Nonlinear wave in granular systems based on elastoplastic dashpot model

Abstract

The dynamic dashpot models are widely used in EDEM commercial software. However, most dashpot models suffer from a serious numerical issue in calculating the granular chain because the denominator of damping force includes the initial impact velocity. Moreover, the existing dynamic dashpot models extended from the original Hertz contact law overestimated the contact stiffness in the elastoplastic contact phase. These two reasons above result in most dynamic dashpot models confronting some issues in calculating the multiple collision of the granular chain. Therefore, this investigation aims to propose a new composite dynamic dashpot model for the dynamic simulation of granular matters. First, the entire contact process is divided into three different phases: elastic, elastoplastic, and full plastic phases. The Hertz contact stiffness is still used in the elastic contact phase when the contact comes into the elastoplastic or full plastic phase. Hertz contact stiffness in the dynamic dashpot model is replaced by linearizing the contact stiffness from the Ma-Liu (ML) model in each time step. Second, the whole contact behavior is treated as a linear mass-spring-damper model, and the damping factor is obtained by solving the single-degree-freedom underdamped vibration equation. The new dynamic dashpot model is proposed by combining the contact stiffnesses in different contact phases and corresponding damping factors, which not only removes the initial impact velocity from the denominator of damping force but also updates the contact stiffness based on the constitutive relation of the contact body when the contact comes into the elastoplastic or full plastic phase. Finally, a granular chain is treated as numerical examples to check the reasonability and effectiveness of the new dynamic dashpot model by comparing it to the experimental data. The simulation shows that the solitary waves obtained using the new dashpot model are more accurate than the dashpot model used in EDEM software.