Implicit yield function formulation for granular and rock-like materials

The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or false elastic domains) preventing the use of efficient return-mapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a return-mapping integration scheme is implemented and tested for elastic-plastic (or -damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately.Comment: 19 page

Macroscopic stress and strain in a doubly periodic array of dislocation dipoles

It is known that in two-dimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the long-range character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem

Formulation of the Reynolds equation on a time-dependent lubrication surface

The Reynolds equation, which describes the lubrication effect arising through the interaction of two physical surfaces that are separated by a thin fluid film, is formulated with respect to a continuously evolving third surface that is described by a time-dependent curvilinear coordinate system. The proposed formulation essentially addresses lubrication mechanics at interfaces undergoing large deformations and a priori satisfies all objectivity requirements, neither of which are features of the classical Reynolds equation. As such, this formulation may be particularly suitable for non-stationary elastohydrodynamic lubrication problems associated with soft interfaces. The ability of the formulation to capture finite-deformation effects and the influence of the choice of the third surface are illustrated through analytical examples. © 2016 The Author(s)

Finite deformations govern the anisotropic shear-induced area reduction of soft elastic contacts

Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is usually explained using adhesion models. Here we show that quantitative agreement with recent high-load experiments can be obtained, with no adjustable parameter, using a non-adhesive model, provided that finite deformations are taken into account. Analysis of the model uncovers the basic mechanisms underlying shear-induced area reduction, local contact lifting being the dominant one. We confirm experimentally the relevance of all those mechanisms, by tracking the shear-induced evolution of tracers inserted close to the surface of a smooth elastomer sphere in contact with a smooth glass plate. Our results suggest that finite deformations are an alternative to adhesion, when interpreting a variety of sheared contact experiments involving soft materials.Comment: Version accepted at J. Mech. Phys. Solids. It includes Supplementary Informatio

Modeling and simulation in tribology across scales: An overview

This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and micro-scales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions