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Roberts, D. H.; Green, W. A.

Large axisymmetric deformation of a non-linear viscoelastic circular membrane. (English) Zbl 0429.73071

Acta Mech. 36, 31-42 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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MSC:

74K15 Membranes
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
45G10 Other nonlinear integral equations
35F20 Nonlinear first-order PDEs

Keywords:

viscoelastic circular membrane deforming under its own weight; non-linear viscoelastic material; non-linear single integral constitutive equation; ordinary differential equations; step-wise integration process
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References:

[1] Green, A. E., Adkins, J. E.: Large elastic deformations and nonlinear continuum mechanics. O.U.P. 1960. · Zbl 0090.17501
[2] Wineman, A. S.: Large axially symmetric stretching of a nonlinear viscoelastic membrane. Int. J. Solids Structures8, 775-790 (1972). · Zbl 0263.73045 · doi:10.1016/0020-7683(72)90042-X
[3] Wineman, A. S.: Large axisymmetric deformation of a nonlinear viscoelastic membrane due to spinning. J. Appl. Mech.39, 848-854 (1972). · doi:10.1115/1.3422813
[4] Wineman, A. S.: Large axisymmetric inflation of a nonlinear viscoelastic membrane by lateral pressure. Trans. Soc. Rheol.20, 203-235 (1976). · Zbl 0388.73066 · doi:10.1122/1.549410
[5] Feng, W. W.: Inflation of a bonded nonlinear viscoelastic toroidal membrane. Int. J. Non-Lin. Mechs.11, 183-189 (1976). · Zbl 0346.73029 · doi:10.1016/0020-7462(76)90029-9
[6] Buckley, C. P., Green, A. E.: Small deformations of a nonlinear viscoelastic tube. Phil. Trans. A(G.B.)281, 1306, 543-566 (1976). · Zbl 0352.73036
[7] Pipkin, A. C., Rogers, T. G.: A nonlinear integral representation for viscoelastic behaviour. J. Mechs. and Phys. Solids16, 59 (1968). · Zbl 0158.43601 · doi:10.1016/0022-5096(68)90016-1
[8] Rivlin, R. S.: Proceedings first symposium naval structural mechanics, pp. 169-198. Oxford: Pergamon. 1960.
[9] Mooney, M.: A theory of large elastic deformation. J. Appl. Phys.11, 582-592 (1940). · JFM 66.1021.04 · doi:10.1063/1.1712836
[10] Roberts, D. H.: Non-linear viscoelastic behaviour. Ph. D. Thesis, University of Nottingham, 1977. · Zbl 0345.70017
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