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A Stochastic Galerkin Method for the Fokker–Planck–Landau Equation with Random Uncertainties Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Localization of Adiabatic Deformations in Thermoviscoplastic Materials

Authors : Min-Gi Lee, Theodoros Katsaounis, Athanasios E. Tzavaras

Published in: Theory, Numerics and Applications of Hyperbolic Problems II

Publisher: Springer International Publishing

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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.

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previous chapter Mathematical Theory of Two-Phase Geochemical Flow with Chemical Species
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Metadata
Title
Localization of Adiabatic Deformations in Thermoviscoplastic Materials
Authors
Min-Gi Lee
Theodoros Katsaounis
Athanasios E. Tzavaras
Copyright Year
2018
Book
Theory, Numerics and Applications of Hyperbolic Problems II

Print ISBN: 978-3-319-91547-0

Electronic ISBN: 978-3-319-91548-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91548-7_21

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