Localization of Adiabatic Deformations in Thermoviscoplastic Materials

Min-Gi Lee, Theodoros Katsaounis, Athanasios Tzavaras

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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
PublisherSpringer Nature
Number of pages12
ISBN (Print)9783319915470
StatePublished - Jun 27 2018

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