Remarks on W 1,p -quasiconvexity, interpenetration of matter, and function spaces for elasticity
James, R. D. ; Spector, S. J.
Annales de l'I.H.P. Analyse non linéaire, Tome 9 (1992), p. 263-280 / Harvested from Numdam
@article{AIHPC_1992__9_3_263_0,
     author = {James, R. D. and Spector, S. J.},
     title = {Remarks on $W^{1,p}$-quasiconvexity, interpenetration of matter, and function spaces for elasticity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {9},
     year = {1992},
     pages = {263-280},
     mrnumber = {1168303},
     zbl = {0773.73022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1992__9_3_263_0}
}
James, R. D.; Spector, S. J. Remarks on $W^{1,p}$-quasiconvexity, interpenetration of matter, and function spaces for elasticity. Annales de l'I.H.P. Analyse non linéaire, Tome 9 (1992) pp. 263-280. http://gdmltest.u-ga.fr/item/AIHPC_1992__9_3_263_0/

[1950] A.S. Besicovitch, Parametric Surfaces, Bull. Amer. Math. Soc., Vol. 56, pp. 228-296. | MR 36825 | Zbl 0038.20401

[1952] C.B. Morrey, Quasi-Convexity and the Lower Semicontinuity of Multiple Integrals, Pacific J. Math., Vol. 2, pp. 25-53. | MR 54865 | Zbl 0046.10803

[1958] A.N. Gent and P.B. Lindley, Internal Rupture of Bonded Rubber Cylinders in Tension, Proc. Roy. Soc. London, Vol. A 249, pp. 195-205.

[1965] N.G. Meyers, Quasi-Convexity and the Lower Semi-Continuity of Multiple Variational Integrals of Any Order, Trans. Amer. Math. Soc., Vol. 119, pp. 125-149. | MR 188838 | Zbl 0166.38501

[1975] R. Adams, Sobolev Spaces, Academic Press. | MR 450957 | Zbl 0314.46030

[1977] J.M. Ball, Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 63, pp. 337-403. | MR 475169 | Zbl 0368.73040

[1981] J.M. Ball, Global Invertibility of Sobolev Functions and the Interpenetration of Matter, Proc. Royal Soc. Edinburgh, Vol. 88 A, pp. 315-328. | MR 616782 | Zbl 0478.46032

[1982] J.M. Ball, Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity, Phil. Trans. Roy. Soc. London, Vol. A 306, pp. 557-611. | MR 703623 | Zbl 0513.73020

[1984] J.M. Ball and F. Murat, W1,p-Quasiconvexity and Variational Problems for Multiple Integrals, J. Funct. Anal., Vol. 58, pp. 225-253. | MR 759098 | Zbl 0549.46019

[1985] C.A. Stuart, Radially Symmetric Cavitation for Hyperelastic Materials, Ann. Inst. Henri Poincaré: Anal. non linéaire, Vol. 2, pp. 33-66. | Numdam | MR 781591 | Zbl 0588.73021

[1986] C.O. Horgan and R. Abeyaratne, A Bifurcation Problem for a Compressible Nonlinearly Elastic Medium: Growth of a Microvoid, J. Elasticity, Vol. 16, pp. 189-200. | MR 849671 | Zbl 0585.73017

P. Podio-Guidugli, G. Vergara Caffarelli and E.G. Virga, Discontinuous Energy Minimizers in Nonlinear Elastostatics: an Example of J. Ball Revisited, J. Elasticity, Vol. 16, pp. 75-96. | MR 835366 | Zbl 0575.73021

[1986 a] J. Sivaloganathan, Uniqueness of Regular and Singular Equilibria for Spherically Symmetric Problems of Nonlinear Elasticity, Arch. Rational Mech. Anal., Vol. 96, pp. 97-136. | MR 853969 | Zbl 0628.73018

[1986 b] J. Sivaloganathan, A Field Theory Approach to Stability of Radial Equilibria in Nonlinear Elasticity, Math. Proc. Camb. Phil. Soc., Vol. 99, pp. 589-604. | MR 830370 | Zbl 0612.73013

[1987] S.S. Antman and P.V. Negron-Marrero, The Remarkable Nature of Radially Symmetric Equilibrium States of Aeolotropic Nonlinearly Elastic Bodies, J. Elasticity, Vol. 18, pp. 131-164. | MR 905811 | Zbl 0631.73016

J.M. Ball and R.D. James, Fine Phase Mixtures as Minimizers of Energy, Arch. Rational Mech. Anal, Vol. 100, pp. 13-52. | MR 906132 | Zbl 0629.49020

P.G. Ciarlet and J. Nečas, Injectivity and Self-Contact in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 97, pp. 171-188. | MR 862546 | Zbl 0628.73043

[1988] P.G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity, Amsterdam: North-Holland. | MR 936420 | Zbl 0648.73014

K.A. Pericak-Spector and S.J. Spector, Nonuniqueness for a Hyperbolic System: Cavitation in Nonlinear Elastodynamics, Arch. Rational Mech. Anal., Vol. 101, pp. 293-317. | MR 930330 | Zbl 0651.73005

V. Šverák, Regularity Properties of Deformations with Finite Energy, Arch. Rational Mech. Anal., Vol. 100, pp. 105-127. | MR 913960 | Zbl 0659.73038

S. Müller, Weak Continuity of Determinants and Nonlinear Elasticity, C. R. Acad. Sci. Paris, 307, Séries I, pp. 501-506. | MR 964116 | Zbl 0679.34051

[1989] M. Giaquinta, G. Modica and J. Souček, Cartesian Currents, weak Diffeomorphisms and Existence Theorems in Nonlinear Elasticity, Arch. Ration. Mech. Anal., Vol. 106, pp. 97-159. | MR 980756 | Zbl 0677.73014

P. Marcellini, The Stored Energy of Some Discontinuous Deformations in Nonlinear Elasticity, in Partial Differential Equations and the Calculus of Variations Volume II, Essays in Honor of Ennio De Giorgi, F. COLOMBINI et al. Ed., Birkhaüser, pp. 767-786. | MR 1034028 | Zbl 0679.73006

[1989 a] M.S. Chou-Wang and C.O. Horgan, Cavitation in Nonlinear Elastodynamics for Neo-Hookean Materials, Int. J. Engng. Sci., Vol. 27, pp. 967-973. | MR 1015839 | Zbl 0694.73005

[1989 b] M.S. Chou-Wang and C.O. Horgan, Void Nucleation and Growth for a Class of Incompressible Nonlinearly Elastic Materials, Int. J. Solids Structures, Vol. 25, pp. 1239-1254. | MR 1025383 | Zbl 0703.73025

[1989 a] C.O. Horgan and T. Pence, Void Nucleation in Tensile Dead-Loading of a Composite Incompressible Nonlinearly Elastic Sphere, J. Elasticity, Vol. 21, pp. 61-82. | MR 995580 | Zbl 0687.73017

[1989 b] C.O. Horgan and T. Pence, Cavity Formation at the Center of a Composite Incompressible Nonlinearly Elastic Sphere, J. Appl. Mech., Vol. 111, pp. 302-308. | MR 1001749 | Zbl 0711.73042

[1991] R.D. James and S.J. Spector, The Formation of Filamentary Voids in Solids, J. Mech. Phys. Solids, Vol. 39, pp. 783-813. | MR 1120242 | Zbl 0761.73020