An analytical solution for a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate

An analytical solution for a low velocity impact between a thin transversely isotropic plate made of a strain-hardening material supported by a rigid substrate and a rigid sphere is presented. One of the novelties of this work is employing a linear strain-hardening model for investigating the indentation phenomenon in the plastic zone, rather than the traditional perfectly plastic model. Another novelty of this work is employing the homotopy perturbation method to derive analytical solutions for the highly nonlinear governing equations of contact. Since it is very important to accurately predict the contact force and its time history, the three stages of the indentation process, i.e., (1) the elastic indentation, (2) the plastic indentation, and (3) the elastic unloading stages, are investigated in detail. Comparison of the present results with results obtained from the iterative numerical time integration method confirms the accuracy and efficiency of the present solution.