Laboratoire de Mécanique des Contacts et des Structures

Abstract A methodology for solving three‐dimensional crack problems with geometries that are independent of the mesh is described. The method is based on the extended finite element method, in which the crack discontinuity is introduced as a Heaviside step function via a partition of unity. In addition, branch functions are introduced for all elements containing the crack front. The branch functions include asymptotic near‐tip fields that improve the accuracy of the method. The crack geometry is described by two signed distance functions, which in turn can be defined by nodal values. Consequently, no explicit representation of the crack is needed. Examples for three‐dimensional elastostatic problems are given and compared to analytic and benchmark solutions. The method is readily extendable to inelastic fracture problems. Copyright © 2002 John Wiley & Sons, Ltd.

Generally, the shape of the S – N curve beyond 107 cycles is unknown except in some statistical approaches, and this is also true for the fatigue limit. In the case of a statistical approach, the standard deviation applied to the average fatigue limit is certainly not the best way to reduce the risk of rupture in fatigue. Only the exploration of the life range between 106 and 10 10 cycles will create a safer basis for modelling. Today, some piezoelectric fatigue machines are very reliable, capable of producing 10 10 cycles in less than 1 week. We based our research on accelerated fatigue tests which were performed at 20 kHz in the gigacyclic fatigue regime in order to study several typical alloys from the aeronautical and space industries.

International audience

In this paper, we analyze the impact of the cavitation model on the numerical assessment of lubricated journal bearings. We compare results using the classical Reynolds model and the so-called p-θ model proposed by Elrod and Adams [1974, “A Computer Program for Cavitation and Saturation Problems,” Proceedings of the First LEEDS-LYON Symposium on Cavitation and Related Phenomena in Lubrication, Leeds, UK] to fix the lack of mass conservation of Reynolds’ model. Both models are known to give quite similar predictions of load-carrying capacity and friction torque in nonstarved conditions, making Reynolds’ model the preferred model for its better numerical behavior. Here, we report on numerical comparisons of both models in the presence of microtextured bearing surfaces. We show that in the microtextured situation, Reynolds’ model largely underestimates the cavitated area, leading to inaccuracies in the estimation of several variables, such as the friction torque. This dictates that only mass-conserving models should be used when dealing with microtextured bearings.

International audience

Abstract This paper proposes a generalization of the eXtended finite element method (X‐FEM) to model dynamic fracture and time‐dependent problems from a more general point of view, and gives a proof of the stability of the numerical scheme in the linear case. First, we study the stability conditions of Newmark‐type schemes for problems with evolving discretizations. We prove that the proposed enrichment strategy satisfies these conditions and also ensures energy conservation. Using this approach, as the crack propagates, the enrichment can evolve with no occurrence of instability or uncontrolled energy transfer. Then, we present a technique based on Lagrangian conservation for the estimation of dynamic stress intensity factors for arbitrary 2D cracks. The results presented for several applications are accurate for stationary or moving cracks. Copyright © 2005 John Wiley & Sons, Ltd.

Johnson-Cook constitutive model is still the most used model in metal cutting simulation, although several drawbacks reported in the literature. A high number of Johnson-Cook model parameters can be found in the literature for the same work material. One question that may arise is “What is the most suitable set of Johnson-Cook model parameters for a given material?”. The present paper puts in evidence some issues related with the selection of these parameters from the literature. In this contribution, two sets of Johnson-Cook model parameters for Ti-6A-4 V are evaluated, using three types of metal cutting models. These models are based on three different formulations: Lagrangian, Arbitrary Eulerian-Lagrangian (ALE) and Couple Lagrangian-Eulerian (CEL). This evaluation is based on the comparison between measured and predicted chip geometry, chip compression ratio, forces, plastic deformation and temperature distributions.

Uniaxial tension tests were conducted on thin commercially pure (CP) titanium sheets subjected to electrically assisted deformation using a new experimental setup to decouple thermal–mechanical and possible electroplastic behavior. The observed absence of stress reductions for specimens air-cooled to near room temperature motivated the need to reevaluate the role of temperature on modeling the plastic behavior of metals subjected to electrically assisted deformation, an item that is often overlooked when invoking electroplasticity theory. As a result, two empirical constitutive models, a modified-Hollomon and the Johnson–Cook models of plastic flow stress, were used to predict the magnitude of stress reductions caused by the application of constant dc current and the associated Joule heating temperature increase during electrically assisted tension experiments. Results show that the thermal–mechanical coupled models can effectively predict the mechanical behavior of commercially pure titanium in electrically assisted tension and compression experiments.

In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.

Abstract This paper focuses on the introduction of a lumped mass matrix for enriched elements, which enables one to use a pure explicit formulation in X‐FEM applications. A proof of stability for the 1D and 2D cases is given. We show that if one uses this technique, the critical time step does not tend to zero as the support of the discontinuity reaches the boundaries of the elements. We also show that the X‐FEM element's critical time step is of the same order as that of the corresponding element without extended degrees of freedom. Copyright © 2006 John Wiley & Sons, Ltd.

The present paper studies the occurrence of micropitting damage in gear teeth contacts. An existing general micropitting model, which accounts for mixed lubrication conditions, stress history, and fatigue damage accumulation, is adapted here to deal with transient contact conditions that exist during meshing of gear teeth. The model considers the concurrent effects of surface fatigue and mild wear on the evolution of tooth surface roughness and therefore captures the complexities of damage accumulation on tooth flanks in a more realistic manner than hitherto possible. Applicability of the model to gear contact conditions is first confirmed by comparing its predictions to relevant experiments carried out on a triple-disc contact fatigue rig. Application of the model to a pair of meshing spur gears shows that under low specific oil film thickness conditions, the continuous competition between surface fatigue and mild wear determines the overall level as well as the distribution of micropitting damage along the tooth flanks. The outcome of this competition in terms of the final damage level is dependent on contact sliding speed, pressure and specific film thickness. In general, with no surface wear, micropitting damage increases with decreasing film thickness as may be expected, but when some wear is present micropitting damage may reduce as film thickness is lowered to the point where wear takes over and removes the asperity peaks and hence reduces asperity interactions. Similarly, when wear is negligible, increased sliding can increase the level of micropitting by increasing the number of asperity stress cycles, but when wear is present, an increase in sliding may lead to a reduction in micropitting due to faster removal of asperity peaks. The results suggest that an ideal situation in terms of surface damage prevention is that in which some mild wear at the start of gear pair operation adequately wears-in the tooth surfaces, thus reducing subsequent micropitting, followed by zero or negligible wear for the rest of the gear pair life. The complexities of the interaction between the contact conditions, wear and surface fatigue, as evident in the present results, mean that a full treatment of gear micropitting requires a numerical model along the lines of that applied here, and that use of overly simplified criteria may lead to misleading predictions.

Measurement technique for the study of very thin lubrication films down to one nanometer in a point contact between a steel ball and a transparent disc is used to explore the relationship between central and minimum film thickness and rolling speed at the interface between elastohydrodynamic and boundary lubrication for a series of lubricating fluids. This technique based on the colorimetric interferometry combines powerful film thickness mapping capabilities with high accuracy. It was confirmed that both hexadecane and mineral base oil obey the linear relationship between log central and minimum film thickness and log rolling speed predicted by elastohydrodynamic theory down to approximately one nanometer. Conversely, squalane and additive-treated mineral base oil showed film thickness enhancement at slow speeds caused by boundary layers formation within the lubricant film. Obtained experimental data was used for the determination of pressure-viscosity coefficients of test fluids. The measurement technique also enabled us to produce information about the influence of boundary layers on film thickness shape.

Abstract A triangular shell element for the simulation of textile composite reinforcements forming is proposed. This element is made up of unit woven cells. The internal virtual works are added on all woven cells of the element. They depend on tensions, in‐plane shear and bending moments that are directly those given by the experimental tests that are specific to textile composite reinforcement. The element has only displacement degrees of freedom; the bending curvatures are obtained from the displacement of the neighbouring elements. A set of example shows the efficiency of the approach and the relative roles of the tensile, in‐plane shear and bending rigidities. Especially their influence on the appearance and the development of wrinkles in draping and forming tests is analysed. Copyright © 2009 John Wiley & Sons, Ltd.

Abstract Velocity accommodation across rubbing surfaces lubricated with thick films is well understood and can be determined from fluid dynamics theory. The situation is not the same in "dry" friction as the question is not usually formulated in the same terms. This paper shows that in "dry" friction, velocity can be accommodated through 20 different mechanisms (5 sites and 4 modes per site) known as velocity accommodation mechanisms. The situation is therefore more complex than that found in thick film lubrication where only one such mechanism (shear) exists. Friction and wear are shown to depend on the acting mechanism. Examples are given for each mechanism. The factors that control these mechanism are identified. Visualisation studies show that more than one mechanisms can act simultaneously and that the mechanisms can change during a test. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Baltimore, Maryland, October 16–19, 1988 Notes Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Baltimore, Maryland, October 16–19, 1988

A two-scale model is developed for fluid flow in a deforming, unsaturated and progressively fracturing porous medium. At the microscale, the flow in the cohesive crack is modelled using Darcy’s relation for fluid flow in a porous medium, taking into account changes in the permeability due to the progressive damage evolution inside the cohesive zone. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for an unsaturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.

This paper investigates the influence of a transverse ridge on the film thickness in a circular EHL contact under rolling/sliding conditions. It is a numerical simulation of the optical EHL work of Kaneta et al. (1992). One of the purposes of this investigation is to check the validity of the algorithm and the Newtonian, isothermal lubricant assumption for film thickness predictions under these conditions (ph = 0.54 GPa). It will be shown that, both quantitatively, the film thickness on the central axis Y = 0, and qualitatively, the film thickness profile through “pseudo interference graphs”, the agreement between experiment and Newtonian isothermal theory is good. This supports the argument that the rheological and the thermal behavior of the fluid only slightly influence the film thickness and pressure distribution of the lightly loaded non-smooth contact case.

The blown extrusion of poly(lactic acid) (PLA) presents several challenges mainly due to the poor shear and elongation properties of this biopolymer. This article highlights some promising routes to enhance the processability of PLA for blown extrusion. To achieve this objective, various formulations of PLA with multifunctionalized epoxy, nucleating agents, and plasticizer were elaborated and studied on the basis of their linear viscoelasticity and elongational properties. We further characterized both the structure and thermomechanical properties of blown films produced with these PLA formulations. Stability charts for the film blowing of neat and modified PLA were thus established at different processing conditions. On the basis of these results, we managed to achieve a large enhancement of the blown processing windows of PLA with high blow‐up ratio (BUR) and take‐up ratio attained. We were able to demonstrate that a higher kinetic of crystallization can also be reached for chain‐extended and branched PLA formulated with adequate amounts of nucleating agents and plasticizers. Induced crystallization during process was also demonstrated. Through this work, blown films with interesting thermomechanical and mechanical properties have been elaborated using an optimal formulation for PLA. POLYM. ENG. SCI., 54:840–857, 2014. © 2013 Society of Plastics Engineers

Abstract Constitutive parameter identification has been greatly improved by the achievement of full‐field measurements. In this context, noise sensitivity has been shown to be of great importance. It is crucial to incorporate noise sensitivity minimization in the design of robust identification procedures. In this paper, we investigate noise sensitivity reduction techniques for constitutive parameter identification based on Finite Element Model Updating. After examining the existing strategies, we propose a single step algorithm based on a mixed optical/mechanical cost function. The key point of this novel procedure is that no boundary conditions are needed. A first example on a real case illustrates the advantages of the proposed methodology in terms of noise sensitivity. A second example shows its capabilities to identify a non‐linear consitutive law. Copyright © 2010 John Wiley & Sons, Ltd.

Origami (paperfolding) has greatly progressed since its first usage for design of cult objects in Japan, and entertainment in Europe and the USA. It has now entered into artistic areas using many other materials than paper, and has been used as an inspiration for scientific and engineering realizations. This article is intended to illustrate several aspects of origami that are relevant to engineering structures, namely: geometry, pattern generation, strength of material, and mechanisms. It does not provide an exhaustive list of applications nor an in-depth chronology of development of origami patterns, but exemplifies the relationships of origami to other disciplines, with selected examples.

Abstract This paper develops two aspects improving crack propagation modelling with the X‐FEM method. On the one hand, it explains how one can use at the same time a regular structured mesh for a precise and efficient level set update and an unstructured irregular one for the mechanical model. On the other hand, a new numerical scheme based on the X‐FEM method is proposed for dynamic elastic–plastic situations. The simulation results are compared with two experiments on PMMA for which crack speed and crack path are provided. Copyright © 2006 John Wiley & Sons, Ltd.