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Waves in approximately constrained materials and applications to fiber-reinforced composites. (English) Zbl 1163.74319
Summary: Wave propagation in approximately constrained elastic homogeneous materials is investigated by a suitable ray method; propagation speeds and evolution equations are determined and a comparison is provided by the results of other authors. The theory is applied to isotropic and anisotropic materials and to a model for unidirectionally fiber-reinforced composites.

MSC:
74-XX Mechanics of deformable solids
76-XX Fluid mechanics
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[1] Marzano, S.; Podio-Guidugli, P., Materiali elastici approssimativamente vincolati, Rend. sem. mat. univ. Padova, 73, 1-19, (1985)
[2] G. Grioli, Onde di discontinuità in elasticità finita: questioni di linearizzazione, in: Atti Convegno Onde e Stabilità, Catania, Quad. CNR, 1981, pp. 1-17.
[3] Grioli, G., On the stress in rigid bodies, Meccanica, 18, 3-7, (1983) · Zbl 0557.73002
[4] Pastrone, F.; Tonon, M.L., Wave propagation in approximately constrained elastic materials, Eur. J. mech. A, 4, 695-707, (1997) · Zbl 0880.73019
[5] Pastrone, F.; Tonon, M.L., Nonlinear waves in approximately constrained bodies, Rend. circolo matematico Palermo serie II, 57, Suppl., 393-398, (1998) · Zbl 0967.74036
[6] Pastrone, F.; Tonon, M.L., Nonlinear acceleration waves in approximately constrained elastic bodies, Proc. Estonian acad. sci. phys. math., 48, 3/4, (1999)
[7] Jeffrey, A.; Kakutani, T., Weak nonlinear dispersive waves: a discussion centered around the korteweg – de Vries equation, SIAM rev., 14, 582-643, (1972) · Zbl 0221.35038
[8] Boillat, G., Ondes asymptotiques nonlinéaires, Ann. mat. pura appl., 111, 4, 31-44, (1976)
[9] Fusco, D., Onde nonlineari dispersive e dissipative, Bull. UMI A, 16, 5, 450-458, (1979) · Zbl 0413.35044
[10] J. Engelbrecht, Nonlinear wave processes of deformation in solid, Pitman, London, 1983. · Zbl 0574.73044
[11] Hegemier, H.; Murakami, G.A., A mixture model for unidirectionally fiber-reinforced composites, J. appl. mech., 53, 765-773, (1986) · Zbl 0606.73087
[12] Scott, N., Acceleration waves in constrained elastic materials, Arch. rat. mech. anal., 58, 1, 57-75, (1975) · Zbl 0339.73006
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