OFFICIAL Illustration 3; Hertz-Mindlin contact model (Dem-Solution, 2010). As can be seen in Illustration 3, the Hertz-Mindlin viscoelastic model is basically represented by a system consisting of a spring and a dashpot (normal and tangential). The stiffness of the bodies is represented by a spring, while the property of absorbing the energy of the bodies is represented by the dashpot. The equation that governs this phenomenon is: = ∙ + ത ത ത + 2 ത ത തതത2 (6) Where: F = Force. k = Coefficient of Rigidity. C = Damping coefficient. m = Reduced system mass. x = Distance (overlap of particles). To avoid numerical problems in the models, it is necessary to consider a sufficiently small timestep, since, when a high overlap value is generated between particles, the damping does not absorb the energy necessary to soften the effect of the collision, producing an unwanted particle expulsion. A conservative model is to calculate the timestep, as described by Juan Mellado in his thesis (Mellado, 2005). ∆ = 2 ቀඥ1+ 2 − ቁ (7) Where: Ωma x = Higher natural frequency of the system. ξ = Fraction of critical damping corresponds to the highest frequency. To couple the pressure generated by the gases produced by the detonation of the explosives, only the pressures on the surfaces are interpolated with the discrete elements for each timestep and by means of an iterative process, the interaction of the discrete elements in the gas mesh is recalculated. Figure 3 shows the cyclical operation of
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