Encyclopedia of Thermal Stresses

2014 Edition
| Editors: Richard B. Hetnarski

Phase Transitions in Thermoviscoelastic Shells

Reference work entry
DOI: https://doi.org/10.1007/978-94-007-2739-7_915


A phase transition is the transformation of a thermodynamic system from one state of matter to another. In shell structures it consists primarily of a diffusionless displacive change of the material lattice. Such phase transition process can usually be induced by changing the temperature or by applying an external stress. Experiments indicate that the new solid phase nucleates in narrow regions across which large changes occur in some material properties. Thus, the two-phase shell can be regarded as a deformable material surface consisting of two material phases divided by a movable nonmaterial surface curve.


The interest in thin-walled structures undergoing phase transitions (PT) grows recently from their prospective applications in engineering. As examples of such structures, martensitic films and biological membranes can be considered. The stress- and temperature-induced PT are widely observed in thin-walled structures made of superelastic shape memory alloys...

This is a preview of subscription content, log in to check access



The second author (WP) was supported in part by the Polish National Centre of Science, grant DEC-2012/05/D/ST8/02298.


  1. 1.
    Bhattacharya K (2003) Microstructure of martensite: Why it forms and how it gives rise to the shape-memory effect. Oxford University Press, OxfordGoogle Scholar
  2. 2.
    Miyazaki S, Fu YQ, Huang WM (eds) (2009) Thin film shape memory alloys: Fundamentals and device applications. Cambridge University Press, CambridgeGoogle Scholar
  3. 3.
    Abeyaratne R, Knowles JK (2006) Evolution of phase transitions: A continuum theory. Cambridge University Press, CambridgeGoogle Scholar
  4. 4.
    Berezovski A, Engelbrecht J, Maugin GA (2008) Numerical simulation of waves and fronts in inhomogeneous solids. World Scientific, New JerseyMATHGoogle Scholar
  5. 5.
    Eremeyev VA, Pietraszkiewicz W (2004) The non-linear theory of elastic shells with phase transitions. J Elasticity 74(1):67–86MATHMathSciNetGoogle Scholar
  6. 6.
    Libai A, Simmonds JG (1998) The nonlinear theory of elastic shells, 2nd edn. Cambridge University Press, CambridgeMATHGoogle Scholar
  7. 7.
    Chróścielewski J, Makowski J, Pietraszkiewicz W (2004) Statics and dynamics of multi-shells: Nonlinear theory and finite element method (in Polish). Wydawnictwo IPPT PAN, WarszawaGoogle Scholar
  8. 8.
    Pietraszkiewicz W, Eremeyev VA, Konopińska V (2007) Extended non-linear relations of elastic shells undergoing phase transitions. ZAMM 87(2):150–159MATHMathSciNetGoogle Scholar
  9. 9.
    Eremeyev VA, Pietraszkiewicz W (2009) Phase transitions in thermoelastic and thermoviscoelastic shells. Arch Mech 61(1):41–67MATHMathSciNetGoogle Scholar
  10. 10.
    Eremeyev VA, Pietraszkiewicz W (2011) Thermomechanics of shells undergoing phase transition. J Mech Phy Solids 59:1395–1442MATHMathSciNetGoogle Scholar
  11. 11.
    Bhattacharya K, James RD (2005) The material is the machine. Science 307(5706):53–54Google Scholar
  12. 12.
    Pietraszkiewicz W (2011) Refined resultant thermomechanics of shells. Int J Eng Sci 49(10):1112–1124MathSciNetGoogle Scholar
  13. 13.
    Simmonds JG (2011) A classical, nonlinear thermodynamic theory of elastic shells based on a single constitutive assumption. J Elasticity 105(1–2):305–312MATHMathSciNetGoogle Scholar
  14. 14.
    Truesdell C (1984) Rational thermodynamics, 2nd edn. Springer, New YorkMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Victor A. Eremeyev
    • 1
    • 2
  • Wojciech Pietraszkiewicz
    • 3
  1. 1.Otto–von–Guericke University MagdeburgMagdeburgGermany
  2. 2.South Scientific Center of RASci and South Federal UniversityRostov on DonRussia
  3. 3.Institute of Fluid-Flow Machinery, Polish Academy of SciencesGdańskPoland