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Initial response of a micro-polar hypoplastic material under plane shearing

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Mathematics and Mechanics of Granular Materials

Abstract

The behavior of an infinite strip of a micro-polar hypoplastic material located between two parallel plates under plane shearing is investigated. The evolution equation of the stress tensor and the couple-stress tensor is described using tensor-valued functions, which are nonlinear and positively homogeneous of first order in the rate of deformation and the rate of curvature. For the initial response of the sheared layer an analytical solution is derived and discussed for different micro-polar boundary conditions at the bottom and top surfaces of the layer. It is shown that polar quantities appear within the shear layer from the beginning of shearing with the exception of zero couple stresses prescribed at the boundaries.

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Authors and Affiliations

  1. Institute of General Mechanics, Graz University of Technology, A-8010, Graz, Austria

    Erich Bauer

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  1. Erich Bauer
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Editors and Affiliations

  1. University of Wollongong, Australia

    James M. Hill

  2. McGill Univeristy, Montreal, ON, Canada

    A.P.S. Selvadurai

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Bauer, E. (2005). Initial response of a micro-polar hypoplastic material under plane shearing. In: Hill, J.M., Selvadurai, A. (eds) Mathematics and Mechanics of Granular Materials. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4183-7_3

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  • DOI: https://doi.org/10.1007/1-4020-4183-7_3

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  • Print ISBN: 978-1-4020-3781-8

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