The soft-sphere model design of the discrete element method is based on types of dynamic systems for determining the contact forces. These forces are computed considering the solution of equation of motion for the overlap between the particles during the contact. The dynamic systems can be modeled as linear or nonlinear mass spring-damper. In the present work we derive two new approximate relations for determining the damping coefficient and duration of contact for a specific non-linear soft-sphere contact model where the contact force is continuous at the start and end of the contact. The proposed relations are applied in three different problems: single freely falling particle, 3D bubbling fluidized bed and 3D hopper. All results are obtained using the MFIX computational code and are compared with literature data showing good agreement. In these simulations, when we compare the nonlinear contact force models, the proposed approximate relations reduced the computational time. This behavior is caused because the proposed contact model simulates better the contact process between particles. (C) 2016 Elsevier B.V. All rights reserved.