No abstract

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.