Surface waves in a deformed isotropic hyperelastic material subject to an isotropic internal constraint

Wave Motion

Volumn 40, Issue 4, 2004, Pages 347-357

  Destrade, M ^a   Scott, N H ^b  

^a CNRS   (France)

^b UNIVERSITY OF EAST ANGLIA   (United Kingdom)

Author keywords

Bifurcation criterion; Finite deformation; Internal constraints; Surface waves

Indexed keywords

ELASTIC MODULI; INCOMPRESSIBLE FLOW; STRAIN; TRACE ANALYSIS; WALL FLOW;

BOUNDING PLANE; ISOTROPIC CONSTRAINTS;

SURFACE WAVES;

BIFURCATION; ISOTROPIC MEDIUM; SURFACE WAVE; WAVE BEHAVIOR;

EID: 4344650723     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.wavemoti.2003.09.003     Document Type: Article

References (21)

1. Rayleigh LordOn waves propagated along the plane surface of an elastic solid Proc. R. Soc. London 17 1885 4-11
2. Stroh A.N.Dislocations and cracks in anisotropic elasticity Phil. Mag. 3 1958 625-646
3. T.C.T. Ting, Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York, 1996.
4. Hayes M.Rivlin R.S.Surface waves in deformed elastic materials Arch. Ration. Mech. Anal. 8 1961 358-380
5. Dowaikh M.A.Ogden R.W.On surface waves and deformations in a pre-stressed incompressible elastic solid IMA J. Appl. Math. 44 1990 261-284
6. M.F. Beatty, Hyperelastic Bell materials: retrospection, experiment, theory, in: Y.B. Fu, R.W. Ogden (Eds.), Nonlinear Elasticity: Theory and Applications, Cambridge University Press, London, 2001, pp. 58-96.
7. Podio-Guidugli P.Vianello M.Constraint manifolds for isotropic solids Arch. Ration. Mech. Anal. 105 1989 105-121
8. R.W. Ogden, Non-Linear Elastic Deformations, Ellis Horwood, Chichester, 1984.
9. Bosi M.Salvatori M.C.Some non homogeneous deformations for a special class of isotropic constrained materials Rend. Mat. VII 16 1996 689-713
10. Ericksen J.L.Constitutive theory for some constrained elastic crystals Int. J. Solids Struct. 22 1986 951-964
11. Scott N.H.Plane waves in twinned crystals modelled as multi-constrained and nearly constrained elastic materials J. Mech. Phys. Solids 40 1992 1607-1619
12. S.S. Antman, Nonlinear Problems in Elasticity, Springer-Verlag, New York, 1995.
13. G. Saccomandi, Universal results in finite elasticity, in: Y.B. Fu, R.W. Ogden (Eds.), Nonlinear Elasticity: Theory and Applications, Cambridge University Press, London, 2001, pp. 97-134.
14. Chadwick P.Whitworth A.M.Borejko P.Basic theory of small-amplitude waves in a constrained elastic body Arch. Ration. Mech. Anal. 87 1985 339-354
15. Knowles J.K.Sternberg E.On the failure of ellipticity of the equations for finite elastostatic plane strain Arch. Ration. Mech. Anal. 63 1977 321-336
16. M. Destrade, Stoneley waves and interface stability for Bell materials in compression; comparison with rubber, Math. Mech. Solids, in press.
17. M.A. Biot, Mechanics of Incremental Deformations, Wiley, New York, 1965.
18. P. Chadwick, Interfacial and surface waves in pre-strained isotropic elastic media, Z. angew. Math. Phys. 46 (1995) S51-S71.
19. M. Destrade, Rayleigh waves and surface stability for Bell materials in compression; comparison with rubber, Quart. J. Mech. Appl. Math. 56 (2003) 593-604.
20. Horgan C.O.Saccomandi G.A description of arterial wall mechanics using limiting chain extensibility constitutive models Biomech. Model. Mechanobiol. 1 2003 251-266
21. Gent A.N.A new constitutive relation for rubber Rubber Chem. Technol. 69 1996 59-61