The non smooth contact dynamic method: recent LMGC90 software developments and application

Abstract

The Non Smooth Contact Dynamics method (NSCD) deals with frictional unilateral contact between rigid or deformable bodies. It was originated around 1984 by J.J. Moreau as the Contact Dynamics method (CD). It was extended as the (NSCD) method by M. Jean to deal with more general applications, such as nite element modelling. Numerical applications of the CD method for granular materials are currently customized in C language by J.J. Moreau. The NSCD method has been implemented by M. Jean in a now obsolete fortran77 general purpose software. F. Dubois is the author of a completely remodelled new version LMGC90 written in fortran90, open to research scientists for further developments and applications. This is an open source software governed by a Cecill license (i.e. GPL). In the NSCD method the basic laws such as Coulomb’s law and the inelastic shock law are described as non smooth laws in terms of multimappings. The dynamical equation is discretized according to a low order implicit algorithm. The main unknowns are the relative velocities between contactors at some overlapping moments with the time steps (leap frog technique) and the mean reaction impulses during the time step. Assuming provisional values for contacts neighbouring of a given contact, values of the reactions for this given contact are obtained discussing the intersection of the graphs of affine mappings. Values of the reactions are updated, and all contacts are processed successively as long as necessary to obtain a satisfactory convergence. This may be described as a non linear block Gauss Seidel method. The LMGC90 software is dedicated to applications with a large number of 2D or 3D contactors. It is a modular software written in fortran90 with an object oriented organisation: