The discrete element method (DEM) has been used extensively in simulating multiple interacting bodies undergoing relative motion and breakage. The key to the success of this method lies in correctly establishing the interaction rules and the associated contact parameters. In this paper, this is done by analyzing the impact behavior of a steel ball. Experimental data using an ultra fast load cell (UFLC) allowed the material response at the contact to be adequately modeled by a nonlinear differential equation. In turn, the contact parameters to be used in the DEM were directly extracted from the model. The nonlinear contact behavior led to values of contact parameters that limit the critical time step in the numerical integration. This is unsuitable for any large simulation involving thousands of interacting balls as in the case of a ball mill. This disadvantage is overcome by using the equivalent linearization technique to transform the nonlinear contact model to an analogous linear model. Not only did the linearized parameters allow a larger time step but also the use of a linear spring-dashpot model significantly reduced the overall computational effort, which is illustrated by simulating a 54.5-cm diameter ball mill.