Non-elastic models of interaction of an impactor and an Uflyand–Mindlin Plate

This paper is devoted to the mathematical modeling of the low velocity impact of a solid body upon a thin elastic isotropic plate whose dynamic behavior is described by wave equations. As a method of analysis the ray method, the Laplace transform method for the viscoelastic impact and the method of spliced asymptotic expansions received for small times in the contact area and outside it are used. The local deformations in the contact area are taken into account in terms of two elastoplastic models (Aleksandrov–Kadomtsev and Kilchevskii models) and the viscoelastic Maxwell model. The stiffness of the Maxwell model’s element is expressed in terms of the integral operator with the exponential kernel of relaxation and thus the relationship for the contact force takes the integral form with a function of relaxation. The results of the present investigation can be used for the projecting and analysis of the planar constructions and their elements to impact loading in civil engineering and automotive industry.