Acta Mechanica

, Volume 230, Issue 5, pp 1811–1823 | Cite as

Micropolar plasticity. Part II: a v.Mises version of micropolar plasticity in terms of curvature tensors related by mixed transformations

  • Daniel JohannsenEmail author
  • Charalampos Tsakmakis
Original Paper


In Part I, we presented a general micropolar plasticity theory which rests on a class of micropolar curvature tensors related to each other by mixed transformations. In this paper, we derive, in the context of the theory of Part I, a micropolar counterpart of v.Mises conventional plasticity with kinematic and isotropic hardening. The predictive capabilities of the resulting model are illustrated for the case of tension loading of plates with a circular hole.


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  1. 1.
    Chaboche, J.-L.: Cyclic viscoplastic constitutive equations, part I: a thermodynamically consistent formulation. J. Appl. Mech. 60(4), 813–821 (1993a). CrossRefzbMATHGoogle Scholar
  2. 2.
    Chaboche, J.-L.: Cyclic viscoplastic constitutive equations, part II: stored energy-comparison between models and experiments. J. Appl. Mech. 60(4), 822–828 (1993b). CrossRefGoogle Scholar
  3. 3.
    de Borst, R.: A generalisation of J2-flow theory for polar continua. Eng. Comput. 10(2), 99–121 (1993)CrossRefGoogle Scholar
  4. 4.
    Eringen, A.C.: Microcontinuum Field Theories: Volume 1, Foundations and Solids. Microcontinuum Field Theories: Foundations and Solids. Springer (1999). ISBN 9780387986203Google Scholar
  5. 5.
    Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial Bauschinger effect. Mater. High Temp. 24(1), 1–26 (2007). CrossRefGoogle Scholar
  6. 6.
    Grammenoudis, P., Tsakmakis, Ch.: Finite element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects. Int. J. Numer. Methods Eng. 62, 1691–1720 (2005)CrossRefzbMATHGoogle Scholar
  7. 7.
    Johannsen, D.: Modelle der nicht-kompatiblen mikropolaren Plastizität und Kontaktmechanik. Ph.D. thesis, Technische Universität, Darmstadt (2014)Google Scholar
  8. 8.
    Johannsen, D., Tsakmakis, C.: Micropolar plasticity. Part I: modelling based on curvature tensors related by mixed transformations. Int. J. Eng. Sci. (2018) (submitted for publication)Google Scholar
  9. 9.
    Kaloni, P.N., Ariman, T.: Stress concentration effects in micropolar elasticity. Z. für Angew. Math. Phys. ZAMP 18(1), 136–141 (1967). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Continuum MechanicsTU-DarmstadtDarmstadtGermany

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