Localization of adiabatic deformations in thermoviscoplastic materials

Min Gi Lee*, Theodoros Katsaounis, Athanasios E. Tzavaras

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 languageEnglish (US)
Title of host publicationTheory, Numerics and Applications of Hyperbolic Problems II
EditorsMichael Westdickenberg, Christian Klingenberg
PublisherSpringer New York LLC
Number of pages12
ISBN (Print)9783319915470
StatePublished - 2018
Event16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany
Duration: Aug 1 2016Aug 5 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Conference16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016


  • Geometric singular perturbations
  • Localization
  • Self similar solutions
  • Shear bands

ASJC Scopus subject areas

  • General Mathematics


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