A numerical model for calculating the impact-induced depression

Materials usually have a quasi-brittle behavior under impact loading, even the ductile materials when loading rate is high enough. In this paper, a new numerical model for calculating the transverse impact on a quasi-brittle target is developed and the theoretical deductions with a strict mathematic logicality are illustrated. Herein, the example of a stiff ball impacting a brittle fiber bundle is investigated and the issues of stress wave propagation, inertia force, energy transformation and stress equilibrium are considered. The numerical model that can describe the impacting procedure is derived. With timing, the deformation of brittle fiber bundle, the kinetic energy of stiff ball as well as their displacements are given. Thus, the overall perspective of the impacting procedure is calculated and analyzed. This work offers a physical illustration of impact events by developing a numerical model and displays the insights into the transient procedure, that will contribute to the development of impact mechanics for engineering.