On the numerical modeling of convex particle assemblies with friction

Abstract

A quasi-static model is proposed for the simulation of dense, randomly packed assemblies consisting of convex bodies and undergoing slow deformation. A second order approximation of the contact and sticking friction conditions is derived. The solution of the assembly equilibrium problem is approximated by a sequence of nonsmooth potential minimization problems which are transformed to smooth minimization subproblems subject to nonlinear constraints. For the treatment of the nonlinearity we introduce a second order approximation: at each step a quadratic programming subproblem is solved to compute a search direction along which a univariate nonsmooth minimization of the potential is then performed. For the line search the nonlinear constraints are expressed with the aid of exact penalty functions. The addition of a second order correction step is critical for the algorithm. The paper concludes with a discussion of algorithm implementation issues and examples that illustrate its applicability.