unique, in that case, the additional, non-classical boundary conditions are needed for the well-posedness of CMSG theory. As the applied shear stress increases, the "domain of determinacy" shrinks and eventually vanishes.

Original languageEnglish (US)
Pages (from-to)176-185
Number of pages10
JournalGongcheng Lixue/Engineering Mechanics
Volume26
Issue number9
StatePublished - Sep 1 2009

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Plasticity
Hardening
Boundary conditions
Finite difference method
Shear stress
Numerical analysis

Keywords

  • CMSG theory
  • Domain of determinacy
  • Method of characteristics
  • Mixed hardening
  • Strain gradient plasticity

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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abstract = "The Conventional Theory of Mechanism-based Strain Gradient Plasticity (CMSG) is of lower-order strain gradient that retains the essential structure of classical plasticity theory. It does not require additional non-classical boundary conditions, thus it can be easily applied in numerical analysis. The constitutive relations of CMSG theory for mixed hardening are established, and its well-posedness is studied by the method of characteristics. For an infinite layer in shear, the {"}domain of determinacy{"} for CMSG theory at different mixed hardening states is determined. Within the {"}domain of determinacy{"}, the presented results agree well with the numerical solution obtained by the finite difference method. Outside the {"}domain of determinacy{"}, the solution may not be unique, in that case, the additional, non-classical boundary conditions are needed for the well-posedness of CMSG theory. As the applied shear stress increases, the {"}domain of determinacy{"} shrinks and eventually vanishes.",
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A study on the conventional theory of mechanism-based strain gradient plasticity for mixed hardening by the method of characteristics. / Qin, Jiang; Hwang, Keh Chih; Huang, Yonggang.

In: Gongcheng Lixue/Engineering Mechanics, Vol. 26, No. 9, 01.09.2009, p. 176-185.

Research output: Contribution to journalArticle

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AU - Hwang, Keh Chih

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N2 - The Conventional Theory of Mechanism-based Strain Gradient Plasticity (CMSG) is of lower-order strain gradient that retains the essential structure of classical plasticity theory. It does not require additional non-classical boundary conditions, thus it can be easily applied in numerical analysis. The constitutive relations of CMSG theory for mixed hardening are established, and its well-posedness is studied by the method of characteristics. For an infinite layer in shear, the "domain of determinacy" for CMSG theory at different mixed hardening states is determined. Within the "domain of determinacy", the presented results agree well with the numerical solution obtained by the finite difference method. Outside the "domain of determinacy", the solution may not be unique, in that case, the additional, non-classical boundary conditions are needed for the well-posedness of CMSG theory. As the applied shear stress increases, the "domain of determinacy" shrinks and eventually vanishes.

AB - The Conventional Theory of Mechanism-based Strain Gradient Plasticity (CMSG) is of lower-order strain gradient that retains the essential structure of classical plasticity theory. It does not require additional non-classical boundary conditions, thus it can be easily applied in numerical analysis. The constitutive relations of CMSG theory for mixed hardening are established, and its well-posedness is studied by the method of characteristics. For an infinite layer in shear, the "domain of determinacy" for CMSG theory at different mixed hardening states is determined. Within the "domain of determinacy", the presented results agree well with the numerical solution obtained by the finite difference method. Outside the "domain of determinacy", the solution may not be unique, in that case, the additional, non-classical boundary conditions are needed for the well-posedness of CMSG theory. As the applied shear stress increases, the "domain of determinacy" shrinks and eventually vanishes.

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