246
Views
16
CrossRef citations to date
0
Altmetric
Part A: Materials Science

Some properties of the dissipative model of strain-gradient plasticity

, , , &
Pages 693-717 | Received 20 Aug 2016, Accepted 11 Dec 2016, Published online: 23 Jan 2017

References

  • E.C. Aifantis, On the microstructural origin of certain inelastic models, J. Eng. Mat. Tech. 106 (1984), pp. 326–330.
  • H. Gao, Y. Huang, and W.D. Nix, Mechanism-based strain gradient plasticity I. Theory, J. Mech. Phys. Solids 47 (1999), pp. 1239–1263.
  • H. Gao, Y. Huang, W.D. Nix, and J.W. Hutchinson, Modeling plasticity at the micrometer scale, Naturwissenschaften 86 (1999), pp. 507–515.
  • N.A. Fleck and J.W. Hutchinson, A reformulation of strain gradient plasticity, J. Mech. Phys. Solids 49 (2001), pp. 2245–2271.
  • P. Gudmundson, A unified treatment of strain gradient plasticity, J. Mech. Phys. Solids 52 (2001), pp. 1379–1406.
  • M.E. Gurtin and L. Anand, A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations, J. Mech. Phys. Solids 53 (2004), pp. 1624–1649.
  • B.D. Reddy, The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity, Continuum Mech. Thermodyn. 23 (2011), pp. 527–549.
  • B.D. Reddy, F. Ebobisse, and A.T. McBride, Well-posedness of a model of strain gradient plasticity for plastically irrotational materials, Int. J. Plast. 24 (2008), pp. 55–73.
  • N.A. Fleck and J.R. Willis, A mathematical basis for strain-gradient plasticity -- Part I: Scalar plastic multiplier, J. Mech. Phys. Solids 57 (2009), pp. 151–177.
  • N.A. Fleck and J.R. Willis, A mathematical basis for strain-gradient plasticity -- Part II: Tensorial plastic multiplier, J. Mech. Phys. Solids 57 (2009), pp. 1045–1057.
  • N.A. Fleck, J.W. Hutchinson, and J.R. Willis, Strain-gradient plasticity under non-proportional loading, Proc. R. Soc A 470 (2015), p. 20140267.
  • N.A. Fleck, J.W. Hutchinson, and J.R. Willis, Guidelines for constructing strain gradient plasticity theories, J. Appl. Mech. 82 (2015), pp. 071002-1-10.
  • L. Anand, M.E. Gurtin, S.P. Lele, and C. Gething, A one-dimensional theory of strain-gradient plasticity: Formulation, analysis, numerical results, J. Mech. Phys. Solids 53(8) (2005), pp. 1789–1826.
  • M. Chiricotto, L. Giacomelli, and G. Tomassetti, Dissipative scale effects in strain-gradient plasticity: the case of simple shear, SIAM J. Appl. Math. 76(2) (2016), pp. 688–704.
  • N.A. Fleck and J.R. Willis, Strain gradient plasticity: Energetic or dissipative?, Acta Mech. Sinica 31 (2015), pp. 465–472.
  • L. Bardella and A. Panteghini, Modelling the torsion of thin metal wires by distortion gradient plasticity, J. Mech. Phys. Solids 78 (2015), pp. 467–492.
  • A. Panteghini and L. Bardella, On the finite element implementation of higher-order gradient plasticity, with focus on theories based on plastic distortion incompatibility, Comp. Methods Appl. Mech. Eng. 310 (2016), pp. 840–865.
  • R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
  • W. Han and B.D. Reddy, Plasticity: Mathematical Theory and Numerical Analysis, 2nd ed., Springer, New York, 2013.
  • A.G. Evans and J.W. Hutchinson, A critical assessment of theories of strain gradient plasticity, Acta Mater. 57 (2009), pp. 1675–1688.
  • I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
  • J. Korelc, Multi-language and multi-environment generation of nonlinear finite element codes, Eng. Comp. 18(4) (2002), pp. 312–327.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.