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A selfsimilar problem on the action of a sudden load on the boundary of an elastic half-space. (English. Russian original) Zbl 0603.73019
J. Appl. Math. Mech. 49, 214-220 (1985); translation from Prikl. Mat. Mekh. 49, 284-291 (1985).
The solution of the nonlinear problem of the action of a constant stress suddenly applied to the plane boundary of an elastic half-space that has homogeneous prestrain is investigated. The problem is selfsimilar, and its solution is constructed from shock and selfsimilar simple waves investigated earlier [the authors, e.g. ibid. 48, 793-798 (1984; Zbl 0585.73023)]. The problem under consideration is the necessary element that should be contained in solutions of different nonstationary problems, for instance, in the problem of the decay of an arbitrary initial discontinuity. Moreover, the selfsimilar solution constructed represents the asymptotic form long times of the corresponding non- selfsimilar problems when the stress on the half-space boundary varies from some values to others according to an arbitrary law over a limited time.

MSC:
74M20 Impact in solid mechanics
74B20 Nonlinear elasticity
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[1] Kulikovskii, A.G.; Sveshnikova, E.I., On shocks propagating over the state of stress in isotropic non-linearly-elastic media, Pmm, Vol.44, No.3, (1980)
[2] Sveshnikova, E.I., Simple waves in a non-linearly-elastic medium, Pmm, Vol.46, No.4, (1982)
[3] Kulikovskii, A.G.; Sveshnikova, E.I., Investigation of the shock adiabat of quasi-transverse shocks in a prestressed elastic medium, Pmm, Vol.46, No.5, (1982)
[4] Sveshnikova, E.I., Quasitransverse shocks in an elastic medium with special kinds of initial strains, Pmm, Vol.47, No.4, (1983)
[5] Kulikovskii, A.G.; Sveshnikova, E.I., On certain properties of the shock adiabat of quasitransverse elastic waves, Pmm, Vol.48, No.5, (1984) · Zbl 0585.73023
[6] Kulikovskii, A.G.; Sveshnikova, E.I., Non-linear deformation waves in previously stressed elastic media. non-linear deformation waves, () · Zbl 0865.73004
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