Phase space of solids under deformation

Yu V. Grinyaev, S. G. Psakhie, N. V. Chertova

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This paper analyzes sequences of various strain-induced defects. The defect is considered as an internal stress source, and hence the deformation is described by a phase curve in the 2D stress-strain space. Notice that the defect as a local discontinuity has eigenenergy and this, if taken into account, increases the phase space dimension because of the parameters to be introduced to characterize defect structures formed under deformation. Analysis of the potential energy of a deformed system makes it possible to elucidate the origin of various defects and to introduce the notion of strain levels in the phase space. Thus, we can distinguish strain levels for which the nature and the number of parameters of the system remain unchanged under deformation and associate the transition of the deformed system from one strain level to another with qualitative and quantitative changes. In this context, the deformation from elasticity to fracture is described by the phase space curve and the phase space dimension is determined, in addition to stresses and strains, by the parameters of defect structures formed under deformation. A standard stress-strain curve is the projection of the phase space curve on the stress-strain plane.

Original languageEnglish
Pages (from-to)228-232
Number of pages5
JournalPhysical Mesomechanics
Issue number5-6
Publication statusPublished - 2008


  • defects
  • gauge theory
  • phase space
  • strain levels

ASJC Scopus subject areas

  • Mechanics of Materials
  • Materials Science(all)
  • Condensed Matter Physics
  • Surfaces and Interfaces

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