Jean-François Molinari

Finite-element analysis of contact between elastic self-affine surfaces.

Finite-element methods are used to study nonadhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with the load at small loads. The mean pressure in the contact regions is independent of load and proportional to the root-mean-square slope of the surface. The constant of proportionality is nearly independent of the Poisson ratio and roughness exponent and lies between previous analytic predictions. The contact morphology is also analyzed. Connected contact regions have a fractal area and perimeter. The probability of finding a cluster of area a(c) drops as a(-tau )(c ) where tau increases with a decrease in roughness exponent. The distribution of pressures shows an exponential tail that is also found in many jammed systems. These results are contrasted to simpler models and experiments.

A new methodology for ranking scientific institutions

We extend the pioneering work of J. E. Hirsch, the inventor of the h-index, by proposing a simple and seemingly robust approach for comparing the scientific productivity and visibility of institutions. Our main findings are that i) while the h-index is a sensible criterion for comparing scientists within a given field, it does not directly extend to rank institutions of disparate sizes and journals, ii) however, the h-index, which always increases with paper population, has an universal growth rate for large numbers of papers; iii) thus the h-index of a large population of papers can be decomposed into the product of an impact index and a factor depending on the population size, iv) as a complement to the h-index, this new impact index provides an interesting way to compare the scientific production of institutions (universities, laboratories or journals).

From infinitesimal to full contact between rough surfaces: Evolution of the contact area

We carry out a statistically meaningful study on self-affine rough surfaces in elastic frictionless non-adhesive contact. We study the evolution of the true contact area under increasing squeezing pressure from zero up to full contact, which enables us to compare the numerical results both with asperity based models at light pressures and with Persson’s contact model for the entire range of pressures. A good agreement of numerical results with Persson’s model is obtained for the shape of the area-pressure curve especially near full contact, however, we obtain qualitatively different results for its derivative at light pressures. We investigate the effects of the longest and shortest wavelengths in surface spectrum, which control the surface Gaussianity and spectrum breadth (Nayak’s parameter). We revisit the influence of Nayak’s parameter, which is frequently assumed to play an important role in mechanics of rough contact.

Finite‐element modeling of dry sliding wear in metals

This paper is concerned with the calibration and validation of a finite‐element model of dry sliding wear in metals. The model is formulated within a Lagrangian framework capable of accounting for large plastic deformations and history‐dependent material behavior. We resort to continuous adaptive meshing as a means of eliminating deformation‐induced element distortion, and of resolving fine features of the wear process such as contact boundary layers. Particular attention is devoted to a generalization of Archard’s law in which the hardness of the soft material is allowed to be a function of temperature. This dependence of hardness on temperature provides a means of capturing the observed experimental transition between severe wear rates at low speeds to mild wear rates at high speeds. Other features of the numerical model include: surface evolution due to wear; finite‐deformation J2 thermoplasticity; heat generation and diffusion in the bulk; non‐equilibrium heat‐transfer across the contact interface; and frictional contact. The model is validated against a conventional test configuration consisting of a brass pin rubbing against a rotating steel plate.

A study of solid-particle erosion of metallic targets

We perform detailed finite element simulations of impact of metallic plates by spherical particles over a range of impact angles and speeds with a view to develop an insight into the fundamental mechanisms underlying solid-particle erosion. The particular experimental configuration and data set which we analyze corresponds to the experiments of Hutchings (Proc. R. Soc. London, Ser. A 348 (1976) 379), consisting of high-strength steel spherical particles striking mild-steel target plates. The material description used in calculations includes finite deformations, strain hardening, thermal softening, rate sensitivity, frictional contact, heat generation due to plastic working and friction, dynamics and heat conduction. The analysis reveals insights into the relative roles played by plastic flow, friction and adiabatic shearing over the full range of impact angles from glancing to normal impact; and over impact velocities ranging from 141 to 2000 m/s.

Mathematical aspects of a new criterion for ranking scientific institutions based on the h-index

We develop and discuss the theoretical basis of a new criterion for ranking scientific institutions. Our novel index, which is related to the h-index, provides a metric which removes the size dependence. We discuss its mathematical properties such as merging rules of two sets of papers and analyze the relations between the underlying rank/citation-frequency law and the h-index. The proposed index should be seen as a complement to the h-index, to compare the scientific production of institutions (universities, laboratories or journals) that could be of disparate sizes.

Characteristic fragment size distributions in dynamic fragmentation

The one-dimensional fragmentation of a dynamically expanding ring (Mott’s problem) is studied numerically to obtain the fragment signatures under different strain rates. An empirical formula is proposed to calculate an average fragment size. Rayleigh distribution is found to describe the statistical properties of the fragment populations.

On the Propagation of Slip Fronts at Frictional Interfaces

The dynamic initiation of sliding at planar interfaces between deformable and rigid solids is studied with particular focus on the speed of the slip front. Recent experimental results showed a close relation between this speed and the local ratio of shear to normal stress measured before slip occurs (static stress ratio). Using a two-dimensional finite element model, we demonstrate, however, that fronts propagating in different directions do not have the same dynamics under similar stress conditions. A lack of correlation is also observed between accelerating and decelerating slip fronts. These effects cannot be entirely associated with static local stresses but call for a dynamic description. Considering a dynamic stress ratio (measured in front of the slip tip) instead of a static one reduces the above-mentioned inconsistencies. However, the effects of the direction and acceleration are still present. To overcome this, we propose an energetic criterion that uniquely associates, independently on the direction of propagation and its acceleration, the slip front velocity with the relative rise of the energy density at the slip tip.

Critical length scale controls adhesive wear mechanisms

The adhesive wear process remains one of the least understood areas of mechanics. While it has long been established that adhesive wear is a direct result of contacting surface asperities, an agreed upon understanding of how contacting asperities lead to wear debris particle has remained elusive. This has restricted adhesive wear prediction to empirical models with limited transferability. Here we show that discrepant observations and predictions of two distinct adhesive wear mechanisms can be reconciled into a unified framework. Using atomistic simulations with model interatomic potentials, we reveal a transition in the asperity wear mechanism when contact junctions fall below a critical length scale. A simple analytic model is formulated to predict the transition in both the simulation results and experiments. This new understanding may help expand use of computer modelling to explore adhesive wear processes and to advance physics-based wear laws without empirical coefficients.

Finite element simulation of shaped charges

This paper analyzes by numerical simulation the formation, the fragmentation, and the penetration in a plate of a copper jet that develops in a shaped charge. A finite element Lagrangian code has been used to gain insight into this problem. The study is conducted in two dimensions, axisymmetric. An explicit contact/friction algorithm is used to treat multi-body dynamics. A remeshing algorithm is needed to follow the high deformation pattern of the copper jet. The calculations account for rate-dependent plasticity, heat conduction and thermal coupling. A criterion is introduced to model the jet break-up. The simulations reveal in particular a gradient of shear deformation across the jet.