On the stability of Varley-Day solutions for harmonic materials
Author:
M. Aron
Journal:
Quart. Appl. Math. 48 (1990), 455-461
MSC:
Primary 73C99; Secondary 73G99, 73H99
DOI:
https://doi.org/10.1090/qam/1074960
MathSciNet review:
MR1074960
Full-text PDF Free Access
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Additional Information
- Eric Varley and Alan Day, Equilibrium phases of elastic materials at uniform temperature and pressure, Arch. Rational Mech. Anal. 22 (1966), 253–269. MR 202368, DOI https://doi.org/10.1007/BF00285419
J. L. Ericksen, Kirchhoff and Gibbs revisited, J. Elasticity 8, 439 (1978)
J. L. Ericksen, On the symmetry and stability of thermoelastic solids, J. Appl. Mech. 45, 740 (1978)
- S. A. Adeleke, Stability of some states of plane deformation, Arch. Rational Mech. Anal. 72 (1979/80), no. 3, 243–263. MR 549643, DOI https://doi.org/10.1007/BF00281591
- M. Aron and C. F. M. Creasy, On a class of exact solutions in nonlinear elasticity, J. Elasticity 21 (1989), no. 1, 27–41. MR 995578, DOI https://doi.org/10.1007/BF00040932
M. F. Beatty, Stability of hyperelastic bodies subject to hydrostatic loading, Int. J. Non-Linear Mech. 5, 367 (1970)
- C. Truesdell and W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, Band III/3, Springer-Verlag, Berlin, 1965, pp. 1–602. MR 0193816
- M. Aron, A note on undistorted states of isotropic elastic solids, J. Elasticity 19 (1988), no. 2, 179–187. MR 937627, DOI https://doi.org/10.1007/BF00040892
- Fritz John, Plane strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13 (1960), 239–296. MR 118022, DOI https://doi.org/10.1002/cpa.3160130206
- J. K. Knowles and Eli Sternberg, On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics, Internat. J. Solids Structures 11 (1975), no. 11, 1173–1201. MR 388930, DOI https://doi.org/10.1016/0020-7683%2875%2990107-9
- J. K. Knowles and Eli Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain, Arch. Rational Mech. Anal. 63 (1976), no. 4, 321–336 (1977). MR 431861, DOI https://doi.org/10.1007/BF00279991
- A. H. Jafari, R. Abeyaratne, and C. O. Horgan, The finite deformation of a pressurized circular tube for a class of compressible materials, Z. Angew. Math. Phys. 35 (1984), no. 2, 227–246 (English, with German summary). MR 756407, DOI https://doi.org/10.1007/BF00947935
E. Varley and A. Day, Equilibrium phases of elastic materials at uniform temperature and pressure, Arch. Rational Mech. Anal. 22, 253 (1966)
J. L. Ericksen, Kirchhoff and Gibbs revisited, J. Elasticity 8, 439 (1978)
J. L. Ericksen, On the symmetry and stability of thermoelastic solids, J. Appl. Mech. 45, 740 (1978)
S. A. Adeleke, Stability of some states of plane deformation, Arch. Rational Mech. Anal. 72, 243 (1980)
M. Aron and C. F. M. Creasy, On a class of exact solutions in nonlinear elasticity, J. Elasticity 21, 27 (1989)
M. F. Beatty, Stability of hyperelastic bodies subject to hydrostatic loading, Int. J. Non-Linear Mech. 5, 367 (1970)
C. Truesdell and W. Noll, The non-linear field theories of mechanics, Encyclopedia of Physics, Vol. III/3, Springer, Berlin-Heidelberg-New York, 1965
M. Aron, A note on undistorted states of isotropic elastic solids, J. Elasticity 19, 179 (1988)
F. John, Plane strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. XIII, 239 (1960)
J. K. Knowles and E. Sternberg, On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics, Int. J. Solids Structures 11, 1173 (1975)
J. K. Knowles and E. Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain, Arch. Rational Mech. Anal. 63, 321 (1977)
A. H. Jafari, R. Abeyaratne, and C. O. Horgan, The finite deformation of a pressurized circular tube for a class of compressible materials, J. Appl. Math. Phys. (ZAMP) 35, 227 (1984)
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Article copyright:
© Copyright 1990
American Mathematical Society