Several processes in nature as well as many industrial applications involve static or dynamic granular materials. Granulates can adopt solid-, liquid-, or gaslike states and thereby reveal intriguing physical phenomena not observable in its versatility for any other form of matter. The frequent occurrence of phase transitions and the related characteristics thereby strongly affect their processing quality and economics. This situation demands for prediction methods for the behavior of granulates. In this context simulations provide a feasible alternative to experimental investigations. Several different simulation approaches are applicable to granular materials. The time-driven discrete element method turns out to be not only the most complex but also the most general simulation approach. Discrete element simulations have been used in a wide variety of scientific fields for more than 30 years. With the tremendous increase in available computer power, especially in the past years, the method is more and more developing to the state of the art simulation technique for granular materials not only in science but also in industrial applications. Several commercial software packages utilizing the time-driven discrete element method have emerged and are becoming more and more popular within the engineering community. Despite the long time of usage of the time-driven discrete element method, model advances derived and theoretical and experimental studies performed in the different branches of application lack harmonization. They thereby provide potential for improvements. Therefore, the scope of this paper is a review of methods and models for contact forces based on theoretical considerations and experimental data from literature. Particles considered are of spherical shape. Through model advances it is intended to contribute to a general enhancement of simulation techniques, which help improve products and the design of the related equipment.
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