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Micropolar Elasto-Plasticity and Its Role in Localization Analysis

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Anisotropy and Localization of Plastic Deformation

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Abstract

In this paper we focus on micropolar elasto-plasticity and the conditions for discontinuous solutions of IBVP’s. To start with, we briefly review the kinematic relations, the balance conditions and introduce linear-elastic and elasto-plastic constitutive models for micropolar continua. An ‘augmented’ localization tensor is then developed which reveals discontinous bifurcation at the constitutive level. This localization condition is constrained however by the balance of angular momentum which restricts the bifurcated stress and couple-stress fields, see also ref. [5].

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References

  1. R. de Borst, “A Generalisation of J 2-Theory for Polar Continua”, TNO-IBBC Report BI-89-195, Delft University of Technology, Delft (1989).

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  2. E. Cosserat and F. Cosserat, “Théorie des Corps Déformables”, Herman et fils, Paris, (1909).

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  3. H.-B. Mühlhaus, “Application of Cosserat Theory in Numerical Solutions of Limit Load Problems” Ingenieur Archiv, Vol. 59, No.2, pp. 124–37 (1989).

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  4. P. Steinmann and K. Willam, “Localization in Micropolar Elasto-Plasticity”, Proc. 3rd Int. Conf. ’Constitutive Laws for Engineering Materials’, C.S. Desai et al. eds., ASME-Press New York, pp. 461–465 (1991).

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  5. P. Steinmann and K. Willam, “Localization within the Framework of Micropolar Elasto-Plasticity”, V. Mannl ed., 60th Anniv.Volume Prof. Lippmann, Springer Verlag Berlin, (1991).

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Author information

Authors and Affiliations

  1. Institute of Mechanics, University of Karlsruhe, D-7500, Karlsruhe 1, Germany

    Andreas Dietsche, Paul Steinmann & Kaspar Willam

  2. CEAE-Department, University of Colorado at Boulder, 80309-0428, CO, USA

    Andreas Dietsche, Paul Steinmann & Kaspar Willam

Authors
  1. Andreas Dietsche
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  2. Paul Steinmann
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  3. Kaspar Willam
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Editor information

Editors and Affiliations

  1. University Joseph Fourier, Grenoble, France

    Jean-Paul Boehler

  2. University of Oklahoma, Norman, USA

    Akhtar S. Khan

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© 1991 Elsevier Science Publishers Ltd

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Dietsche, A., Steinmann, P., Willam, K. (1991). Micropolar Elasto-Plasticity and Its Role in Localization Analysis. In: Boehler, JP., Khan, A.S. (eds) Anisotropy and Localization of Plastic Deformation. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3644-0_11

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  • DOI: https://doi.org/10.1007/978-94-011-3644-0_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-688-1

  • Online ISBN: 978-94-011-3644-0

  • eBook Packages: Springer Book Archive

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