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 language | English (US) |
|---|---|
| Pages (from-to) | 387-394 |
| Number of pages | 8 |
| Journal | European Journal of Mechanics, A/Solids |
| Volume | 23 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 1 2004 |
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Keywords
- Method of characteristics
- Strain gradient plasticity
ASJC Scopus subject areas
- Materials Science(all)
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
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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 journal › Article
TY - JOUR
T1 - A study of lower-order strain gradient plasticity theories by the method of characteristics
AU - Yun, G.
AU - Qin, J.
AU - Huang, Y.
AU - Hwang, K. C.
PY - 2004/5/1
Y1 - 2004/5/1
N2 - 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.
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.
KW - Method of characteristics
KW - Strain gradient plasticity
UR - http://www.scopus.com/inward/record.url?scp=2942543207&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2942543207&partnerID=8YFLogxK
U2 - 10.1016/j.euromechsol.2004.02.003
DO - 10.1016/j.euromechsol.2004.02.003
M3 - Article
VL - 23
SP - 387
EP - 394
JO - European Journal of Mechanics, A/Solids
JF - European Journal of Mechanics, A/Solids
SN - 0997-7538
IS - 3
ER -