Search

National audience; Real-time adaptive production control in the flexible manufacturing cell (FMC) is a complex issue that needs to be addressed to realize good performance and high productivity. In this paper, we have considered a support vector machine (SVM)-based simulation approach to resolve a production control problem in an FMC that operates in a dynamic environment. A SVM-based simulation approach chooses the most relevant scheduling rule out of several predefined ones on the basis of the current states of the system. This paper examines and compares the performance of the SVM-based simulation approach with the competent scheduling rules under two different operational environments which are characterized by the uncertainty of demand. We have also developed a Visual Basic-based simulation approach for scheduling of component parts in the context of FMC under different situations. The SVM methodology to control the production offers better performance than the single-rule-based production control system.

International audience; In this paper, the authors describe a modeling and design method for a permanent magnet drive used in a power train for Hybrid Electric Heavy Vehicle, based on a Series-Parallel architecture. The hybrid powertrain structure enables high requirements for boost mode of acceleration and full electric mode. A 'Ravigneaux' train was integrated in this hybrid powertrain structure in order to split energy among the vehicle wheels, the thermal engine, the electrical motor and the alternator. To compare the classical simple epicyclic train used in series-parallel Toyota hybrid structure, this 'Ravigneaux' train developed by Nexter group presents a better adaptation to high mechanical constraints (high power and torque) because of its double stages compound structure. Several operation modes of vehicle were analyzed by assuming that the two electrical machines were identical and reversible (they can both operate as a motor or an alternator). In this paper, a simple drive is considered: it deals with a Surface-Mounted Permanent Magnet Synchronous Machine (SMPMSM) and a two level Voltage Source Inverter (VSI). An analytical modeling based on three working points: boost working point, nominal working point and maximal rotation speed working point has been elaborated. The analytical modeling makes it possible to model the physical behavior of different components. It enables to analyze quickly the relationship between the different parameters. A numerical modeling using 2D finite elements is also presented in this paper. The aim of 2D finite elements analysis (2DFEA) is to validate the machine performances obtained by analytical modeling. It enables to model some physical phenomena with a better accuracy, such as magnetic saturation. Generally, the results given by 2DFEA will be closer to experimental results. The control law of the electrical machine was investigated by the way of a single-phased electromechanical modeling. With this model, the flux weakening analysis has been taken into account in order to adapt the motor winding according to the rotation speeds defined in the specifications. The flux weakening was realized by considering mechanical and electrical characteristics linked with power, torque, rotation speed, DC-link voltage, feeding voltage of electrical machine, Id and Iq currents, cyclic inductance, winding resistance, back-electromotive force, phase difference between back electromotive force and phase current... The electrical machine losses have been calculated by neglecting the mechanical losses and PM losses. The machine losses calculation includes the copper losses and the iron losses (eddy currents losses and hysteresis losses). The flux density in the stator yoke and the teeth was evaluated by taking into account the magnetic flux created by permanent magnet and the one created by armature reaction (stator current). The inverter losses were calculated too, by considering the commutation and conduction losses of both diodes and IGBT transistors. Thus, the total losses and the global efficiencies of motor and inverter were evaluated and the best working points can be deduced from those calculations. The previous models enable to evaluate global energy performances of electrical machines and inverters by respecting the constraints defined in the specifications. This methodology is general and can be a first step of a complete power train optimal design, including the electrical drive, the gear, the energy storage units and possibly the internal combustion engine.

The constantly increasing market request of high quality vehicles ask the automotive manufacturers to perform lifetime testing in order to verify the reliability levels of new products. In this paper, we deal with two difficulties in reliability assessment for mechanical parts. On one hand, there is the small number of parts available for testing. On the other hand, there is the problem of wear. In the automotive applications, mechanical components subjected to relative motion of parts have to be designed against wear. In this paper, the Bayesian estimation of Wiener process parameters (usually used to define the degradation process) is studied to improve the estimation accuracy in incorporating the available knowledge on the product. In particular, the finite element results and expert knowledge are considered as “a priori”. For wear prediction by FEM, a model based on Archard law was developed for the brake disc wear.

This paper deals with face gear design. The goal is to propose a simple formula for predicting the width of the wheel as a function of the main design parameters. A specific software was used to achieve this goal. This numerical tool is able to simulate the geometry and the quasistatic loaded behavior of a face gear. The statistical method used for analyzing the influence of data is described: The design of experiments leads to a simple regression model taking into account the influential parameters and their couplings. In the last part of this paper, the results of the formulas are compared to those of the software and an optimal design is proposed based on the regression model.

The main idea in this paper deals with the importance of smart machining improvement by introducing physical based understanding. The case of chip formation, in hard turning, is treated via the existence of a direct relationship between serrated-chip morphology simultaneously with force component signals(resulting from a high frequency acquisition) and with the width of facets detected on a workpiece machined surface. The forces component variations can reach several tens of Newton. The shear segmentation of the chip is a high frequency phenomenon. Because it can excites machine-tool, induces insert wear and affects surface integrity, this phenomenon has to be understood and controlled by the smart machining devices. The paper is a contribution by considering an experimental and a numerical approach.

For high-precision mechanisms such as machine tools or gas-turbine engines, which operate at extreme conditions, it is particularly important to accurately predict the behavior of the included bearing. This prediction includes, among other things, its load distribution, stiffness, and power dissipation. Although shaft speeds tend to increase, rings and shaft walls are becoming thinner due to size and weight constraints. Thus, bearing behavior is no longer independent of the housing and ring stiffness. This paper focuses on the problem of elastic ring deformation and certain behaviors of high-speed intershaft cylindrical roller bearings such as heat dissipation, contact pressure, and risk of bearing failure due to scuffing. The paper presents an analytical method to account for the structural deformation of the rings based on Roark's formulas. The elastic deformation of thin cylindrical rings has been introduced in the set of displacement and load equations that describes the bearing equilibrium. A correla...

The paper deals with joint element model used in crashworthiness simulations. The first part of the paper is dedicated to the formulation of a new “global” finite element for spotweld modelling. The mechanical behaviour of the joint is elastic–plastic type and damage is taken into account to model the failure of the welded area. The second part of the paper concerns a new experimental procedure for joint strength analysis in pure and mixed modes I/II and for joint model characterisation. Experiment is based on Arcan principle and results are compared to open literature. In the last part of the paper, the parameters of the new joint model are identified using experiments and used for several shapes of spot-welded specimens. The model predicts reasonably the elastic–plastic part of the response but is unable to predict the post-peak response observed especially in the case of pure shear.

The first part of this two-part paper presents an analytical model to predict the performances of double-row tapered roller bearings (DRTRB). The model has been structured in two major parts: (1)- A conventional quasi-static analysis to determine the internal load distribution, the bearing stiffness and the fatigue life and (2)- A quasi-dynamic analysis which integrates the differential equations for each bearing element in order to determine the amount of skidding, the friction forces and moments and consequently the heat dissipation. The proposed model allows one to take into account a general external loading (shaft tilting moments, radial and axial loads), the initial axial compression introduced while mounting, the operating speed and the lubricant properties. Some numerical results are presented in the second part of this two-part paper. Presented at the 56th Annual Meeting in Orlando, Florida May 20–24, 2001

A multi scale methodology is proposed for the study of the cellular material behavior under dynamic loading. The behavior of polymeric foams studied depends on the constitutive material and the morphology of the porous structure. The cellular material of this study is constituted of millimetric porous beads, these beads are themselves constituted of microscopic closed cells. The methodology proposed to model the multi scale morphology of the structure (the scales of beads and cells) of the cellular material; it consists in implementing simple mechanical models at the different scales to reproduce the complex physical phenomenon observed and to model the macroscopic response of the foam. The observation and the analysis of physical phenomenon is the first step of the multi scale modeling. This paper describes the experimental and numerical methods used to observe and describe the structure of the cellular material, and quantify deformations and damages of these structures at the scales of beads and cells. Two ways of modeling were investigated: a finite-element model to represent the bead structure and another approach, more original, by the use of a modified discrete element model to model the microscopic structure of the cells.

The conversion efficiency of three way catalytic converters is mainly defined by the temperature range wherein they are operating. Traditionally, ignition retard has been used to reduce the light-off time of the catalyst. This is however associated with a fuel penalty. With increasing vehicle electrification, electrically heating facilities present an alternative, especially for hybrid vehicles. Nevertheless, system complexity of hybrid vehicles prevents engineers to evaluate possible heating technologies and their corresponding fuel penalty with respect to traditional solutions. This paper evaluates the application of an electrically heated catalyst on a hybrid vehicle equipped with a Natural Gas (NG) engine. The effect of heating power on light-off time and fuel penalty is determined, using analysis techniques emerging from integrated powertrain control. By means of a case study, the importance of an integral approach is explained by comparing the fuel penalty and conversion efficiency improvement of electric heating with that of ignition retard. In this process, a mix of simulation and test data were combined, forming the foundations for future control developments of a suitable light-off strategy. © 2010 Institut français du pétrole.

The paper proposes a comprehensive model to predict the skew movement of a roller in tapered roller bearings. Numerical solutions are given on a LM48548/LM48510 bearing. The effect of the shaft speed, ring misalignment, and lubricant temperature on the roller skew angle is presented and compared to the experimental data available in the literature. The results indicate that the skew angle depends first on the misalignment angle between the cup and the cone. The roller skew is also greatly influenced by the traction at the roller-flange contact, the skew angle increasing with the traction at this contact, and by the geometry of the roller end.

Nowadays, the wheels of worm gears with a low module can be made of plastic, thus classical modeling can no longer be used satisfactorily. The present paper describes an original method for studying the quasi-static loaded behavior of a worm gear, with a steel worm and a nylon wheel. A generalized Kelvin model is proposed and the computation of load sharing is described by using an equation of displacement compatibility. The history of previous deformation and the effect of the nylon’s structural damping are also taken into account. Experimental measurements of the Loaded Transmission Error are performed with the help of optical encoders rigidly connected to the worm and gear shafts, giving access to their instantaneous angular positions. The numerical simulations fit quite well with the experimental results.Copyright © 2007 by ASME

An analysis of an arched ball bearing that considers centrifugal forces and gyroscopic effects is performed. Based on operating conditions of a 5 DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from 2 to 3 and 4 contacts. The commonly used control criterion of a ball bearing by the inner or outer raceway is debatable and is known to fit experimental data with difficulty, and when more than two contact points are involved it becomes obsolete. The paper presents a mathematical model to describe the ball internal kinematics under the effect of the operating conditions. This analysis makes it clear that the total power loss varies strongly with the one or two added sources of friction. The maximum PV factor is also affected by the full sliding of the lightly loaded contacts induced by the arched design.

When investigating the electrical characteristics of granular assemblies under dynamical solicitations (powder, steel bead assemblies, etc.), it is difficult to distinguish between effects that are purely electrical and those that are strongly dependent on mechanical effects. Although numerous experimental works have permitted better understanding of the static electrical behaviour of such media, it is difficult to determine the effects control the multi-physical behaviour of the medium, especially under dynamical solicitations. In the present paper, numerical investigations of the electrical characteristics of granular material are proposed. Moreover, it presents the formulation of a new model, embedded in the general scheme of discrete element methods, that couples electrical and mechanical effects and takes into account the oxidation phenomenon. Numerical simulations on the basis of experimental works are performed to validate the model, and the results of dynamical simulations are discussed. Copyright © 2007 John Wiley & Sons, Ltd.

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.

The eXtended Finite Element Method (X-FEM) has been applied to a wide range of applications, in particular for crack growth simulations in structural mechanics. However, for real applications (engineering simulations,...), even if one does not need to mesh the crack, it is necessary to take into account the different spatial scales linked to the size of the domain, the geometry of the boundary, the size of the boundary with prescribed displacement or loading, the discretized "representation" of the crack,... In this respect, one proposes in this paper to couple the eXtended Finite Element Method with a multi-grid strategy. Details are given for numerical implementation with a hierarchical finite element strategy. Finally, some examples are given (mixed mode crack growth simulations) to validate the method.

An analysis of double arched ball bearing, which considers centrifugal forces and gyroscopic effects, is performed. Based on operating conditions of a five DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from two to three or four-contact points. The commonly used control criterion of ball bearing by the inner or outer raceway is debatable and is known to fit with difficulty with experimental data. In addition, when more than two-contact points are involved, it becomes obsolete. The paper presents a mathematical model to describe the complex ball bearing internal kinematics under the effect of the external working conditions. Lubricant thickness is taken into account in geometrical equations and the nonlinear system of this quasistatic model is solved by a Newton-Raphson method. The model is first validated through comparisons with published data for conventional or single arched ball bearings. Results are also compared to those provided by the commercial software RBL4. The analysis of a double arched ball bearing is finally performed and the complex motion of the ball highlighted.

In a previous paper (Changenet, and Velex, 2007, “A Model for the Prediction of Churning Losses in Geared Transmissions—Preliminary Results,” ASME J. Mech. Des., 129(1), pp. 128–133), a series of empirical formulas were presented enabling accurate predictions of churning losses for one gear, which is typical of automotive transmission geometry. However, this formulation does not take into account the influence of flanges and deflectors. In order to extend the proposed methodology, a test rig has been set up in which several movable walls can be inserted, thus making it possible to modify the radial and axial clearances, i.e., the distances between the tested gear and the walls. Based on a qualitative evaluation of the various fluid flow regimes possible in gearboxes, the influence of the global volume of the oil sump on churning losses is analyzed. By considering a number of flange and deflector arrangements, the following conclusions are drawn: (a) Radial clearances have a weaker influence than axial clearances and (b) power losses can be minimized by properly chosen axial clearances.

International audience; The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio k—ranging from 1 to 16—and of the normal load—from 4.2 GPa to 8 GPa—are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.

The design of spiral bevel gears in aeronautical gear boxes requires very precise and realistic numerical simulations. One important criteria is the loaded transmission error (LTE) that gear designers attempt to reduce at the nominal torque. This paper presents a numerical tool that simulates the loaded meshing of spiral bevel gears and experimental tests carried out on a real helicopter gear box. Tooth profile is defined by the Gleason cutting process and tooth bending effects and contact deformations are both taken into account. The bending effect computation uses a three-dimensional finite element model, while the contact deformations are obtained by using Boussinesq’s theory. Experimental measurements of the LTE were performed using magnetic and optical encoders rigidly connected with the pinion and gear shafts, giving access to the records of the instantaneous angular positions. The numerical simulations fit quite well the experimental results.

The objective of this paper is to describe the modified Dahl and Masing models used for predicting hysteretic behavior, and tested on a belt tensioner for automotive engines. An experimental study with deflection imposed on the tensioner is first carried out to identify hysteresis loop parameters for the two models. The models are implemented in the general motion equations which govern the behavior of a belt–tensioner–mass system. Particular attention is paid to the use of numerical schemes. The numerical and experimental investigations show the reliability of the modified Dahl model.

The extended finite element method (X-FEM) was used with success in the past few years for linear elastic fracture mechanics (LEFM). In the case of elastic–plastic fracture mechanics (EPFM), this method cannot be used without adequate asymptotic solutions to enrich the shape function basis. In this paper, we propose to use the well-known Hutchinson–Rice–Rosengren (HRR) fields to represent the singularities in EPFM. The analysis we are presenting is done in the context of confined plasticity, and shall be used to predict fatigue crack growth without remeshing. A Fourier analysis of the HRR fields is done in order to extract a proper elastic–plastic enrichment basis. Several strategies of enrichment, based on the Fourier analysis results, are compared and a six-enrichment-functions basis is proposed. This new tip enrichment basis is coupled with a Newton like iteration scheme and a radial return method for plastic flow. Numerical comparisons with and without unloading of fracture parameters are made with classical finite element results and show good agreements.

In order to characterize the timing, mode and size of a possible lower head failure (LHF) of the reactor pressure vessel (RPV) in the event of a core meltdown accident, several large-scale LHF experiments were performed under the USNRC/SNL LHF program. The experiments examined lower head failure at high pressures (10 MPa in most cases) and with small throughwall temperature differentials. Another USNRC/SNL LHF program, called the OLHF program, has been undertaken in the framework of an OECD project. This was an extension of the first program and dealt with low and moderate pressures (2–5 MPa) but with large through wall temperature differentials. These experiments should lead to a better understanding of the mechanical behavior of the reactor vessel lower head, which is of importance both in severe accident assessment and the definition of accident mitigation strategies. A well-characterized failure of the lower head is of prime importance for the evaluation of the quantity of core material that can escape into the containment, since this defines the initial conditions for all external-vessel events. The large quantity of escaping corium may lead to direct heating of the containment. This is an important severe accident issue because of its potential to cause early containment failure. The experiments also provide data for model development and validation. For our part, as one of the program partners, numerical modeling was performed to simulate these experiments. This paper presents a detailed description of three of our numerical models used for the simulation. The first model is a simplified semi-analytical approach based on the theory of a spherical shell subjected to internal pressure. The two other methods deal with 2D finite element (2D-FE) modeling: one combines the Norton–Bailey creep law with a damage model proposed by Lemaitre–Chaboche while the other uses only a creep failure criterion but takes into account thermo-metallurgical phase transformations. One of the objectives of the simulation is the development of a simplified and valid analytical code that can be implemented in integral severe accident computer codes. The numerical results are consistent with the experimental measurements. The effect on the numerical results of the multiphase transformation of the shell material and of the two failure criteria used, one involving necking (Considere's criterion) and the other involving creep damage (Lemaitre–Chaboche) is discussed.

This paper describes tools for numerical modelisation which enable the understanding of the appearance of the vibration of structure generated by the frictional contact between two bodies (the excitation source being friction). The dynamic finite element code PLASTD is used to reproduce transitory phenomena generated at the contact interface. This code includes contact and friction algorithms based upon the formulation of Lagrange multipliers. A numerical study of the dynamic response of a 2D mechanical model composed of a deformable plane in relative translation and unilateral contact with Coulomb friction with a rigid surface is presented. The steady sliding solution is generically unstable and leads to a dynamic response which leads to the generation of instabilities characterized by the appearance of sliding-sticking or sliding-sticking-separation waves. It is important to notice that those instabilities appear even with a constant friction coefficient. These simulations have permitted to obtain the local contact conditions (kinematics, tribological state, contact stresses, etc). The kinematics shows the existence of local impacts and sliding at high frequencies. Furthermore, local normal pressure is much higher than that expected for a smooth surface. Finally, a 3D simulation of braking is carried out. We focused on the vibration of the disc and the brake pad which caused noises due to the generation of interface instabilities.

This paper deals with the application of indirect measurement techniques to an operating diesel engine. Internal loads exciting the engine block during operation are not directly measurable with force sensors; they have to be assessed from the dynamic deformation of the structure. The idea is to use the structure itself as a multi-force sensor, which requires the knowledge of the transfer functions between considered excitations and measured responses. The first part is devoted to the description of the methodology. In Section 1, the extraction of uncorrelated deflection shapes from stationary measurements is presented. Then the pseudo-inversion technique, needed to invert the transfer system, is reviewed. Optimization of the inversion, based on a weighing technique, is presented in Section 3. Then a regularization process based on the truncated singular value decomposition and the L-curve principle is suggested. In the second part, a basic model of a drive train is used to directly assess internal excitations from the measured cylinder pressures. Outputs of this model are compared with excitations indirectly measured on the operating engine in a third part. The efficiency of the optimization and regularization processes is illustrated, and encouraging results are presented, allowing information on defects of the drive train model to be obtained. Finally, a ranking operation is realized on internal excitations to illustrate the strong interest of the results of indirect force measurement.

International audience; This paper presents a general study of the stability of variable-mesh dynamic calculations using an energy approach. This study, whose scope is limited to the calculation of dynamic crack propagation with remeshing, enables us to establish the conditions which are necessary to ensure stability and allow control of energy transfers during the evolution of the mesh. The problem of the implicit calculation of the crack length is also presented. The results obtained on an sample problem are analyzed to illustrate the effectiveness of the proposed methods.

The model developed to predict the performance of double-row tapered roller bearings (DRTRB) and described in the first part of the paper is now exemplified. For a given example results on the internal load distribution, bearing fatigue life and hear generation are presented and discussed for various operating conditions including the mounting preload. It is revealed that some sliding occurs at the contact between the rollers and the cone that contributes significantly to the total power dissipated within the bearing. It is also shown that an optimum axial compression (or mounting preload) may be found in terms of fatigue life and heat dissipated. As the main conclusion the initial compression between bearing rows was found to play a major role upon the bearing behavior and therefore should be considered carefully for each application. Presented at the 56th Annual Meeting in Orlando, Florida May 20–24, 2001

At present, optimizing control of maximum wheel-rail adhesion, from the anti-skidding systems piloting the sliding and the rolling speeds of locomotives, is done on the basis of the wheel-rail contact models available in the literature. Improved accuracy of power train control has highlighted the limits of this optimization technique since the contact conditions of the models, i.e. the stick/slip zones, do not take into account the physical phenomena involved, although they are hardly known. To attenuate this difficulty, the recent works presented in this paper, allow describing the tribological reality of a wheel-rail contact, i.e. the progression of the stick/slip zones. This reality is achieved thanks to monitoring the changes in the the characteristics of the third body present between wheel and rail. The results of tests under initial condition show that there is a correlation between the progressions of the third body flows and that of the adhesion for the various phases of the adhesion-sliding curve. Therefore activation of the intermal flow of third body is in fact the physical manifestation of the theoretical condition of stick. On the other hand, the activation of the internal source and recirculation flows of the third body are the physical manifestation of the theoretical condition of slip. This tribological reality therefore allows us to update the theoretical stick/slip conditions and by consequence, anti-skidding systems.

This paper presents a design method for prediciting the fatigue life of T-joint assemblies loaded by random loads, based on a statistical analysis of tests. This sduty was on the correclation between the types of loading observed in practive and test results obtained for fatigue life determination. The work follows three steps: analysis tof the statistical distributions of random loads that illustrate extremen value from Markov matrix representations; statistical analysis of lifetimes obtained when the specimens are sbumitted to random loads defined earlier; design of a set of endurance curves [stress-number of cycles to failure ( S-N) curves], called ‘random’ S-N curves. These SN curves. These S-N curves are shifted compared with that obtained under sinusoidal loading. Random S-N curve positions in the S-N plane are obtimized depending on the lifetime able to take into account the damege due to the small cycles that are often present in actual loading. The use of random S-N curves for fatigue life calculations gives results matching with theral fatigue lifetime obtained with a T-joint assembly of a bogie chassis used for railway applications. Different analyses show the robustness of the proposed approach.

The author deals with the property of involute gears according to which the velocity ratio is constant for any distance between axes. It is known that the involute is the only shape which has this property, but it is not well known in a detailed way, and the only complete demonstration dates from Bricard. For this reason the present paper has an historical interest and, on the other hand, it proposes a new proof better understandable nowadays for it is based on Euler-Savary properties only.

The paper considers the behavior of third bodies in dry contacts. A description of the mechanism operating in contacts is given and the influence of external parameters outlined. Both physicochemical and mechanical conditions greatly influence third body behavior. Depending on third-body composition, the external influence can be more or less dramatic. Due to difficulties with experimentation, numerical modeling is suggested as a complementary tool. Two approaches for such modeling are described, the continuum and the discrete approach. At present these models are at an early development stage (two-dimensional simulations), and great efforts should be made for their further development. While an experimental apparatus can study phenomena at only one scale; namely the nanometer with AFM, or the micron to millimeter with fretting machines, modeling is able to range from the microscopic properties (particle interactions like coefficient of restitution) to the macroscopic properties by integration or averaging (load capacity, friction coefficient).

Numerical simulation of creep rupture of a reactor pressure vessel in a severe hypothetical accident needs to perfectly take account of interactions between creep phenomena and damage. This paper presents a numerical method for solving constitutive equations of a material behaviour model coupling elastoviscoplasticity and creep damage through the effective stress concept. The numerical technique rests upon a semi-implicit time integration of the constitutive equations. The method is validated on both simple ID cases the results of which can be compared to other numerical or analytical solutions and in the case of an axisymmetric reference problem (RUPTHER 4 test) under thermal and mechanical loading. The efficiency of different tangent stiffness matrices is analysed.