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The Taylor Estimate of Recoverable Strains in Shape-Memory Polycrystals

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IUTAM Symposium on Transformation Problems in Composite and Active Materials

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 60))

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References

  1. Acerbi, E. and Fusco, N. (1984) Semicontinuity problems in the calculus of variations, Arch. Rat. Mech. Anal. 86, 125–145.

    Article  MathSciNet  Google Scholar 

  2. Avellaneda, M., Cherkaev, A.V., Gibiansky, L.V., Milton, G.W., and Rudelson, M. (1996) A complete characterization of the possible bulk and shear moduli of planar polycrystals, J. Mech. Phys. Solids 44, 1179–1218.

    Google Scholar 

  3. Ball, J.M. and James, R.D. (1987) Fine phase mixtures as minimizers of energy, Arch. Rat. Mech. Anal. 100, 13–52.

    Article  MathSciNet  Google Scholar 

  4. Bhattacharya, K. (1992) Self-accommodation in martensite, Arch. Rat. Mech. Anal. 120, 201–244.

    Article  MATH  Google Scholar 

  5. Bhattacharya, K. (1993) Comparison of the geometrically nonlinear and linear theories of martensitic transformation, Cont. Mech. Thermodyn. 5, 205–242.

    MATH  Google Scholar 

  6. Bhattacharya, K., Firoozye, N.B., James, R.D. and Kohn, R.V. (1994) Restrictions on microstructure, Proc. Roy. Soc. Edinburgh 124A, 843–878.

    MathSciNet  Google Scholar 

  7. Bhattacharya, K. and Kohn, R.V. (1996) Symmetry, texture, and the recoverable strain of shape-memory polycrystals, Acta Mater. 44, 529–542.

    Article  Google Scholar 

  8. Bhattacharya, K. and Kohn, R.V. (1997) Elastic energy minimization and recoverable strains of polycrystalline shape-memory materials, Arch. Rat. Mech. Anal. 139, 99–180.

    Article  MathSciNet  Google Scholar 

  9. Bishop, J.F.W. and Hill, R. (1951) A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, Phil. Mag. 42, 414–427.

    MathSciNet  Google Scholar 

  10. Geymonat, G., Müller, S., and Triantafyllidis, N. (1993) Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity, Arch. Rat. Mech. Anal. 122, 231–290.

    Article  Google Scholar 

  11. Lurie, K.A. and Cherkaev, A.V. (1984) G-closure of some particular sets of admissible material characteristics for the problem of bending of thin plates, J. Optim. Th. Appl. 42, 305–316.

    MathSciNet  Google Scholar 

  12. Saburi, T. and Nenno, S. (1981) The shape memory effect and related phenomena, in H.I. Aaronson et al. (eds.), Proc. Int. Conf. on Solid-Solid Phase Transformations, The Metall. Soc. AIME, New York, pp. 1455–1479.

    Google Scholar 

  13. Shu, Y. C., PhD. Thesis, California Institute of Technology, in preparation.

    Google Scholar 

  14. Shu, Y. C., and Bhattacharya, K. (1997) The effect of texture on the shapememory effect in polycrystals, in preparation.

    Google Scholar 

  15. Šveràk, V. (1992) Rank-one convexity does not imply quasiconvexity, Proc. Royal Soc. Edin. 120A, 185–189.

    Google Scholar 

  16. Taylor, G.I. (1938) Plastic strain in metals, J. Inst. Metals 62, 307–324.

    Google Scholar 

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Author information

Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, 91125, USA

    K. Bhattacharya & Y. C. Shu

  2. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    R. V. Kohn

Authors
  1. K. Bhattacharya
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  2. R. V. Kohn
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  3. Y. C. Shu
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Editor information

Editors and Affiliations

  1. Structural Engineering Department, Cairo University, Giza, Egypt

    Yehia A. Bahei-El-Din

  2. Centre for Composite Materials and Structures, Rensselaer Polytechnic Institute, Troy, NY, USA

    George J. Dvorak

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© 1998 Kluwer Academic Publishers

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Bhattacharya, K., Kohn, R.V., Shu, Y.C. (1998). The Taylor Estimate of Recoverable Strains in Shape-Memory Polycrystals. In: Bahei-El-Din, Y.A., Dvorak, G.J. (eds) IUTAM Symposium on Transformation Problems in Composite and Active Materials. Solid Mechanics and its Applications, vol 60. Springer, Dordrecht. https://doi.org/10.1007/0-306-46935-9_9

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  • DOI: https://doi.org/10.1007/0-306-46935-9_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5122-1

  • Online ISBN: 978-0-306-46935-0

  • eBook Packages: Springer Book Archive

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