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Some Results Concerning the Mathematical Treatment of Finite Plasticity

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Deformation and Failure in Metallic Materials

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 10))

Abstract

The initial-boundary value problems arising in the context of finite elasto-plasticity models relying on the multiplicative split F = Fe F p are investigated. First, we present such a model based on the elastic Eshelby tensor. We highlight the behaviour of the system at frozen plastic flow. It is shown how the direct methods of variations can be applied to the resulting boundary value problem. Next the coupling with a viscoplastic flow rule is discussed. With stringent elastic stability assumptions and with a nonlocal extension in space local existence in time can be proved.

Subsequently, a new model is introduced suitable for small elastic strains. A key feature of the model is the introduction of an independent field of elastic rotations R e . An evolution equation for R e is presented which relates R e to F e . The equilibrium equations at frozen plastic flow are now linear elliptic leading to a local existence and uniqueness result without further stability assumptions or other modifications. An extended Korn’s first inequality is used taking the plastic incompatibility of F p into account.

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Authors and Affiliations

  1. Department of Mathematics, Darmstadt University of Technology, Schlossgartenstr. 7, D-64289, Darmstadt, Germany

    Patrizio Neff

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  1. Patrizio Neff
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  1. Department of Mechanics, Technical University of Darmstadt, Hochschulstr. 1, D-64289, Darmstadt, Germany

    Kolumban Hutter  & Herbert Baaser  & 

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Neff, P. (2003). Some Results Concerning the Mathematical Treatment of Finite Plasticity. In: Hutter, K., Baaser, H. (eds) Deformation and Failure in Metallic Materials. Lecture Notes in Applied and Computational Mechanics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36564-8_10

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  • DOI: https://doi.org/10.1007/978-3-540-36564-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05649-9

  • Online ISBN: 978-3-540-36564-8

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