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Equilibrium configurations of defective crystals

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References

  1. Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337–403.

    Google Scholar 

  2. Ball, J. M., Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh 88 A (1981), 315–328.

    Google Scholar 

  3. Chipot, M. & D. Kinderlehrer, Equilibrium configurations of crystals, Arch. Rational Mech. Anal. 103 (1988), 237–277.

    Google Scholar 

  4. Ciarlet, P. G. & J. Nečas, Injectivity and self-contact in nonlinear elasticity, Arch. Rational Mech. Anal. 19 (1987), 171–188.

    Google Scholar 

  5. Coleman, B. D. & D. R. Owen, On the thermodynamics of elastic-plastic materials, Arch. Rational Mech. Anal. 59 (1975), 25–51.

    Google Scholar 

  6. Coleman, B. D. & D. R. Owen, Thermodynamics of elastic-plastic materials, Rend. Accad. Naz. Lincei (VIII) Classe di Scienze Fis., Mat., Nat. 61 (1976), 77–81.

    Google Scholar 

  7. Coleman, B. D. & D. R. Owen, On the thermodynamics of elastic-plastic materials with temperature dependent moduli and yield stresses, Arch. Rational Mech. Anal. 70 (1979), 339–354.

    Google Scholar 

  8. Cottrell, A. H., Theory of Crystal Dislocations, Blackie and Son, 1964.

  9. Dacorogna, B., Direct Methods in the Calculus of Variations, Springer, 1989.

  10. Dacorogna, B. & I. Fonseca, A minimization problem involving variation of the domain, Comm. Pure Math. 45 (1992), 871–897.

    Google Scholar 

  11. Dacorogna, B. & J. Moser, On a partial differential equation involving the jacobian determinant, Ann. Inst. H. Poincaré, Anal. Nonlinéaire 7 (1990), 1–26.

    Google Scholar 

  12. Davini, C., A proposal for a continuum theory of defective crystals, Arch. Rational Mech. Anal. 96 (1986), 295–317.

    Google Scholar 

  13. Davini, C. & G. Parry, On defect-preserving deformations in crystals, Int. J. Plasticity 5 (1989), 337–369.

    Google Scholar 

  14. Davini, C. & G. Parry, A complete list of invariants for defective crystals, Proc. Roy. Soc. Lond. A 432 (1991), 341–365.

    Google Scholar 

  15. Del Piero, G. & D. R. Owen, New concepts in the mechanics of fractured continua, Report of Istituto di Meccanica Teorica ed Applicata, Udine, 1990.

  16. Ericksen, J. L., Loading devices and stability of equilibrium, in Nonlinear Elasticity, Academic Press, 1973, 161–173.

  17. Ericksen, J. L., Thermoelastic considerations for continuously dislocated crystals, Proc. Int. Symp. on Mechanics of Dislocations, Houghton, MI, 1983.

  18. Ericksen, J. L., Twinning of crystals I, in Metastability and Incompletely Posed Problems, IMA Vol. in Appl. Math 3 (1987), 77–96.

    Google Scholar 

  19. Fonseca, I., Variational methods for elastic crystals, Arch. Rational Mech. Anal. 97 (1987), 189–220.

    Google Scholar 

  20. Fonseca, I., The lower quasiconvex envelope of the stored energy function for an elastic crystal, J. Math. Pures et Appl. 67 (1988), 175–195.

    Google Scholar 

  21. Fonseca, I., The Wulff Theorem revisited, Proc. Roy. Soc. Lond. A 432 (1991), 125–145.

    Google Scholar 

  22. Fonseca, I. & S. Müller, An uniqueness proof for the Wulff Problem, Proc. Roy. Soc. Edin. A 119 (1991), 125–136.

    Google Scholar 

  23. Fonseca, I. & G. Parry, On a class of invariant integrals, Proc. Roy. Soc. Lond. A 436 (1992), 317–329.

    Google Scholar 

  24. Herring, C., Some theorems on the free energies of crystal surfaces, Phys. Rev. 82 (1951), 87–93.

    Google Scholar 

  25. Kinderlehrer, D., Twinning of crystals II, in Metastability and Incompletely Posed Problems, IMA Vol. in Appl. Math 3 (1987), 185–211.

    Google Scholar 

  26. Marcus, M. & V. J. Mizel, Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational problems, Bull. Amer. Math. Soc. 79 (1973), 790–795.

    Google Scholar 

  27. Read, W. T. Jr., Dislocations in Crystals, McGraw-Hill, 1953.

  28. Ricou, M., The laws of thermodynamics for non-cyclic processes, in New Perspectives in Thermodynamics, ed. J. Serrin, Springer, 1986, 85–91.

  29. Serrin, J., An outline of thermodynamical structure, in New Perspectives in Thermodynamics, ed. J. Serrin, Springer 1986, 3–31.

  30. Tartar, L., Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics: Heriot-Watt Symposium, vol. IV, Res. Notes in Math. 39, Pitman, 1979, 136–212.

    Google Scholar 

  31. Taylor, G. I., The mechanism of plastic deformation of crystals, I, II, Proc. Roy. Soc. A 145 (1934), 362–387, 388–404.

    Google Scholar 

  32. Taylor, J., Existence and structure of solutions to a class of nonelliptic variational problems, Symposia Mathematica 14 (1974), 499–508.

    Google Scholar 

  33. Taylor, J., Unique structure of solutions to a class of nonelliptic variational problems, Proc. Symp. Pure Math., Amer. Math. Soc. 27 (1975), 419–427.

    Google Scholar 

  34. Taylor, J., Crystalline variational problems, Bull. Amer. Math. Soc. 84 (1978), 568–588.

    Google Scholar 

  35. Wulff, G., Zur Frage der Geschwindigkeit des Wachstums und der Auflösung der Kristallflächen, Z. f. Kristallographie 34 (1901), 449–530.

    Google Scholar 

  36. Young, L. C., Generalized surfaces in the calculus of variations I, II, Ann. Math. 43 (1942), 84–103, 530–544.

    Google Scholar 

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Fonseca, I., Parry, G. Equilibrium configurations of defective crystals. Arch. Rational Mech. Anal. 120, 245–283 (1992). https://doi.org/10.1007/BF00375027

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