On enhanced descent algorithms for solving frictional multicontact problems: application to the discrete element method

In this article, we present various numerical methods to solve multi-contact problems within the Non-Smooth Discrete Element Method. The techniques considered to solve the frictional unilateral conditions are based both on the bi-potential theory and the Augmented Lagrangian theory. A new Newton method is developed to improve the classical algorithms.

[1]  J. Moreau.  Numerical aspects of the sweeping process , 1999 .

[2]  Jean-Michel Cros,et al.  The bi-potential method applied to the modeling of dynamic problems with friction , 2005 .

[3]  F. Jourdan,et al.  A Gauss-Seidel like algorithm to solve frictional contact problems , 1998 .

[4]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[5]  G. de Saxcé,et al.  Numerical simulation of granular materials by an improved discrete element method , 2005 .

[6]  P. Wriggers.  Finite element algorithms for contact problems , 1995 .

[7]  Mohammed Hjiaj,et al.  An improved discrete element method based on a variational formulation of the frictional contact law , 2002 .

[8]  Pierre Alart,et al.  A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media , 2004 .

[9]  Modélisation et simulation bi et tridimensionnelles de la dynamique unilatérale des systèmes multicorps de grandes tailles : application aux milieux granulaires , 2006 .

[10]  J. Fortin.  SIMULATION NUMERIQUE DE LA DYNAMIQUE DES SYSTEMES MULTICORPS APPLIQUEE AUX MILIEUX GRANULAIRES , 2000 .

[11]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[12]  R. Luciano,et al.  Stress-penalty method for unilateral contact problems: mathematical formulation and computational aspects , 1994 .

[13]  G. Saxcé,et al.  New Inequality and Functional for Contact with Friction: The Implicit Standard Material Approach∗ , 1991 .

[14]  Pierre Alart,et al.  Numerical simulation of two-dimensional steady granular flows in rotating drum: On surface flow rheology , 2005 .

[15]  Zhi-Qiang Feng,et al.  Uzawa and Newton algorithms to solve frictional contact problems within the bi‐potential framework , 2008 .

[16]  Pierre Alart,et al.  Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials , 2005 .