Shock front analysis for axial shear wave propagation in a hyperelastic incompressible solid

Acta Mechanica

Volumn 133, Issue 1-4, 1999, Pages 105-129

  Barclay, D W ^a,b  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012585182     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01179013     Document Type: Article

References (18)

1. Moodie, T. B., Tait, R. J., Barclay, D. W.: Ray analysis and punching problems for stretched elastic-plates. J. Aust. Math. Soc. Ser. B 24, 98-119 (1982).
2. Barclay, D. W., Moodie, T. B., Tait, R. J.: Padé extensions to ray series methods and analysis of transients in inhomogeneous viscoelastic media of hereditary type, Int J. Eng. Sci. 21, 663-675 (1983).
3. Moodie, T. B., Barclay, D. W.: Instantaneous plugging of stretched elastic plates. IAM J. Appl. Math. 30, 289-301 (1983).
4. Öncü, T. S., Moodie, T. B:: Finite speed thermal transients generated by nonuniform sources applied to circular boundaries in inhomogeneous conductors. Int J. Eng. Sci. 27, 611 -621 (1989).
5. Karal, F. C., Keller, J. B.: Elastic wave propagation in homogeneous and inhomogeneous media. J. Acoust. Soc. Am. 31, 694-705 (1959).
6. Rossikhin, Y. A., Shitikova, M. V.: Ray method for solving dynamic problems connected with propagation of wave surfaces of strong and weak discontinuities. Appl. Mech. Rev. 48, 1-39 (1995).
7. Moodie, T. B., Barclay, D. W.: Padé-extended wavefronl expansions and non-linear dissipative waves. Int J. Non-Lin. Mech. 26, 25-39 (1991).
8. Moodie, T. B., He, Y., Barclay, D. W.: Wavefront expansions and non-linear hyperbolic waves. Wave Motion 14, 347-367 (1991).
9. Ogden, R. W.: Non-linear elastic deformations. Chichester: Ellis Horwood 1984.
10. Haddow, J. B:, Lorimer, S. A:, Tail, R: J.: Nonlinear axial shear wave propagation in a hyperelastic incompressible solid. Acta Mech. 66, 205-216 (1987).
11. Barclay, D. W.: Wavefront expansions for non-linear axial shear wave propagation. Int. J. Non-Lin. Mech. 33, 259-274 (1998).
12. Alexander, H.: A constitutive relation for rubber-like materials. Int. J. Eng. Sci. 6, 549-563 (1968).
13. Tschoegl, N. W.: Constitutive equations for elastometers. J. Polym. Sci. A 9, 1959-1970 (1971).
14. James, A. G., Green, A., Simpson, G. M.: Strain energy functions of rubber. I. Characterization of gum vulcanizates. J. Appl. Polym. Sci. 19, 2033-2058 (1975).
15. Haines, D. W., Wilson, W. D.: Strain-energy density function for rubber-like materials. J. Mech. Phys. Solids 27, 345-360 (1979).
16. Jin, J., Xin, Z.: The relaxation schemes for systems of conservation laws in arbitrary space dimension. Comm. Pure Appl. Math. 48, 235-276 (1995).
17. van Leer, B.: Towards the ultimate conservative difference schemes V. A second-order sequal to Godunov's method. J. Comput. Phys. 32, 101-136 (1979).
18. Jin, J.: Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys. 122, 51-67 (1995).