On Kinetic Nature of Hysteresis Phenomena in Stress-Induced Phase Transformations

  • A. B. FreidinEmail author
  • Victor A. Eremeyev
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 103)


A simplest model is developed which demonstrates that hysteresis phenomena in stress-induced phase transformations may have a kinetic nature and follow from the discrepancy between strain rate and characteristic rate of the new phase growth.



A. B. Freidin greatly appreciates the financial support of the Russian Foundation for Basic Research (Grant No. 16-01-00815).


  1. 1.
    Shaw, J.A., Kyriakides, S.: Thermomechanical aspects on NiTi. J. Mech. Phys. Solids 43(8), 1243–1281 (1995)CrossRefGoogle Scholar
  2. 2.
    Ma, J., Karaman, I., Noebe, R.D.: High temperature shape memory alloys. Int. Mater. Rev. 55(5), 257–315 (2010)CrossRefGoogle Scholar
  3. 3.
    Abeyaratne, R., Knowles, J.K.: Kinetic relations and the propagation of phase boundaries in solids. Arch. Rat. Mech. Anal. 114, 119–154 (1991)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Abeyaratne, R., Knowles, J.K.: Evolution of Phase Transitions. A Continuum Theory. Cambridge, New York; Melbourne et al.: Cambridge University Press, Cambridge (2006)Google Scholar
  5. 5.
    Le, K.C.: On kinetics of hysteresis. Contin. Mech. Thermodyn. 18, 335–342 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ericksen, J.L.: Equilibrium of bars. J. Elast. 5, 191–201 (1975)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Freidin, A.B., Sharipova, L.L.: On a model of heterogenous deformation of elastic bodies by the mechanism of multiple appearance of new phase layers. Meccanica 41, 321–339 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Freidin, A.B.: On a chemical affinity tensor for chemical reactions in deformable solids. Mech. Solids 50(3), 260–285 (2015)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Peter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia
  3. 3.St. Petersburg UniversitySt. PetersburgRussia
  4. 4.Beijing University of Civil Engineering and ArchitectureBeijingChina
  5. 5.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland
  6. 6.Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia

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