Shear waves in a class of nonlinear viscoelastic solids

Quarterly Journal of Mechanics and Applied Mathematics

Volumn 56, Issue 2, 2003, Pages 311-326

  Rajagopal, Kumbakonam R ^a   Saccomandi, Giuseppe ^b  

^a Texas AandM University   (United States)

^b UNIVERSITY OF SALENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; INITIAL VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS; SHEAR DEFORMATION; SHEAR WAVES; TENSORS; VISCOELASTICITY; VISCOUS FLOW; WAVE EQUATIONS;

VISCOELASTIC SOLIDS;

FLOW OF SOLIDS;

EID: 0038443889     PISSN: 00335614     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmam/56.2.311     Document Type: Article

References (17)

1. J. Muralikrishran and K. R. Rajagopal, A brief review of the uses and modelling of bitumen from ancient to modern times, Applied Mechanics Reviews 56 (2003) 149-214.
2. W. Thomson, Stability of fluid motion: rectilinear motion of viscous fluid between two parallel planes, Phil. Mag. 24 (1887) 188-196.
3. M. M. Carroll, Some results on finite amplitude elastic waves, Acta Mechanica 3 (1967) 167-181.
4. M. F. Beatty and Z. Zhou, Universal motions for a class of viscoelastic materials of differential type, Continuum Mech. Thermodyn. 3 (1991) 169-191.
5. R. L. Fosdick and J. H. Yu, Thermodynamics, stability and non-linear oscillations of viscoelastic solids - I, Int. J. Non-Linear Mech. 31 (1996) 495-516.
6. C. A. Truesdell and W. Noll, The nonlinear field theories, Handbuch der Physik, Vol. III/3 (ed. S. Flügge; Springer, Berlin 1965).
7. D. P. Pioletti, L. R. Rokotomanana, J. F. Benvenuti and P. F. Leyvraz, Viscoelastic constitutive law in large deformation: applications to human knee ligaments and tendons, J. Biomech. 31 (1998) 753-757.
8. E. Pucci and G. Saccomandi, Evolution equations, invariant surface conditions and functional separation of variables, Physica D 129 (2000) 28-47.
9. M. M. Carroll, Finite amplitude standing waves in compressible elastic solids, J. Elast. 8 (1978) 323-328.
10. _, Plane circular shearing of incompressible fluids and solids, Q. Jl Mech. Appl. Math. 30 (1976) 223-234.
11. M. A. Hayes and G. Saccomandi, Finite amplitude transverse waves in special incompressible viscoelastic solids, J. Elast. 59 (2000) 213-225.
12. M. M. Carroll, Controllable deformations in incompressible simple elastic materials, Int. J. Engng Sci. 5 (1967) 515-525.
13. R. L. Fosdick, Dynamically possible motions of isotropic incompressible simple materials, Arch. Rat. Mech. Anal. 29 (1968) 272-288.
14. xt), Indiana Univ. Math. J. 20 (1970) 231-238.
15. C. Dafermos, The mixed initial-boundary value problem for the equations of nonlinear one dimensional visco-elasticity, Diff. Equations 6 (1969) 71-86.
16. 16. S. S. Antman and T. I. Seidman, Quasilinear hyperbolic-parabolic equations of one-dimensional viscoelasticity, ibid. 124 (1996) 132-185.
17. _ and _, Large shearing motions of nonlinearly viscoelastic slabs, Bull. Tech. Univ. Istanbul 47 (1994) 41-56.