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Strain gradient plasticity: the flow rule of Fleck and Hutchinson violates thermodynamics ?

Mike Ciavarella's picture

A recent paper on JMPS has seriously questioned the foundation of the SGP theory of Fleck and Hutchinson.  The matter is not simple, but is it a good bench test for imechanica to discuss?

doi:10.1016/j.jmps.2008.12.002    

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Copyright © 2009 Elsevier Ltd All rights reserved.

Thermodynamics applied to gradient theories involving the accumulated
plastic strain: The theories of Aifantis and Fleck and Hutchinson and
their generalization

Morton E. Gurtina, 1, E-mail The Corresponding Author and Lallit Anandb, Corresponding Author Contact Information, E-mail The Corresponding Author

aDepartment of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA

bDepartment of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Received 4 December 2007; 

revised 2 December 2008; 

accepted 9 December 2008. 

Available online 16 December 2008.

Abstract

We discuss the physical nature of flow
rules for rate-independent (gradient) plasticity laid down by Aifantis
and by Fleck and Hutchinson. As a central result we show that:


the flow rule of Fleck and Hutchinson is incompatible with
thermodynamics unless its nonlocal term is dropped. If the underlying
theory is augmented by a general defect energy dependent on γp and backward differenceγp, then compatibility with thermodynamics requires that its flow rule reduce to that of Aifantis.

We
establish this result (and others) within a general framework obtained
by combining a virtual-power principle of Fleck and Hutchinson with the
first two laws of thermodynamics—balance of energy and the
Clausius–Duhem inequality—under isothermal conditions.

Keywords: Constitutive behavior; Viscoplasticity; Strain-gradient plasticity; Prinicipla of virtual power; Thermodynamics

Comments

Mike Ciavarella's picture

In this more recent paper from Fleck and Willis "due attention is paid to ensure that positive plastic work is done".  I am not sure if they refer to the "Drucker stability" postulates, but I wonder if a non-associative SGP theory could be imagined.

 

4.
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A mathematical basis for strain-gradient plasticity theory—Part I: Scalar plastic multiplier
Journal of the Mechanics and Physics of Solids, Volume 57, Issue 1, January 2009, Pages 161-177
N.A. Fleck, J.R. Willis

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5.
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Formulation of strain gradient plasticity with interface energy in a consistent thermodynamic framework
International Journal of Plasticity, In Press, Corrected Proof, Available online 31 December 2008
George Z. Voyiadjis, Babur Deliktas

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dabiao liu's picture

dear  Mike Ciavarella:
        I am very interested in strain gradient plasticity theory .Now I am focusing on this theory ,unfortunately ,you say that "Strain gradient plasticity: the flow rule of Fleck and Hutchinson violates thermodynamics ?"   This is a serious thing .I really want to read your papers and look forward to your further study on this issue.

Mike Ciavarella's picture

I warn you, the paper is not trivial to read, it is very advanced material, and a little "academic". Why you want to read his so much?   

 

doi:10.1016/j.jmps.2008.12.002    

How to<br />
Cite or Link Using DOI (Opens New Window)

Copyright © 2009 Elsevier Ltd All rights reserved.

Thermodynamics applied to gradient theories involving the accumulated
plastic strain: The theories of Aifantis and Fleck and Hutchinson and
their generalization

 

Morton E. Gurtina,
1,
E-mail The Corresponding Author and Lallit Anand

 

 maybe you prefer

The very bizzare story of the
paper: FFEMS-4283 - A simplified "damage ...

 

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal

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