References
Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337–403.
Ball, J. M., Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh 88 A (1981), 315–328.
Chipot, M. & D. Kinderlehrer, Equilibrium configurations of crystals, Arch. Rational Mech. Anal. 103 (1988), 237–277.
Ciarlet, P. G. & J. Nečas, Injectivity and self-contact in nonlinear elasticity, Arch. Rational Mech. Anal. 19 (1987), 171–188.
Coleman, B. D. & D. R. Owen, On the thermodynamics of elastic-plastic materials, Arch. Rational Mech. Anal. 59 (1975), 25–51.
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.
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.
Cottrell, A. H., Theory of Crystal Dislocations, Blackie and Son, 1964.
Dacorogna, B., Direct Methods in the Calculus of Variations, Springer, 1989.
Dacorogna, B. & I. Fonseca, A minimization problem involving variation of the domain, Comm. Pure Math. 45 (1992), 871–897.
Dacorogna, B. & J. Moser, On a partial differential equation involving the jacobian determinant, Ann. Inst. H. Poincaré, Anal. Nonlinéaire 7 (1990), 1–26.
Davini, C., A proposal for a continuum theory of defective crystals, Arch. Rational Mech. Anal. 96 (1986), 295–317.
Davini, C. & G. Parry, On defect-preserving deformations in crystals, Int. J. Plasticity 5 (1989), 337–369.
Davini, C. & G. Parry, A complete list of invariants for defective crystals, Proc. Roy. Soc. Lond. A 432 (1991), 341–365.
Del Piero, G. & D. R. Owen, New concepts in the mechanics of fractured continua, Report of Istituto di Meccanica Teorica ed Applicata, Udine, 1990.
Ericksen, J. L., Loading devices and stability of equilibrium, in Nonlinear Elasticity, Academic Press, 1973, 161–173.
Ericksen, J. L., Thermoelastic considerations for continuously dislocated crystals, Proc. Int. Symp. on Mechanics of Dislocations, Houghton, MI, 1983.
Ericksen, J. L., Twinning of crystals I, in Metastability and Incompletely Posed Problems, IMA Vol. in Appl. Math 3 (1987), 77–96.
Fonseca, I., Variational methods for elastic crystals, Arch. Rational Mech. Anal. 97 (1987), 189–220.
Fonseca, I., The lower quasiconvex envelope of the stored energy function for an elastic crystal, J. Math. Pures et Appl. 67 (1988), 175–195.
Fonseca, I., The Wulff Theorem revisited, Proc. Roy. Soc. Lond. A 432 (1991), 125–145.
Fonseca, I. & S. Müller, An uniqueness proof for the Wulff Problem, Proc. Roy. Soc. Edin. A 119 (1991), 125–136.
Fonseca, I. & G. Parry, On a class of invariant integrals, Proc. Roy. Soc. Lond. A 436 (1992), 317–329.
Herring, C., Some theorems on the free energies of crystal surfaces, Phys. Rev. 82 (1951), 87–93.
Kinderlehrer, D., Twinning of crystals II, in Metastability and Incompletely Posed Problems, IMA Vol. in Appl. Math 3 (1987), 185–211.
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.
Read, W. T. Jr., Dislocations in Crystals, McGraw-Hill, 1953.
Ricou, M., The laws of thermodynamics for non-cyclic processes, in New Perspectives in Thermodynamics, ed. J. Serrin, Springer, 1986, 85–91.
Serrin, J., An outline of thermodynamical structure, in New Perspectives in Thermodynamics, ed. J. Serrin, Springer 1986, 3–31.
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.
Taylor, G. I., The mechanism of plastic deformation of crystals, I, II, Proc. Roy. Soc. A 145 (1934), 362–387, 388–404.
Taylor, J., Existence and structure of solutions to a class of nonelliptic variational problems, Symposia Mathematica 14 (1974), 499–508.
Taylor, J., Unique structure of solutions to a class of nonelliptic variational problems, Proc. Symp. Pure Math., Amer. Math. Soc. 27 (1975), 419–427.
Taylor, J., Crystalline variational problems, Bull. Amer. Math. Soc. 84 (1978), 568–588.
Wulff, G., Zur Frage der Geschwindigkeit des Wachstums und der Auflösung der Kristallflächen, Z. f. Kristallographie 34 (1901), 449–530.
Young, L. C., Generalized surfaces in the calculus of variations I, II, Ann. Math. 43 (1942), 84–103, 530–544.
Author information
Authors and Affiliations
Additional information
Communicated by D. Owen
Rights and permissions
About this article
Cite this article
Fonseca, I., Parry, G. Equilibrium configurations of defective crystals. Arch. Rational Mech. Anal. 120, 245–283 (1992). https://doi.org/10.1007/BF00375027
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00375027