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 Kkn and a dashpot with viscosity Ckn, and the Maxwell model provides a linear spring with stiffness Kmn and a dashpot with viscosity Cmn. The Burger's model can sustain tensile forces (Mt =0) or not (Mt =1). In the shear direction, , the Kelvin model provides a linear spring with stiffness Kks and a dashpot with viscosity Cks, and the Maxwell model provides a linear spring with stiffness Kmsand a dashpot with viscosity Cms. A slider with friction coefficient fs limits the value of the shear force according to a Coulomb law.

Rheological components of the Burger's model.

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.

Time history of normal contact force of Burger's model. The simulation results are shown in red marks, the analytical solution with the blue dashed line (2D model).

Latest News
  • 2021 Tekne Award Work on machine learning to advance safety and efficiency in wind energy construction earned a...
    Read More
  • Itasca Software now Available for Linux Version 7 or greater of Itasca software (FLAC3D, 3DEC, PFC3D, and PFC2D) are now operable...
    Read More
  • Model Plot Contest Winners Itasca is pleased to announce the winners and honorary mentions of our Model Plot Contest...
    Read More

Upcoming Events
1 Feb
SPE Hydraulic Fracturing Technology Conference and Exhibition
The SPE Hydraulic Fracturing Technology Conference and Exhibition showcases existing and new hydraulic fracturing technologies, using e... Read More
7 Feb
Stanford Geothermal Workshop
The Stanford Geothermal Workshop bring together engineers, scientists and managers involved in geothermal reservoir studies and develop... Read More
14 Feb
Global Waste Management Symposium (GWMS)
Global Waste Management Symposium (GWMS) is a technical conference for research and case studies on waste management.... Read More