Forbidden Strains and Stresses in Mechanochemistry of Chemical Reaction Fronts

  • Alexander B. Freidin
  • Leah L. Sharipova
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)


The influence of stresses and strains on a chemical reaction rate and a chemical reaction front velocity is studied basing on the concept of the chemical affinity tensor. The notion of forbidden zones formed by strains or stresses at which the reaction cannot go is discussed. Examples of forbidden zones are constructed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



Gérard Maugin was one of those who determined the face of modern mechanics, and Alexander Freidin was privileged to communicate with him and to have a very supporting and encouraging discussions. Leah Sharipova spent six months in Gérard Maugin’s laboratory where she learned important lessons of a deep scientific research. She will always remember his paternal relation. The subject of the present paper reflects the discussions of those times and now, with feeling deep sorrow, we dedicate this paper to memory of Gérard Maugin.

This work was supported by the Russian Foundation for Basic Research (Grants No 16-01-00815, No 17-51-12055).


  1. Abeyaratne R, Knowles J (2006) Evolution of Phase Transitions. A Continuum Theory. Cambridge University Press, CambridgeGoogle Scholar
  2. Bower AF, Guduru PR, Chason E (2015) Analytical solutions for composition and stress in spherical elastic-plastic lithium-ion electrode particles containing a propagating phase boundary. International Journal of Solids and Structures 69-70:328–342Google Scholar
  3. Brassart L, Suo Z (2013) Reactive flow in solids. Journal of the Mechanics and Physics of Solids 61(1):61–77Google Scholar
  4. Cui Z, Gao F, Qu J (2012) A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries. Journal of the Mechanics and Physics of Solids 60(7):1280–1295Google Scholar
  5. Deal BE, Grove AS (1965) General relationship for the thermal oxidation of silicon. Journal of Applied Physics 36(12):3770–3778Google Scholar
  6. Freidin A (2014) Chemical affinity tensor and stress-assist chemical reactions front propagation in solids. In: ASME 2013 International Mechanical Engineering Congress and Exposition, November 13-21, 2013, San Diego, California, USAGoogle Scholar
  7. Freidin A, Morozov N, Petrenko S, Vilchevskaya E (2016a) Chemical reactions in spherically symmetric problems of mechanochemistry. Acta Mechanica 227(1):43–56Google Scholar
  8. Freidin AB (2007) On new phase inclusions in elastic solids. ZAMM 87(2):102–116Google Scholar
  9. Freidin AB (2009) On chemical reaction fronts in nonlinear elastic solids. In: Indeitsev D, Krivtsov AM (eds) Proceedings of XXXVII International Summer School-Conference Advanced Problems in Mechanics, pp 231–237Google Scholar
  10. Freidin AB (2015) On the chemical affinity tensor for chemical reactions in deformable materials. Mechanics of Solids 50(3):260–285Google Scholar
  11. Freidin AB, Sharipova LL (2006) On a model of heterogenous deformation of elastic bodies by the mechanism of multiple appearance of new phase layers. Meccanica 41(3):321–339Google Scholar
  12. Freidin AB, Vilchevskaya EN, Sharipova LL (2002) Two-phase deformations within the framework of phase transition zones. Theoretical and Applied Mechanics 28-29:149–172Google Scholar
  13. Freidin AB, Vilchevskaya EN, Korolev IK (2014) Stress-assist chemical reactions front propagation in deformable solids. International Journal of Engineering Science 83:57–75Google Scholar
  14. Freidin AB, Korolev IK, Aleshchenko SP, Vilchevskaya EN (2016b) Chemical affinity tensor and chemical reaction front propagation: theory and fe-simulations. International Journal of Fracture 202(2):245–259Google Scholar
  15. Glansdorff P, Prigogine I (1971) Thermodynamic Theory of Stability and Fluctuation. Wiley- Interscience, New YorkGoogle Scholar
  16. Grinfeld M (1991) Thermodynamic Methods in the Theory of Heterogeneous Systems. Longman, New YorkGoogle Scholar
  17. Gurtin M (2000) Configurational Forces as Basic Concepts of Continuum Physics. Springer, New YorkGoogle Scholar
  18. Jia Z, Li T (2015) Stress-modulated driving force for lithiation reaction in hollow nano-anodes. Journal of Power Sources 275:866–876Google Scholar
  19. Kao DB, McVittie JP, Nix WD, Saraswat KC (1988) Two-dimensional thermal-oxidation of silicon – II. modeling stress effects in wet oxides. IEEE Transactions On Electron Devices 35(1):25–37Google Scholar
  20. Kienzler R, Herrmann G (2000) Mechanics in Material Space with Application to Defect and Fracture Mechanics. Springer, BerlinGoogle Scholar
  21. Knyazeva AG (2003) Cross effects in solid media with diffusion. Journal of Applied Mechanics and Technical Physics 44(3):373–384Google Scholar
  22. Kunin I (1983) Elastic Media with Microstructure. Springer, BerlinGoogle Scholar
  23. Levitas VI, Attariani H (2014) Anisotropic compositional expansion in elastoplastic materials and corresponding chemical potential: Large-strain formulation and application to amorphous lithiated silicon. Journal of the Mechanics and Physics of Solids 69:84–111Google Scholar
  24. Loeffel K, Anand L (2011) A chemo-thermo-mechanically coupled theory for elastic-viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction. International Journal of Plasticity 27(9):1409–1431Google Scholar
  25. Maugin G (1993) Material Inhomogeneities in Elasticity. Chapman & Hall, LondonGoogle Scholar
  26. Maugin G (2010) Configurational Forces. Thermomechanics, Physics, Mathematics, and Numerics. CRC, Boca RatonGoogle Scholar
  27. Morozov NF, Freidin AA (1998) Phase transition zones and phase transformations of elastic solids under different stress states. Proc Steklov Mathe Inst 223:220–232Google Scholar
  28. Prigogine I, Defay R (1988) Chemical Thermodynamics. Longmans, Green, LondonGoogle Scholar
  29. Rafferty CS (1990) Stress effects in silicon oxidation - simulation and experiments. PhD thesis, Stanford UniversityGoogle Scholar
  30. Rao VS, Hughes TJR (2000) On modelling thermal oxidation of Silicon I: theory. International Journal for Numerical Methods in Engineering 47(1-3):341–358Google Scholar
  31. Rao VS, Hughes TJR, Garikipati K (2000) On modelling thermal oxidation of Silicon II: numerical aspects. International Journal for Numerical Methods in Engineering 47(1-3):359–377Google Scholar
  32. Rusanov AI (2005) Surface thermodynamics revisited. Surface Science Reports 58(5):111–239Google Scholar
  33. Rusanov AI (2006) Thermodynamic Foundations of Mechanochemistry. Nauka, St. PetersburgGoogle Scholar
  34. Sutardja P, Oldham WG (2005) Modeling of stress effects in silicon oxidation. IEEE Transactions on Electron Devices 36(11):2415–2421Google Scholar
  35. Toribio J, Kharin V, Lorenzo M, Vergara D (2011) Role of drawing-induced residual stresses and strains in the hydrogen embrittlement susceptibility of prestressing steels. Corrosion Science 53(10):3346–3355Google Scholar
  36. Wilmanski K (1998) Thermomechanics of Continua. Springer, BerlinGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Problems in Mechanical Engineering of the Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Peter the Great St.Petersburg Polytechnic UniversitySt. PetersburgRussia

Personalised recommendations