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On fronts of strong and weak discontinuities in solutions of the equations of different-modulus elasticity theory. (English. Russian original) Zbl 0735.73013
J. Appl. Math. Mech. 53, No. 2, 230-235 (1989); translation from Prikl. Mat. Mekh. 53, No. 2, 294-300 (1989).
The fronts in a different-modulus elastic body on which a change in the elastic properties occurs are classified. Fronts representing strong discontinuities (shocks) of low intensity as well as their corresponding simple waves are considered. The existence of weak discontinuities on which the conditions of continuity and the condition giving the change in the elastic properties do not yield a complete system of relationships on the front is proved. In this case an additional relationship is postulated.
Plane waves that are described by a complete system of elasticity equations, that are a hyperbolic system of seventh-order equations are examined in an arbitrary elastic body.

MSC:
74M20 Impact in solid mechanics
35L67 Shocks and singularities for hyperbolic equations
74J10 Bulk waves in solid mechanics
74R99 Fracture and damage
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