As an important indicator for the quantification of energy dissipation during the contact/impact process, in-depth researches of the restitution coefficient are of great significance not only for the prediction performance improvement of the existing contact force models, but also for the accurate quantification of contact/impact responses, and the further exploration towards the influence laws of the contact phenomena on the overall system dynamical characteristics. Due to the limitations of current researches, a new restitution coefficient model considering the material properties and initial contact velocities is proposed based on the dimensionless analyses in this work. The specific implementation process can be summarized as follows: Firstly, the contact/impact FEM simulation model between the elastic sphere and the elastic-perfectly plastic substrate is established by using the commercial software ABAQUS, of which the effectiveness can be verified from the setting of minimum mesh sizes of the contact domain and the changing curves of all types of energies during one contact/impact process. Then, large numbers of simulation examples under different working conditions are conducted, and the effects of material property and initial contacting velocity on the contact/impact responses can be thus analyzed. After that, two dimensionless variables, E*
, are introduced and the mapping relationships among the restitution coefficient, material properties, and initial contact velocities are explored. In addition, combined with the Johnson theory, the mapping relationship between the yield velocity and material properties is reversely calculated, and thus the novel restitution coefficient model based on the dimensional analyses can be finally established. Comparisons with the experimental data under low contacting velocities and FEM results for high contacting velocities validate the effectiveness and generalization abilities of the presented restitution coefficient model.