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The decay of an arbitrary initial discontinuity in an elastic medium. (English. Russian original) Zbl 0717.73027
J. Appl. Math. Mech. 52, No. 6, 786-790 (1988); translation from Prikl. Mat. Mekh. 52, No. 6, 1007-1012 (1988).
Summary: The solution of the problem of the decay of an arbitrary discontinuity in elastic theory is studied. It is assumed that a plane boundary separates an elastic homogeneous, non-heat-conducting medium into two half-spaces with different elastic properties and densities. Each of the media possesses an arbitrary kind of homogeneous initial strain (stress) and velocity. In the sequel the stresses and velocities of the media are assumed to be continuous at the boundary. This results in the formation of a system of plane selfsimilar waves (simple and shock), which propagate in each of the half-spaces. The problem is solved under the assumption of weak nonlinearity and anisotropy of the materials. This permits an approximate evaluation of the stress and strain at the contact discontinuity. After this the problem on the decay of an arbitrary initial discontinuity is reduced to two problems on the sudden change of load on a half-space boundary, which are solved independently for each of the media.

MSC:
74J99 Waves in solid mechanics
74B20 Nonlinear elasticity
74E10 Anisotropy in solid mechanics
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