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    Localization of Adiabatic Deformations in Thermoviscoplastic Materials

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    Type
    Conference Paper
    Authors
    Lee, Min-Gi cc
    Katsaounis, Theodoros
    Tzavaras, Athanasios cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2018-06-27
    Online Publication Date
    2018-06-27
    Print Publication Date
    2018
    Permanent link to this record
    http://hdl.handle.net/10754/628076
    
    Metadata
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    Abstract
    We study an instability occurring at high strain-rate deformations, induced by thermal softening properties of metals, and leading to the formation of shear bands. We consider adiabatic shear deformations of thermoviscoplastic materials and establish the existence of a family of focusing self-similar solutions that capture this instability. The self-similar solutions emerge as the net response resulting from the competition between Hadamard instability and viscosity. Their existence is turned into a problem of constructing a heteroclinic orbit for an associated dynamical system, which is achieved with the help of geometric singular perturbation theory.
    Citation
    Lee M-G, Katsaounis T, Tzavaras AE (2018) Localization of Adiabatic Deformations in Thermoviscoplastic Materials. Springer Proceedings in Mathematics & Statistics: 269–280. Available: http://dx.doi.org/10.1007/978-3-319-91548-7_21.
    Sponsors
    This research was supported by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Springer Nature
    Journal
    Theory, Numerics and Applications of Hyperbolic Problems II
    Conference/Event name
    16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
    DOI
    10.1007/978-3-319-91548-7_21
    Additional Links
    https://link.springer.com/chapter/10.1007%2F978-3-319-91548-7_21
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-91548-7_21
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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