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Geometry, Mechanics, and Dynamics pp 61–90Cite as

Finite Elastoplasticity Lie Groups and Geodesics on SL(d)

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Abstract

The notions of nonlinear plasticity with finite deformations is interpreted in the sense of Lie groups. In particular, the plastic tensor P=F −1p is considered as element of the Lie group SL(d). Moreover, the plastic dissipation defines a left-invariant Finsler metric on the tangent bundle of this Lie group. In the case of single crystal plasticity this metric is given interms of the different slip systems and is piecewise affine on each tangent space. For von Mises plasticity the metric is a left-invariant Riemannian metric. A main goal is to study the associated distance metric and the geodesic curves.

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Authors
  1. Alexander Mielke
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Editor information

Editors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, 90089-1191, USA

    Paul Newton

  2. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089-1191, USA

    Paul Newton

  3. Department of Applied and Computational Mathematics Engineering Quadrangle, Princeton University, Princeton, NJ, 08544-1000, USA

    Philip Holmes

  4. Department of Mathematics, University of California, Berkeley, Berkeley, CA, 94720, USA

    Alan Weinstein

Additional information

To Jerry Marsden on the occasion of his 60th birthday

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© 2002 Springer-Verlag New York, Inc.

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Mielke, A. (2002). Finite Elastoplasticity Lie Groups and Geodesics on SL(d). In: Newton, P., Holmes, P., Weinstein, A. (eds) Geometry, Mechanics, and Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-21791-6_2

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  • DOI: https://doi.org/10.1007/0-387-21791-6_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-95518-6

  • Online ISBN: 978-0-387-21791-8

  • eBook Packages: Springer Book Archive

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