A reliable algorithm to solve 3D frictional multi-contact problems: application to granular media
The paper presents an improved non-smooth Discrete Element Method (DEM) in 3D based on the Non-Smooth Contact Dynamics (NSCD) and the bi-potential concept. It is considered a 3D collection of rigid spheres during the motion of which contacts can occur or break. The dynamics of system is governed by Newton's second law. Additional equations describe interaction between bodies. The interaction law is described by Coulomb's unilateral contact law with dry friction in the framework of the bi-potential theory. Coulomb's law is typically non-associated, i.e. during the contact the sliding vector is not normal to the friction cone. The dissipative nonlinear law takes into account the cases of no contact, contacts with sticking and sliding. The bi-potential of the contact is bi-convex with respect to each of the variables considered. The nonassociativity of the constitutive law poses numerical challenges. The main feature of the author's algorithm is that by adopting a variational inequality-based formulation of the frictional contact law, its time-integration is reduced to a single predictor-corrector step involving only an orthogonal projection onto the friction cone. This contrasts with the classical method where contact and friction are regarded separately leading to a time stepping algorithm that involves two predictor-corrector steps, namely (i) for the contact problem, and (ii) for the friction problem. The numerical simulations are made with the extension in 3D of the MULTICORE software developed by using the improved DEM based on the NSCD model. At each time step an iterative algorithm is used to compute the values of the variables at the end of the step. In the local stage for each particle the forces are computed from the relative displacements using an interaction law with the bi-potential concept which models the friction contact and shocks. In the global stage Newton's second law is used to determine, for each particle, the resulting acceleration which is then time-integrated to find the new particle positions. This process is repeated up to the simulation finish. The numerical examples consider (i) discharge of a silo with inclined bottom consisting of particles subjected to gravity and contact forces, (ii) formation of a pile of particles from the discharge of a silo subjected to gravity and contact forces, (iii) impact of a particle on a canon-ball arrangement, and (iv) granular segregation due to vertical shaking of a mixture of small and large particles and initiation of Brazil nut effect where the large particles accumulate at the top.
scientific article; zbMATH DE number 5708966