Burger's Model in PFC

Introduction

The Burger's model provides a Kelvin model acting in series with a Maxwell model, in both the normal and shear direction. The Kelvin model is the combination of a linear spring and dashpot components that act in parallel with one another. The Maxwell model is the combination of a linear spring and dashpot components that act in series. The Burger's model act over a vanishingly small area, and thus transmit only a force.

Behavior Summary

The rheological components of the Burger's model are shown in the figure below, for both the normal and shear directions. In both directions, the model combines a Kelvin and a Maxwell model acting in series. In the normal direction, the Kelvin model provides a linear spring with stiffness K_kn and a dashpot with viscosity C_kn, and the Maxwell model provides a linear spring with stiffness K_mn and a dashpot with viscosity C_mn. The Burger's model can sustain tensile forces (M_t=0) or not (M_t=1). In the shear direction, , the Kelvin model provides a linear spring with stiffness K_ks and a dashpot with viscosity C_ks, and the Maxwell model provides a linear spring with stiffness K_msand a dashpot with viscosity C_ms. A slider with friction coefficient f_s limits the value of the shear force according to a Coulomb law.

The following figure shows the time-decay of the normal force calculated by PFC2D, compared to the analytical solution for two balls fixed with a non-zero overlap. In both PFC2D and PFC3D models, the numerical solution shows that the contact force exponentially decreases as time increases, which coincides with the analytical solution shown by the blue dashed line in the figures.

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