The problem on normal low-velocity impact of elastic bodies of finite dimensions upon an elastic spherical shell is studied with considering the changes in the geometrical dimensions of the contact domain. At the moment of impact, shock waves (surfaces of strong discontinuity) are generated in the target, which then propagate along the body during the process of impact. Behind the wave fronts up to the boundary of the contact domain, the solution is constructed with the help of the theory of discontinuities and one-term ray expansions. Nonlinear Hertz's theory is employed within the contact region. For the analysis of the processes of shock interactions of an elastic sphere with a spherical shell, a nonlinear integral-differential equation has been obtained with respect to the value characterizing the local indentation of the impactor into the target, which has been solved analytically in terms of time series with integer and fractional powers. The time dependence of the contact force has been determined for different values of the shell radii. It is shown that the maximal values of the contact force and duration increase with the increase in the shell curvature, which is in agreement with the experimental data.
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