Skip to main content

Modeling and Numerical Simulation of Nonclassical Effects of Waves, Including Phase Transition Front

  • Chapter
Universality of Nonclassical Nonlinearity

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Abeyaratne and J.K. Knowles, Kinetic relations and the propagation of phase boundaries in solids, Arch. Rat. Mech. Anal. 114, 119-154 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  2. J.A. Shaw and S. Kyriakydes, Thermomechanical aspects of NiTi, J. Mech. Phys. Solids 43, 1243-1281(1995).

    Article  ADS  Google Scholar 

  3. J.A. Shaw and S. Kyriakydes, On the nucleation and propagation of phase transformation fronts in a NiTi alloy, Acta Mater. 45, 673-700 (1997).

    Article  Google Scholar 

  4. B.C. Goo and C. Lexcellent, Micromechnics-based modeling of two-way memory effect of a single-crystalline shape-memory alloy, Acta Mater. 45, 727-737 (1997).

    Article  Google Scholar 

  5. R. Abeyaratne, K. Bhattacharya, and J.K. Knowles, Strain-energy functions with local minima: Modeling phase transformations using finite thermoelasticity, in: Nonlinear Elasticity: Theory and Application, edited by Y. Fu and R. W. Ogden (Cambridge University Press, Cambridge, UK, 2001), pp. 433-490.

    Chapter  Google Scholar 

  6. R. Abeyaratne and J.K. Knowles, On the driving traction acting on a surface of strain discontinuity in a continuum, J. Mech. Phys. Solids 38, 345-360 (1990).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. L. Truskinovsky, Dynamics of nonequilibrium phase boundaries in a heat conducting nonlinear elastic medium, J. Appl. Math. Mech. (PMM) 51, 777-784 (1987).

    Article  MathSciNet  Google Scholar 

  8. G.A. Maugin and C. Trimarco, The dynamics of configurational forces at phase-transition fronts, Meccanica 30, 605-619 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  9. J.K. Knowles, Stress-induced phase transitions in elastic solids, Comp. Mech. 22, 429-436 (1999).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. W. Muschik, Fundamentals of nonequilibrium thermodynamics, in: nonequilibrium Thermodynamics with Application to Solids, edited by W. Muschik (Springer, Wien, 1993), pp. 1-63.

    Google Scholar 

  11. Y.C. Chen and D.C. Lagoudas, Impact induced phase transformation in shape memory alloys, J. Mech. Phys. Solids 48, 275-300 (2000).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. A. Bekker, J.C. Jimenez-Victory, P. Popov, and D.C. Lagoudas, Impact induced propagation of phase transformation in a shape memory alloy rod, Int. J. Plasticity 18, 1447-1479 (2002).

    Article  MATH  Google Scholar 

  13. D.C. Lagoudas, K. Ravi-Chandar, K. Sarh, and P. Popov, Dynamic loading of polycrystalline shape memory alloy rods, Mech. Mater. 35, 689-716 (2003).

    Article  Google Scholar 

  14. J.A. Shaw, A thermomechanical model for a 1-D shape memory alloy wire with propagating instabilities, Int. J. Solids Struct. 39, 1275-1305 (2002).

    Article  MATH  Google Scholar 

  15. V. Stoilov and A. Bhattacharyya, A theoretical framework of one-dimensional sharp phase fronts in shape memory alloys, Acta Mater. 50, 4939-4952 (2002).

    Article  Google Scholar 

  16. M.A. Grinfeld, Thermodynamic Methods in the Theory of Heterogeneous Systems (Longman, London, 1991).

    Google Scholar 

  17. P. Cermelli and S. Sellers, Multi-phase equilibrium of crystalline solids, J. Mech. Phys. Solids 48, 765-796 (2000).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. A. Berezovski and G. A. Maugin, On the thermodynamic conditions at moving phase-transition fronts in thermoelastic solids, J. Non-Equilib. Thermodyn. 29, 37-51 (2004).

    Article  MATH  ADS  Google Scholar 

  19. X. Zhong, T.Y. Hou, and P.G. LeFloch, Computational methods for propagating phase boundaries, J. Comp. Phys. 124, 192-216 (1996).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. R.J. LeVeque, Wave propagation algorithms for multidimensional hyperbolic systems, J. Comp. Phys. 131, 327-353 (1997).

    Article  MATH  ADS  Google Scholar 

  21. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems (Cambridge University Press, Cambridge, UK, 2002).

    Book  MATH  Google Scholar 

  22. A. Berezovski and G.A. Maugin, Simulation of thermoelastic wave propagation by means of a composite wave-propagation algorithm, J. Comp. Phys. 168, 249-264 (2001).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. A. Berezovski, J. Engelbrecht, and G.A. Maugin, Thermoelastic wave propagation in inhomogeneous media, Arch. Appl. Mech. 70, 694-706 (2000).

    Article  MATH  Google Scholar 

  24. G.A. Maugin, Material Inhomogeneities in Elasticity (Chapman and Hall, London, 1993).

    MATH  Google Scholar 

  25. G.A. Maugin, Thermomechanics of inhomogeneous - heterogeneous systems: application to the irreversible progress of two- and three-dimensional defects, ARI 50, 41-56 (1997).

    Google Scholar 

  26. G.A. Maugin, On shock waves and phase-transition fronts in continua, ARI 50, 141-150 (1998).

    Article  Google Scholar 

  27. W. Muschik and A. Berezovski, Thermodynamic interaction between two discrete systems in non-equilibrium, J. Non-Equilib. Thermodyn. 29, 237-255 (2004).

    Article  MATH  ADS  Google Scholar 

  28. H.B. Callen, Thermodynamics (Wiley & Sons, New York, 1960).

    MATH  Google Scholar 

  29. D.S. Bale, R.J. LeVeque, S. Mitran, and J.A. Rossmanith, A wave propagation method for conservation laws and balance laws with spatially varying flux functions, SIAM J. Sci. Comp. 24, 955-978 (2003).

    Article  MathSciNet  Google Scholar 

  30. A. Berezovski and G.A. Maugin, Thermoelastic wave and front propagation, J. Thermal Stresses 25, 719-743 (2002).

    Article  MathSciNet  Google Scholar 

  31. A. Berezovski and G.A. Maugin, Thermodynamics of discrete systems and martensitic phase transition simulation, Technische Mechanik 22, 118-131 (2002).

    Google Scholar 

  32. A. Berezovski, J. Engelbrecht, and G.A. Maugin, A thermodynamic approach to modeling of stress-induced phase-transition front propagation in solids, in: Mechanics of Martensitic Phase Transformation in Solids, edited by Q.P. Sun (Kluwer, Dordrecht, 2002), pp. 19-26.

    Google Scholar 

  33. J.C. Escobar and R.J. Clifton, On pressure-shear plate impact for studying the kinetics of stress-induced phase-transformations, Mat. Sci. Eng. A170, 125-142 (1993).

    Google Scholar 

  34. Y. Emel'yanov, S. Golyandin, N.P. Kobelev, S. Kustov, S. Nikanorov, G. Pugachev, K. Sapozhnikov, A. Sinani, Ya.M. Soifer, J. Van Humbeeck, and R. De Batist, Detection of shock-wave-induced internal stresses in Cu-Al-Ni shape memory alloy by means of acoustic technique, Scripta mater. 43,1051-1057 (2000).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Berezovski, A., Engelbrecht, J., Maugin, G.A. (2006). Modeling and Numerical Simulation of Nonclassical Effects of Waves, Including Phase Transition Front. In: Delsanto, P.P. (eds) Universality of Nonclassical Nonlinearity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35851-2_13

Download citation

Publish with us

Policies and ethics