Numerical simulation of granular materials by an improved discrete element method

In this paper, we present an improved discrete element method based on the non-smooth contact dynamics and the bi-potential concept. The energy dissipated during the collisions is taken into account by means of restitution coefficients. The interaction between particles is modelled by Coulomb unilateral contact law with dry friction which is typically non-associated: during the contact, the sliding vector is not normal to the friction cone. The main feature of our algorithm is to overcome this difficulty by means of the bi-potential theory. It leads to an easy implement predictor–corrector scheme involving just an orthogonal projection onto the friction cone. Moreover the convergence test is based on an error estimator in constitutive law using the corner stone inequality of the bipotential. Then we present numerical simulations which show the robustness of our algorithm and the various possibilities of the software ‘MULTICOR’ developed with this approach