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International audienceThis paper presents gradient type algorithms to solve frictional multi contact problems written as quasi optimization problems. A single loop scheme formally close to the classical conjugate gradient method is proposed with some adap tations of the iterate corrections and gradient projections. Since the convergence is difficult to prove, various tests in the field of granular media are performed with comparison with the non linear Gauss Seidel scheme

Tribologists are confronted on a daily basis by the need to understand the causes and consequences of friction on the behaviour of bodies in contact. Understanding contact behaviour is not only a scientific curiosity but the key to solving numerous industrial issues. Numerical tools have been developed to overcome the problems encountered in experiments due to limitations in the local dynamic analysis of multi-scale systems (mechanisms, bodies in contact, interfaces). More than an exhibition of numerical results, the present paper proposes reviewing the literature on the numerical tribology of dry contacts by analysing the different scales involved. © 2011 Elsevier Ltd. All rights reserved

The compaction behavior of deformable grain assemblies beyond jamming remains bewildering, and existing models that seek to find the relationship between the confining pressure P and solid fraction ϕ end up settling for empirical strategies or fitting parameters. Using a coupled discrete-finite element method, we analyze assemblies of highly deformable frictional grains under compression. We show that the solid fraction evolves nonlinearly from the jamming point and asymptotically tends to unity. Based on the micromechanical definition of the granular stress tensor, we develop a theoretical model, free from ad hoc parameters, correctly mapping the evolution of ϕ with P. Our approach unveils the fundamental features of the compaction process arising from the joint evolution of grain connectivity and the behavior of single representative grains. This theoretical framework also allows us to deduce a bulk modulus equation showing an excellent agreement with our numerical data.

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.

As the rheology of the third body does not only depend on its mechanical properties, classical discrete element simulations are not capable of modeling its flows. Consequently to take into account the third body's mechanical, thermal and physicochemical properties, an extended discrete element approach is proposed and applied to the simulation of third body flows. Each extension of the standard DEM model is compared to experimental results. The extended model's efficiency is demonstrated by using an arbitrary physicochemical law that simulates different types of behaviour observed experimentally.

We confront a recent visco-plastic description of dense granular flows [P. Jop et al., Nature, 441 (2006) 727] with multi-directional inhomogeneous steady flows observed in nonsmooth contact dynamics simulations of 2D half-filled rotating drums. Special attention is paid to check separately the two underlying fundamental statements into which the considered theory can be recast, namely (i) a single relation between the invariants of stress and strain rate tensors and (ii) the alignment between these tensors. Interestingly, the first prediction is fairly well verified over more than four decades of small strain rate, from the surface rapid flow to the quasi-static creep phase, where it is usually believed to fail because of jamming. On the other hand, the alignment between stress and strain rate tensors is shown to fail over the whole flow, what yields an apparent violation of the visco-plastic rheology when applied without care. In the quasi-static phase, the particularly large misalignment is conjectured to be related to transient dilatancy effects.

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized...