New perspectives for discrete element modeling: Merging computational geometry and molecular dynamics

One of the most challenging problems in the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate systems with complex-shaped particles. This method integrates developments in two traditionally separate research areas: computational geometry and molecular dynamics. The computational geometry involves the implementation of techniques of computer graphics to represent particle shape and collision detection. Traditional techniques from molecular dynamics are used to integrate the equations of motion and to perform an efficient calculation of contact forces. The algorithm to solve the dynamics of the system is much more efficient, accurate and easier to implement than other models. The algorithm is used to simulate quasistatic deformation of granular materials using two different models. The first model consists of non-circular particles interacting via frictional forces. The second model consists of circular particles interacting via rolling and sliding resistance. The comparison of both models help us to understand and quantify the extend to which the effects of particle shape can be captured by the introduction of artificial rolling resistance on circular particles. Biaxial test simulation show that the overall response of the system and the collapse of force chains at the critical state is qualitatively similar in both 2D and 3D simulations.