Localization of Adiabatic Deformations in Thermoviscoplastic Materials

Min-Gi Lee; Theodoros Katsaounis; Athanasios Tzavaras

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

Localization of Adiabatic Deformations in Thermoviscoplastic Materials

Min-Gi Lee, Theodoros Katsaounis, Athanasios Tzavaras

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

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 (US)
Title of host publication	Theory, Numerics and Applications of Hyperbolic Problems II
Publisher	Springer Nature
Pages	269-280
Number of pages	12
ISBN (Print)	9783319915470
DOIs	https://doi.org/10.1007/978-3-319-91548-7_21
State	Published - Jun 27 2018

Bibliographical note

KAUST Repository Item: Exported on 2021-09-14
Acknowledgements: This research was supported by King Abdullah University of Science and Technology (KAUST).

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

https://repository.kaust.edu.sa/bitstream/10754/628076/1/shbndhyp2016.pdf

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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.",

author = "Min-Gi Lee and Theodoros Katsaounis and Athanasios Tzavaras",

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

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AU - Lee, Min-Gi

AU - Katsaounis, Theodoros

AU - Tzavaras, Athanasios

N1 - KAUST Repository Item: Exported on 2021-09-14 Acknowledgements: This research was supported by King Abdullah University of Science and Technology (KAUST).

PY - 2018/6/27

Y1 - 2018/6/27

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.

UR - http://hdl.handle.net/10754/628076

UR - https://link.springer.com/chapter/10.1007%2F978-3-319-91548-7_21

UR - http://www.scopus.com/inward/record.url?scp=85049438780&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91548-7_21

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

M3 - Conference contribution

AN - SCOPUS:85049438780

SN - 9783319915470

SP - 269

EP - 280

BT - Theory, Numerics and Applications of Hyperbolic Problems II

PB - Springer Nature

ER -

Localization of Adiabatic Deformations in Thermoviscoplastic Materials

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