On the force–displacement law of contacts between spheres pressed to high relative densities

A finite element study of the interparticle force–displacement laws on contacts of spheres at conditions corresponding to compacts pressed to high relative densities is presented here. Under these conditions, the response of a contact can be affected by the presence of neighboring contacts. Finite element simulations of axisymmetric models of equispaced and equally loaded contacts show that the force–displacement law is not unique and depends on the number of neighboring contacts. The force at a given interparticle deformation is minimum for Z = 2 but at higher coordination numbers becomes larger after a critical deformation due to the interaction of the stress fields of neighboring contacts. This difference is magnified when the local porosity closes. Furthermore, numerical simulations of periodic arrays of spheres were conducted to assess the effect of loading path and the formation of new contacts on the response of existing contacts. In both cases, it was found that, the contact response depends on the overall triaxiality of the deformation of the particle. A new deformation fabric tensor is proposed based on the deformation and direction of all contacts on a particle. The first and second invariants of this tensor are used to characterize the triaxiality of the deformation on a particle. These results form the basis for more appropriate force–displacement laws at contacts that can be implemented in discrete element simulations for high density problems.