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Some Aspects of Adiabatic Shear Bands

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Metastability and Incompletely Posed Problems

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 3))

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Abstract

A one dimensional continuum formulation for the initiation and growth of adiabatic shear bands is reviewed, including some remarks on the underlying assumptions. A short description of some perturbation calculations introduces the idea of stress collapse and band formation as a bifurcation from homogeneous deformation. An approach for estimating the critical time of collapse for infinitesimal perturbations is introduced. Steady solutions are exhibited and their interpretation as central boundary layers is suggested. Finally it is shown that in a certain limit shear bands occur following a hyperbolic to elliptic transition in the governing equation. In a concluding remark dipolar plasticity is introduced as a possible alternative continuum description.

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References

Material Aspects, Occurance and Qualitative Description

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Author information

Authors and Affiliations

  1. Ballistic Research Laboratory, Aberdeen Proving Ground, MD, 21005, USA

    T. W. Wright

Authors
  1. T. W. Wright
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Stuart S. Antman

  2. School of Mathematics and Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, USA

    J. L. Ericksen

  3. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    David Kinderlehrer

  4. FB9-Hermann Föttinger Institut, Technical University, Berlin, Germany

    Ingo Müller

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© 1987 Springer-Verlag New York Inc.

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Wright, T.W. (1987). Some Aspects of Adiabatic Shear Bands. In: Antman, S.S., Ericksen, J.L., Kinderlehrer, D., Müller, I. (eds) Metastability and Incompletely Posed Problems. The IMA Volumes in Mathematics and Its Applications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8704-6_22

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  • DOI: https://doi.org/10.1007/978-1-4613-8704-6_22

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8706-0

  • Online ISBN: 978-1-4613-8704-6

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