A study of lower-order strain gradient plasticity theories by the method of characteristics

G. Yun, J. Qin, Y. Huang*, K. C. Hwang

*Corresponding author for this work

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The lower-order strain gradient plasticity theory retains the essential structure of classical plasticity theory, and does not seem to require additional, non-classical boundary conditions. We study the well-posedness of lower-order strain gradient plasticity theory by the method of characteristics for nonlinear partial differential equations. For Niordson and Hutchinson's (2003) problem of an infinite layer in shear, we have obtained the "domain of determinacy" for Bassani's (2001) lower-order strain gradient plasticity theory. It is established that, as the applied shear stress increases, the "domain of determinacy" shrinks and eventually vanishes. The additional, non-classical boundary conditions are needed for Bassani's (2001) lower-order strain gradient plasticity in order to obtain the solution outside the "domain of determinacy". Within the "domain of determinacy", the present results agree well with Niordson and Hutchinson's (2003) finite difference solution. Outside the "domain of determinacy", the solution may not be unique.

Original languageEnglish (US)
Pages (from-to)387-394
Number of pages8
JournalEuropean Journal of Mechanics, A/Solids
Volume23
Issue number3
DOIs
StatePublished - May 1 2004

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method of characteristics
plastic properties
Plasticity
gradients
Boundary conditions
boundary conditions
partial differential equations
shear stress
Partial differential equations
Shear stress
shear

Keywords

  • Method of characteristics
  • Strain gradient plasticity

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Cite this

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A study of lower-order strain gradient plasticity theories by the method of characteristics. / Yun, G.; Qin, J.; Huang, Y.; Hwang, K. C.

In: European Journal of Mechanics, A/Solids, Vol. 23, No. 3, 01.05.2004, p. 387-394.

Research output: Contribution to journalArticle

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AU - Qin, J.

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AB - The lower-order strain gradient plasticity theory retains the essential structure of classical plasticity theory, and does not seem to require additional, non-classical boundary conditions. We study the well-posedness of lower-order strain gradient plasticity theory by the method of characteristics for nonlinear partial differential equations. For Niordson and Hutchinson's (2003) problem of an infinite layer in shear, we have obtained the "domain of determinacy" for Bassani's (2001) lower-order strain gradient plasticity theory. It is established that, as the applied shear stress increases, the "domain of determinacy" shrinks and eventually vanishes. The additional, non-classical boundary conditions are needed for Bassani's (2001) lower-order strain gradient plasticity in order to obtain the solution outside the "domain of determinacy". Within the "domain of determinacy", the present results agree well with Niordson and Hutchinson's (2003) finite difference solution. Outside the "domain of determinacy", the solution may not be unique.

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