An axisymmetric contact-impact problem is considered for an elastic layer subjected to normal indentation of a rigid body. An exact analytical solution is obtained in the case of a blunt shape of the indenter having a given velocity, and the stress pattern under multiple reflections is analyzed depending on the layer thickness. A numerical solution of the problem with arbitrary indenter shape is obtained on the basis of the simplified model of the theory of elasticity having a single displacement coincident with the impact direction. The explicit finite difference algorithm is designed on the basis of the mesh dispersion minimization technique. A parametric analysis is presented of the stress pattern developed with time with respect to variations of irregular shapes of the indenter and its masses.
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Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 1, pp. 138–152, January–March, 2010.
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Kubenko, V.D., Osharovich, G. & Ayzenberg-Stepanenko, M.V. Impact indentation of a rigid body into an elastic layer. Axisymmetric problem. J Math Sci 176, 670–687 (2011). https://doi.org/10.1007/s10958-011-0429-0
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DOI: https://doi.org/10.1007/s10958-011-0429-0