Discrete element simulation provides some insight into the alteration of railway ballast after repeated train passings. The present Part 1 is devoted to a 2D model of this granular layer interposed between the deformable ground and the rail sleeper, to which a large number of loading cycles is applied. Ballast grains are modelled as indeformable polygonal solids. A detailed account of the application to this frictional dynamical problem of the Non-Smooth Contact Dyna- mics numerical method is given. Validation is obtained through comparison with physical experiments performed on assemblies of prismatic mineral grains. Numerical results on the settlement of a track submitted to 20,000 loading cycles or more are presented.

The deterioration of the railway track under a large number of train runnings, in particular the settlement mechanism of the ballast layer or the lateral buckling of track, remains insufficiently known. In order to study the behaviour of ballast layer a three-dimensional Discrete Element Method (DEM), based on the Non Smooth Contact Dynamic (NSCD) approach has been developed.

The aim of this paper is to present a discrete element approach for the study of stonework. In the present work, a masonry structure is considered as a collection of rigid or deformable blocks, interacting together by contact laws. In this paper, we use the non-smooth contact dynamics (NSCD) resolution method mainly used for the modelling of granular media. In the considered masonry structures we define, on an elementary cell, average local strain and stress tensors. These definitions are valid under dynamical loading of the structure, taking into account rotations. We present their use on academic and on real masonry structures.

The rheology of two-dimensional steady surface flow of cohesionless cylinders in a rotating drum is investigated through nonsmooth contact dynamics simulations. Profiles of volume fraction, translational and angular velocity, rms velocity, strain rate, and stress tensor are measured at the midpoint along the length of the surface-flowing layer, where the flow is generally considered as steady and homogeneous. Analysis of these data and their interrelations suggest the local inertial number-defined as the ratio between local inertial forces and local confinement forces-to be the relevant dimensionless parameter to describe the transition from the quasistatic part of the packing to the flowing part at the surface of the heap. Variations of the components of the stress tensor as well as the ones of rms velocity as a function of the inertial number are analyzed within both the quasistatic and the flowing phases. Their implications are discussed. (c) 2005 American Institute of Physics.

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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

In Civil Engineering soils may be reinforced by different structures. Wires will interest us. Mixed sand and wire, known as TexSol, may be modelled as a continuous medium with classical behaviour laws [6] or with more sophisticated ones taking into account remote interactions [1].Our approach consists of a discrete model based on the Non Smooth Contact Dynamics. Different choices have been tested on some numerical examples to exhibit at the macroscopic scale the influence of the local models of interaction [5]. First of all we make some numerical tests to compare the mechanical behaviour of a TexSol and a sand sample. Then, we compute in both samples the stress tensors of the wires and the sand in order to understand the role of each component. Our final goal is to define a micro-macro approach and a homogenized realistic behaviour law; if this study is only a first step, it is essential.