Remarks on -quasiconvexity, interpenetration of matter, and function spaces for elasticity
Annales de l'I.H.P. Analyse non linéaire (1992)
- Volume: 9, Issue: 3, page 263-280
- ISSN: 0294-1449
Access Full Article
topHow to cite
topJames, R. D., and 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 9.3 (1992): 263-280. <http://eudml.org/doc/78279>.
@article{James1992,
author = {James, R. D., Spector, S. J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {elastic energy function; minimizer of the energy; elastic ball; local minimum; formation of voids},
language = {eng},
number = {3},
pages = {263-280},
publisher = {Gauthier-Villars},
title = {Remarks on $W^\{1,p\}$-quasiconvexity, interpenetration of matter, and function spaces for elasticity},
url = {http://eudml.org/doc/78279},
volume = {9},
year = {1992},
}
TY - JOUR
AU - James, R. D.
AU - Spector, S. J.
TI - Remarks on $W^{1,p}$-quasiconvexity, interpenetration of matter, and function spaces for elasticity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 3
SP - 263
EP - 280
LA - eng
KW - elastic energy function; minimizer of the energy; elastic ball; local minimum; formation of voids
UR - http://eudml.org/doc/78279
ER -
References
top- [1950] A.S. Besicovitch, Parametric Surfaces, Bull. Amer. Math. Soc., Vol. 56, pp. 228-296. Zbl0038.20401MR36825
- [1952] C.B. Morrey, Quasi-Convexity and the Lower Semicontinuity of Multiple Integrals, Pacific J. Math., Vol. 2, pp. 25-53. Zbl0046.10803MR54865
- [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. Zbl0166.38501MR188838
- [1975] R. Adams, Sobolev Spaces, Academic Press. Zbl0314.46030MR450957
- [1977] J.M. Ball, Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 63, pp. 337-403. Zbl0368.73040MR475169
- [1981] J.M. Ball, Global Invertibility of Sobolev Functions and the Interpenetration of Matter, Proc. Royal Soc. Edinburgh, Vol. 88 A, pp. 315-328. Zbl0478.46032MR616782
- [1982] J.M. Ball, Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity, Phil. Trans. Roy. Soc. London, Vol. A 306, pp. 557-611. Zbl0513.73020MR703623
- [1984] J.M. Ball and F. Murat, W1,p-Quasiconvexity and Variational Problems for Multiple Integrals, J. Funct. Anal., Vol. 58, pp. 225-253. Zbl0549.46019MR759098
- [1985] C.A. Stuart, Radially Symmetric Cavitation for Hyperelastic Materials, Ann. Inst. Henri Poincaré: Anal. non linéaire, Vol. 2, pp. 33-66. Zbl0588.73021MR781591
- [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. Zbl0585.73017MR849671
- 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. Zbl0575.73021MR835366
- [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. Zbl0628.73018MR853969
- [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. Zbl0612.73013MR830370
- [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. Zbl0631.73016MR905811
- J.M. Ball and R.D. James, Fine Phase Mixtures as Minimizers of Energy, Arch. Rational Mech. Anal, Vol. 100, pp. 13-52. Zbl0629.49020MR906132
- P.G. Ciarlet and J. Nečas, Injectivity and Self-Contact in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 97, pp. 171-188. Zbl0628.73043MR862546
- [1988] P.G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity, Amsterdam: North-Holland. Zbl0648.73014MR936420
- 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. Zbl0651.73005MR930330
- V. Šverák, Regularity Properties of Deformations with Finite Energy, Arch. Rational Mech. Anal., Vol. 100, pp. 105-127. Zbl0659.73038MR913960
- S. Müller, Weak Continuity of Determinants and Nonlinear Elasticity, C. R. Acad. Sci. Paris, 307, Séries I, pp. 501-506. Zbl0679.34051MR964116
- [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. Zbl0677.73014MR980756
- 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. Zbl0679.73006MR1034028
- [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. Zbl0694.73005MR1015839
- [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. Zbl0703.73025MR1025383
- [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. Zbl0687.73017MR995580
- [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. Zbl0711.73042MR1001749
- [1991] R.D. James and S.J. Spector, The Formation of Filamentary Voids in Solids, J. Mech. Phys. Solids, Vol. 39, pp. 783-813. Zbl0761.73020MR1120242
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.