Dimensionless input parameters in discrete element modeling and assessment of scaling techniques

A set of dimensionless input parameters were defined for DEM using a characteristic time which is a function of density and elastic modulus of particles and an arbitrary characteristic length. Dimensionless strain rate and mass damping ratio are inversely proportional to the characteristic time, and stress is normalized by elastic modulus to give dimensionless stress. It was demonstrated that the response of a model in the dimensionless scale is invariant with the choice of density, elastic modulus and the characteristic length if dimensionless strain rate and mass damping ratio are kept constant. Small time step is a prohibitive aspect of DEM. Scaling techniques are widely employed to enlarge the time step. Using the dimensionless scheme, it was learned that density scaling is equivalent to the use of a higher strain rate, and stiffness scaling results in a higher strain rate and an elevated stress state in the dimensionless scale.