Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity
Jeyabal Sivaloganathan; Scott J. Spector
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 1, page 201-213
- ISSN: 0294-1449
Access Full Article
topHow to cite
topSivaloganathan, Jeyabal, and Spector, Scott J.. "Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity." Annales de l'I.H.P. Analyse non linéaire 25.1 (2008): 201-213. <http://eudml.org/doc/78782>.
@article{Sivaloganathan2008,
author = {Sivaloganathan, Jeyabal, Spector, Scott J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {compressible neo-Hookean material; nematic liquid crystals},
language = {eng},
number = {1},
pages = {201-213},
publisher = {Elsevier},
title = {Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity},
url = {http://eudml.org/doc/78782},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Sivaloganathan, Jeyabal
AU - Spector, Scott J.
TI - Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 1
SP - 201
EP - 213
LA - eng
KW - compressible neo-Hookean material; nematic liquid crystals
UR - http://eudml.org/doc/78782
ER -
References
top- [1] Almgren F., Browder W., Lieb E.H., Co-area, liquid crystals, and minimal surfaces, in: Partial Differential Equations, Tianjin, 1986, Lecture Notes in Math., vol. 1306, Springer, 1988, pp. 1-22. Zbl0645.58015MR1032767
- [2] Avellaneda M., Lin F.H., Fonctions quasi affines et minimisation de , C. R. Acad. Sci. Paris Sér. I Math.306 (1988) 355-358. MR934618
- [3] Ball J.M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal.63 (1977) 337-403. Zbl0368.73040MR475169
- [4] Ball J.M., Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Philos. Trans. R. Soc. Lond. A306 (1982) 557-611. Zbl0513.73020MR703623
- [5] Ball J.M., Marsden J.E., Quasiconvexity at the boundary, positivity of the second variation and elastic stability, Arch. Rational Mech. Anal.86 (1984) 251-277. Zbl0552.73006MR751509
- [6] Ball J.M., Murat F., -quasiconvexity and variational problems for multiple integrals, J. Funct. Anal.58 (1984) 225-253. Zbl0549.46019MR759098
- [7] Bishop R.F., Hill R., Mott N.F., The theory of indentation and hardness tests, Proc. Phys. Soc.57 (1945) 147-159.
- [8] Brezis H., Coron J.-M., Lieb E.H., Harmonic maps with defects, Comm. Math. Phys.107 (1986) 649-705. Zbl0608.58016MR868739
- [9] Conti S., De Lellis C., Some remarks on the theory of elasticity for compressible Neohookean materials, Ann. Sc. Norm. Super. Pisa Cl. Sci.2 (5) (2003) 521-549. Zbl1114.74004MR2020859
- [10] Coron J.-M., Gulliver R.D., Minimizing p-harmonic maps into spheres, J. Reine Angew. Math.401 (1989) 82-100. Zbl0677.58021MR1018054
- [11] Gent A.N., Lindley P.B., Internal rupture of bonded rubber cylinders in tension, Proc. R. Soc. Lond. A249 (1958) 195-205.
- [12] Hardt R.M., Singularities of harmonic maps, Bull. Amer. Math. Soc.34 (1997) 15-34. Zbl0871.58026MR1397098
- [13] Hardt R., Lin F.H., Wang C.Y., The p-energy minimality of , Comm. Anal. Geom.6 (1998) 141-152. Zbl0922.58015MR1619840
- [14] Hill R.J., The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 1950. Zbl0041.10802MR37721
- [15] Hong M.-C., On the minimality of the p-harmonic map , Calc. Var. Partial Differential Equations13 (2001) 459-468. Zbl0999.58009MR1867937
- [16] Horgan C.O., Polignone D.A., Cavitation in nonlinearly elastic solids: A review, Appl. Mech. Rev.48 (1995) 471-485.
- [17] Jäger W., Kaul H., Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems, J. Reine Angew. Math.343 (1983) 146-161. Zbl0516.35032MR705882
- [18] James R.D., Spector S.J., The formation of filamentary voids in solids, J. Mech. Phys. Solids39 (1991) 783-813. Zbl0761.73020MR1120242
- [19] James R.D., Spector S.J., Remarks on -quasiconvexity, interpenetration of matter and function spaces for elasticity, Anal. Non Linéaire9 (1992) 263-280. Zbl0773.73022MR1168303
- [20] Lin F.H., A remark on the map , C. R. Acad. Sci. Paris Sér. I Math.305 (1987) 529-531. Zbl0652.58022MR916327
- [21] Meyers N.G., Quasi-convexity and lower semi-continuity of multiple variational integrals of any order, Trans. Amer. Math. Soc.119 (1965) 125-149. Zbl0166.38501MR188838
- [22] Meynard F., Existence and nonexistence results on the radially symmetric cavitation problem, Quart. Appl. Math.50 (1992) 201-226. Zbl0755.73027MR1162272
- [23] Morrey C.B., Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math.2 (1952) 25-53. Zbl0046.10803MR54865
- [24] Morrey C.B., Multiple Integrals in the Calculus of Variations, Springer, 1966. Zbl0142.38701MR2492985
- [25] Müller S., Spector S.J., An existence theory for nonlinear elasticity that allows for cavitation, Arch. Rational Mech. Anal.131 (1995) 1-66. Zbl0836.73025MR1346364
- [26] Šilhavý M., The Mechanics and Thermodynamics of Continuous Media, Springer, 1997. Zbl0870.73004MR1423807
- [27] Sivaloganathan J., Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity, Arch. Rational Mech. Anal.96 (1986) 97-136. Zbl0628.73018MR853969
- [28] Sivaloganathan J., Spector S.J., On the existence of minimizers with prescribed singular points in nonlinear elasticity, J. Elasticity59 (2000) 83-113. Zbl0987.74016MR1833327
- [29] Stuart C.A., Radially symmetric cavitation for hyperelastic materials, Anal. Non Linéaire2 (1985) 33-66. Zbl0588.73021MR781591
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.