Effective equations for localization and shear band formation

Theodoros Katsaounis*, Athanasios E. Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We develop a quantitative criterion determining the onset of localization and shear band formation at high strain-rate deformations of metals. We introduce an asymptotic procedure motivated by the theory of relaxation and the Chapman-Enskog expansion and derive an effective equation for the evolution of the strain rate, consisting of a second order nonlinear diffusion regularized by fourth order effects and with parameters determined by the degree of thermal softening, strain hardening, and strain-rate sensitivity. The nonlinear diffusion equation changes type across a threshold in the parameter space from forward parabolic to backward parabolic, what highlights the stable and unstable parameter regimes. The fourth order effects play a regularizing role in the unstable region of the parameter range.

Original languageEnglish (US)
Pages (from-to)1618-1643
Number of pages26
JournalSIAM Journal on Applied Mathematics
Issue number6
StatePublished - 2009
Externally publishedYes


  • Chapman-Enskog expansion
  • Localization
  • Shear band
  • Thermoviscoplasticity

ASJC Scopus subject areas

  • Applied Mathematics


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