The transition of qualitative behaviour between rigid perfectly plastic and viscoplastic solutions

Sergei Alexandrov, Wiktoria Miszuris

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5 Citations (SciVal)

Abstract

An incompressible rigid viscoplastic material is confined between two planar plates which are inclined at an angle 2α. In a certain sense, the viscoplastic model adopted approaches rigid perfectly plastic models as the equivalent strain rate approaches zero and infinity. The plates intersect in a hinged line, and the angle α slowly decreases from an initial value. The maximum-friction law is assumed at the plates. A boundary value problem for the flow of the material is formulated, and its asymptotic analysis is carried out near the friction surface. The solution may exhibit sliding or sticking at the plates. Solutions which exhibit sticking may have a rigidly rotating zone in the region adjacent to the plates. Solutions which exhibit sliding are singular. Solutions which exhibit sticking may also be singular under certain conditions. In general, there are several critical values of α at which changes in the qualitative behaviour of the solution occur. Qualitative features of the solution found are compared with those of the solution for the classical rigid plastic model.
Original languageEnglish
Pages (from-to)67–81
Number of pages14
JournalJournal of Engineering Mathematics
Volume97
Issue number1
Early online date13 Jun 2015
DOIs
Publication statusPublished - 01 Apr 2016

Keywords

  • friction surface
  • saturation stress
  • singularity
  • sticking/sliding
  • viscoplasticity

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