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On the Dislocation Density Tensor in the Cosserat Theory of Elastic Shells

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Advanced Methods of Continuum Mechanics for Materials and Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 60))

Abstract

We consider the Cosserat continuum in its finite strain setting and discuss the dislocation density tensor as a possible alternative curvature strain measure in three-dimensional Cosserat models and in Cosserat shell models. We establish a close relationship (one-to-one correspondence) between the new shell dislocation density tensor and the bending-curvature tensor of 6-parameter shells.

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Authors and Affiliations

  1. Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann Str. 9, 45127, Essen, Germany

    Mircea Bîrsan

  2. Department of Mathematics, Alexandru Ioan Cuza University of Iaşi, Blvd. Carol I, no. 11, 700506, Iaşi, Romania

    Mircea Bîrsan

  3. Head of Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann Str. 9, 45127, Essen, Germany

    Patrizio Neff

Authors
  1. Mircea Bîrsan
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  2. Patrizio Neff
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Correspondence to Mircea Bîrsan .

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Editors and Affiliations

  1. Institute of Mechanics IFME, Otto von Guericke University, Magdeburg, Sachsen-Anhalt, Germany

    Konstantin Naumenko

  2. Otto von Guericke University, Institute of Mechanics, Magdeburg, Germany

    Marcus Aßmus

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Bîrsan, M., Neff, P. (2016). On the Dislocation Density Tensor in the Cosserat Theory of Elastic Shells. In: Naumenko, K., Aßmus, M. (eds) Advanced Methods of Continuum Mechanics for Materials and Structures. Advanced Structured Materials, vol 60. Springer, Singapore. https://doi.org/10.1007/978-981-10-0959-4_22

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  • DOI: https://doi.org/10.1007/978-981-10-0959-4_22

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  • Print ISBN: 978-981-10-0958-7

  • Online ISBN: 978-981-10-0959-4

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