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A view on the variational setting of micropolar continua

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Continuous and Discontinuous Modelling of Cohesive-Frictional Materials

Part of the book series: Lecture Notes in Physics ((LNP,volume 568))

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Abstract

The objective of this contribution is to elaborate upon the variational setting for micropolar continua with constrained and unconstrained rotations. To this end, several mixed variational principles and their regularizations are considered for both the geometrically linear and nonlinear case. The interrelation between the di.erent formulations are highlighted. The most advantageous result is obtained by translating the insight gained for the geometrically linear case to the geometrically nonlinear case involving large strains and large rotations. It turns out that a particular micropolar description involves standard constitutive models for the symmetric stress part together with a nonsymmetric penalty stress thus circumventing the cumbersome need to describe the constitutive law in terms of a nonsymmetric strain measure.

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Authors and Affiliations

  1. Chair for Applied Mechanics, University of Kaiserslautern, 67663, Kaiserslautern, Germany

    P. Steinmann

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  1. P. Steinmann
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Editor information

Editors and Affiliations

  1. Institute of Geotechnical Engineering, University of Stuttgart, Pfaffenwaldring 35, 70569, Stuttgart, Germany

    Pieter A. Vermeer

  2. Institute of Computer Applications 1, University of Stuttgart, Pfaffenwaldring 27, 70569, Stuttgart, Germany

    Hans J. Herrmann  & Stefan Luding  & 

  3. Institute of Applied Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    Wolfgang Ehlers  & Stefan Diebels  & 

  4. Institute of Structural Mechanics, University of Stuttgart, Pfaffenwaldring 27, 70569, Stuttgart, Germany

    Ekkehard Ramm

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© 2001 Springer-Verlag Berlin Heidelberg

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Steinmann, P. (2001). A view on the variational setting of micropolar continua. In: Vermeer, P.A., Herrmann, H.J., Luding, S., Ehlers, W., Diebels, S., Ramm, E. (eds) Continuous and Discontinuous Modelling of Cohesive-Frictional Materials. Lecture Notes in Physics, vol 568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44424-6_6

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  • DOI: https://doi.org/10.1007/3-540-44424-6_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41525-1

  • Online ISBN: 978-3-540-44424-4

  • eBook Packages: Springer Book Archive

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