The prediction of cohesive powder flow, caking and time consolidation of powders presents grand challenges faced today, as fine powders are prone to cohesive arching, flooding, lump formation, triboelectric charging etc.
For fast numerical computations whilst using a large number of small particles, development of simple but realistic contact mechanics models is essential. We propose a linear elasto-plastic adhesive contact model for which the mechanical properties can be characterized by modern instruments based on nano-indentation to provide a realistic particle response. This is particularly suited to particles with complex shape and surface roughness for which the prediction of friction is yet another great challenge.
There are a good number of contact deformation models in the literature for the evaluation of forces arising from inter-particle collisional interactions. They range from simple linear to more rigorous non-linear mathematical models requiring considerably long simulation times. Particulate solids commonly have rough surfaces with asperities which could readily undergo plastic deformation. With the contact area increasing, the role of adhesion becomes notable and hence the contact deformation is elastoplastic and adhesive in nature. This process is non-linear for which the model of Thornton and Ning is most applicable. However, in practice due to the presence of roughness the deformation of particulate solids most often follows a linear trend. We have therefore developed a simplified linear contact model which simulates elasto-plastic-adhesive behavior. This model simulates a realistic contact deformation in a very short simulation time. A schematic diagram of the force-overlap relationship is shown in Figure 1.
Figure 1: Schematic diagram of the normal force-overlap relationship in the proposed model
The initial elastic deformation in the model (BC) is considered to be a linearized version of the JKR model. When two adhesive spheres are brought into contact adhesion causes deformation α0. Applying a tensile force, f0, can revert the deformation back to zero. On pulling the two particles apart the tensile force goes through a maximum fce (at point B) and the contact eventually ruptures at αfe (point A). fce is given in the JKR model. The whole deformation process is assumed to be linear as shown in Figure 1.
If the deformation between the two spheres increases beyond the point that corresponds to the yield stress (αy), plastic deformation occurs (CD). This is also treated linearly. The force-deformation relationship during plastic deformation is governed by the following equation:
On reducing the compressive force, the recovery is elastic. Some elastic work is recovered (DE), and the force-deformation relationship is given by:
Due to plastic deformation, the contact surface area between the two spheres increases and a larger tensile force, fcp, is needed to separate them.
A full comprehensive description of the derivation and sensitivity analysis of the contact model can be found in the paper of Pasha et al.
The model has been used to simulate the ball indentation of cohesive powder beds and analyze the strain rate sensitivity of shear deformations.
Ball indentation experiments
Ball indentation simulations
The model has also been used to simulate the dynamics of the FT4 powder rheometer.
This model was implemented in EDEM software using the Application Programming Interface. EDEM users can get access to this contact model and the supporting documentation in the EDEM User Forum.
 C. Thornton, Z. Ning, A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres, Powder Technol. 99 (1998) 154–162. doi:10.1016/S0032-5910(98)00099-0.
 M. Pasha, S. Dogbe, C. Hare, A. Hassanpour, M. Ghadiri, A linear model of elasto-plastic and adhesive contact deformation, Granul. Matter. 16 (2014) 151–162. doi:10.1007/s10035-013-0476-y.
 K.L. Johnson, K. Kendall, A.D. Roberts, Surface Energy and the Contact of Elastic Solids, Proc. R. Soc. A Math. Phys. Eng. Sci. 324 (1971) 301–313. doi:10.1098/rspa.1971.0141.
 M. Pasha, C. Hare, A. Hassanpour, M. Ghadiri, Numerical analysis of strain rate sensitivity in ball indentation on cohesive powder Beds, Chem. Eng. Sci. 123 (2015) 92–98. doi:10.1016/j.ces.2014.10.026.
 C. Hare, U. Zafar, M. Ghadiri, T. Freeman, J. Clayton, M.J. Murtagh, Analysis of the dynamics of the FT4 powder rheometer, Powder Technol. 285 (2015) 123–127. doi:10.1016/j.powtec.2015.04.039.