A Saint-Venant principle for shear band localization

C. O. Horgan*, W Edward Olmstead

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A type of Saint-Venant principle is derived for a two-dimensional model of shear band formation in thermoviscoplastic solids. To establish that the thermal energy generated during the formation process remains highly localized, a spatially decaying upper bound on the temperature is derived. It is found that the temperature bound decays exponentially along the direction perpendicular to the band, with a rate that decreases in time. The result is established by using maximum principles for second-order nonlinear parabolic partial differential equations.

Original languageEnglish (US)
Pages (from-to)807-814
Number of pages8
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number5
StatePublished - Sep 1 2003


  • Second-order nonlinear parabolic partial differential equations
  • Shear band localization
  • Spatial decay of temperature

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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