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Invariant Dissipative Mechanisms for the Spatial Motion of Rods Suggested by Artificial Viscosity

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Abstract

The introduction of artificial viscosity into the partial differential equations of mechanics is often useful for both analytic and numerical studies. The traditional forms of artificial viscosity, originally designed to treat problems for fluids, when applied to problems for solids often lead to equations describing material properties that are not invariant under rigid motions. Consequently, for rapidly rotating bodies, artificial viscosity could produce serious errors. In this paper it is shown how to introduce artificial viscosity in a properly invariant way, and that the resulting systems have a rich and attractive structure, which beckons analysis.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Physical Science and Technology, and Institute for Systems Research, University of Maryland, College Park, MD, 20742-4015, U.S.A.

    Stuart S. Antman

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  1. Stuart S. Antman
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Antman, S.S. Invariant Dissipative Mechanisms for the Spatial Motion of Rods Suggested by Artificial Viscosity. Journal of Elasticity 70, 55–64 (2003). https://doi.org/10.1023/B:ELAS.0000005549.19254.17

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  • DOI: https://doi.org/10.1023/B:ELAS.0000005549.19254.17

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