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Microstructured Materials: Inverse Problems

Part of the book series: Springer Monographs in Mathematics ((SMM))

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Abstract

Possible generalizations of the methods developed in the book are discussed. Evaluation of original physical parameters from solutions of the inverse problems is described.

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References

  1. Berezovski, A., Engelbrecht, J., Maugin, G.A.: Generalized thermomechanics with dual internal variables. Arch. Appl. Mech. 81, 229–240 (2011)

    Article  Google Scholar 

  2. Chen, W., Zhang, X., Cai, X.: A study on modified Szabo’s wave equation modelling of frequency-dependent dissipation in ultrasonic medical imaging. Phys. Scr. T 136, 014014 (2009)

    Article  Google Scholar 

  3. Engelbrecht, J.: Nonlinear Wave Processes of Deformation in Solids. Pitman, London (1983)

    MATH  Google Scholar 

  4. Engelbrecht, J., Ravasoo, A.: From continuum mechanics to applications in the nondestructive testing. Bull. Tech. Univ. Istanb. 47(1–2), 83–103 (1994) (Suhubi Special Issue)

    MATH  Google Scholar 

  5. Engelbrecht, J., Sillat, T.: Wave propagation in dissipative microstructured materials. Proc. Est. Acad. Sci., Phys. Math. 52, 103–114 (2003)

    MathSciNet  MATH  Google Scholar 

  6. Engelbrecht, J., Berezovski, A., Pastrone, F., Braun, M.: Waves in microstructured materials and dispersion. Philos. Mag. 85(33–35), 4127–4141 (2005)

    Article  Google Scholar 

  7. Engelbrecht, J., Janno, J.: Microstructured solids and inverse problems. Rend. Semin. Mat. (Torino) 65, 159–169 (2007)

    MathSciNet  MATH  Google Scholar 

  8. Engelbrecht, J., Pastrone, F., Braun, M., Berezovski, A.: Hierarchies of waves in nonclassical materials. In: Delsanto, P.-P. (ed.) Universality of Nonclassical Nonlinearity: Application to Non-destructive Evaluation and Ultrasonics, pp. 29–47. Springer, New York (2007)

    Google Scholar 

  9. Engelbrecht, J., Ravasoo, A., Janno, J.: Nonlinear acoustic nondestructive evaluation (NDE): qualitative and quantitative effects. Mater. Manuf. Process. 25, 212–220 (2010)

    Article  Google Scholar 

  10. Janno, J., Engelbrecht, J.: Waves in microstructured solids: inverse problems. Wave Motion 43, 1–11 (2005)

    Article  MathSciNet  Google Scholar 

  11. Janno, J., Engelbrecht, J.: Solitary waves in nonlinear microstructured materials. J. Phys. A, Math. Gen. 38, 5159–5172 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Janno, J., Engelbrecht, J.: An inverse solitary wave problem related to microstructured materials. Inverse Probl. 21, 2019–2034 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Janno, J., Engelbrecht, J.: Determining properties of nonlinear microstructured materials by means of solitary waves. In: Lesnic, D. (ed.) Proc. 5th International Conference on Inverse Problems in Engineering, Cambridge, 11–15 July 2005, vol. II, J02. Leeds Univ. Press, Leeds (2005)

    Google Scholar 

  14. Janno, J., Engelbrecht, J.: Inverse problems related to a coupled system of microstructure. Inverse Probl. 24, 045017 (2008)

    Article  MathSciNet  Google Scholar 

  15. Janno, J., Engelbrecht, J.: Identification of microstructured materials by phase and group velocities. Math. Model. Anal. 14, 57–68 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Johnson, P.: Nonequilibrium nonlinear dynamics in solids: state of the art. In: Delsanto, P.-P. (ed.) Universality of Nonclassical Nonlinearity: Application to Non-destructive Evaluations and Ultrasonics, pp. 49–69. Springer, New York (2007)

    Google Scholar 

  17. Krautkrämer, J., Krautkrämer, H.: Ultrasonic Testing of Materials., 4th edn. Springer, Berlin (1990)

    Google Scholar 

  18. Kundu, T. (ed.): Ultrasonic Nondestructive Evaluation: Engineering and Biological Material Characterization. CRC Press, Boca Raton (2004)

    Google Scholar 

  19. Maugin, G.A.: Material Inhomogeneities in Elasticity. Chapman & Hall, London (1993)

    MATH  Google Scholar 

  20. Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  21. Naugolnykh, K., Ostrovsky, L.: Nonlinear Wave Processes in Acoustics. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  22. Randrüüt, M., Braun, M.: On one-dimensional solitary waves in microstructured solids. Wave Motion 47, 217–230 (2010)

    Article  MathSciNet  Google Scholar 

  23. Ross, R.J., Ward, J.C., TenWolde, A.: Identifying bacterially infected oak by stress wave non-destructive evaluation. US DoA, Research Paper FPL-RP-512 (1992)

    Google Scholar 

  24. Shung, K.K., Thieme, G.A. (eds.): Ultrasonic Scattering in Biological Tissues. Springer, New York (1992)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Tallinn, Estonia

    Jaan Janno & Jüri Engelbrecht

Authors
  1. Jaan Janno
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  2. Jüri Engelbrecht
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Correspondence to Jaan Janno .

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© 2011 Springer-Verlag Berlin Heidelberg

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Janno, J., Engelbrecht, J. (2011). Summary. In: Microstructured Materials: Inverse Problems. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21584-1_8

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