Localization of adiabatic deformations in thermoviscoplastic materials

Min Gi Lee; Theodoros Katsaounis; Athanasios E. Tzavaras

doi:10.1007/978-3-319-91548-7_21

Localization of adiabatic deformations in thermoviscoplastic materials

Min Gi Lee, Theodoros Katsaounis, Athanasios E. Tzavaras

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Theory, Numerics and Applications of Hyperbolic Problems II
Editors	Michael Westdickenberg, Christian Klingenberg
Publisher	Springer New York LLC
Pages	269-280
Number of pages	12
ISBN (Print)	9783319915470
DOIs	https://doi.org/10.1007/978-3-319-91548-7_21
State	Published - 2018
Event	16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany Duration: 1 Aug 2016 → 5 Aug 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	237
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
Country/Territory	Germany
City	Aachen
Period	1/08/16 → 5/08/16

Keywords

Geometric singular perturbations
Localization
Self similar solutions
Shear bands

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10.1007/978-3-319-91548-7_21

Cite this

Lee, M. G., Katsaounis, T., & Tzavaras, A. E. (2018). Localization of adiabatic deformations in thermoviscoplastic materials. In M. Westdickenberg, & C. Klingenberg (Eds.), Theory, Numerics and Applications of Hyperbolic Problems II (pp. 269-280). (Springer Proceedings in Mathematics and Statistics; Vol. 237). Springer New York LLC. https://doi.org/10.1007/978-3-319-91548-7_21

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title = "Localization of adiabatic deformations in thermoviscoplastic materials",

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.",

keywords = "Geometric singular perturbations, Localization, Self similar solutions, Shear bands",

author = "Lee, {Min Gi} and Theodoros Katsaounis and Tzavaras, {Athanasios E.}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 ; Conference date: 01-08-2016 Through 05-08-2016",

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doi = "10.1007/978-3-319-91548-7_21",

language = "English",

isbn = "9783319915470",

series = "Springer Proceedings in Mathematics and Statistics",

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Lee, MG, Katsaounis, T & Tzavaras, AE 2018, Localization of adiabatic deformations in thermoviscoplastic materials. in M Westdickenberg & C Klingenberg (eds), Theory, Numerics and Applications of Hyperbolic Problems II. Springer Proceedings in Mathematics and Statistics, vol. 237, Springer New York LLC, pp. 269-280, 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016, Aachen, Germany, 1/08/16. https://doi.org/10.1007/978-3-319-91548-7_21

Localization of adiabatic deformations in thermoviscoplastic materials. / Lee, Min Gi; Katsaounis, Theodoros; Tzavaras, Athanasios E.
Theory, Numerics and Applications of Hyperbolic Problems II. ed. / Michael Westdickenberg; Christian Klingenberg. Springer New York LLC, 2018. p. 269-280 (Springer Proceedings in Mathematics and Statistics; Vol. 237).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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Localization of adiabatic deformations in thermoviscoplastic materials

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