CNRS Mechanics and Rheology Laboratory

Tours, France

CNRS Mechanics and Rheology Laboratory

Tours, France
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Cortes L.,CNRS Mechanics and Rheology Laboratory | Mencik J.-M.,CNRS Mechanics and Rheology Laboratory | Meo S.,CNRS Mechanics and Rheology Laboratory
Proceedings of ISMA 2016 - International Conference on Noise and Vibration Engineering and USD2016 - International Conference on Uncertainty in Structural Dynamics | Year: 2016

An interpolatory model order reduction (MOR) strategy is proposed to compute the harmonic forced response of structures built up of substructures with frequency-dependent parameters. In this framework, the Craig-Bampton (CB) method is used for modeling each substructure by means of static modes and a reduced number of fixed-interface modes which are interpolated between several master frequencies. Emphasis is on the analysis of several substructures which can vibrate at different scales and, as such, do not need to be modeled with the same sets of interpolation points, depending on whether their modal density is low or high. For this purpose, an error indicator is developed to determine, through greedy algorithm procedure, the optimal number of interpolation points needed for each substructure. Additional investigations concern the selection of the fixed-interface modes which need to be retained for each substructure. Numerical experiments are carried out to highlight the relevance of the proposed approach, in terms of computational saving and accuracy.


Mencik J.-M.,CNRS Mechanics and Rheology Laboratory | Duhamel D.,University Paris Est Creteil
Proceedings of ISMA 2016 - International Conference on Noise and Vibration Engineering and USD2016 - International Conference on Uncertainty in Structural Dynamics | Year: 2016

A wave finite element (WFE) based approach is proposed to analyze the dynamic behavior of finite-length periodic structures which are made up of identical substructures but also contain several substructures whose material and geometric characteristics are slightly perturbed. Within the WFE framework, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two unperturbed substructures, and considering perturbed parts which are composed of perturbed substructures surrounded by two unperturbed ones. In doing so, a few wave modes are only required for modeling the central periodic structure, outside the perturbed parts. For forced response computation purpose, a reduced wave-based matrix formulation is established which follows from the consideration of transfer matrices between the right and left sides of the perturbed parts. Numerical experiments are carried out on a periodic 2D structure with two perturbed substructures which can be randomly located. The relevance of the WFE-based approach is clearly established in comparison with the FE method, in terms of accuracy and computational saving. Additional simulations are made to examine the feasibility to improve the robustness of periodic structures to the occurrence of a arbitrary slight perturbation, by artificially adding several "controlled" perturbed substructures.


Duhamel D.,University Paris Est Creteil | Mencik J.-M.,CNRS Mechanics and Rheology Laboratory
COMPDYN 2015 - 5th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering | Year: 2015

The wave finite element (WFE) method is investigated to describe the dynamic behavior of periodic structures like those composed of arbitrary-shaped substructures along a certain straight direction. A generalized eigenproblem based on the so-called S + S-1 transformation is proposed for accurately computing the wave modes which travel in right and left directions along those periodic structures. Besides, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two extra substructures. In doing so, a few wave modes are only required for modeling the central periodic structure. A comprehensive validation of the technique is performed on a 2D periodic structure. Also, its efficiency in terms of CPU time savings is highlighted regarding a 3D periodic structure that exhibits substructures with large-sized FE models.


Mencik J.-M.,CNRS Mechanics and Rheology Laboratory | Duhamel D.,University Paris Est Creteil
Finite Elements in Analysis and Design | Year: 2016

The wave finite element (WFE) method is investigated to describe the dynamic behavior of finite-length periodic structures with local perturbations. The structures under concern are made up of identical substructures along a certain straight direction, but also contain several perturbed substructures whose material and geometric characteristics undergo arbitrary slight variations. Those substructures are described through finite element (FE) models in time-harmonic elasticity. Emphasis is on the development of a numerical tool which is fast and accurate for computing the related forced responses. To achieve this task, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two unperturbed substructures, and considering perturbed parts which are composed of perturbed substructures surrounded by two unperturbed ones. In doing so, a few wave modes are only required for modeling the central periodic structure, outside the perturbed parts. For forced response computation purpose, a reduced wave-based matrix formulation is established which follows from the consideration of transfer matrices between the right and left sides of the perturbed parts. Numerical experiments are carried out on a periodic 2D structure with one or two perturbed substructures to validate the proposed approach in comparison with the FE method. Also, Monte Carlo (MC) simulations are performed with a view to assessing the sensitivity of a purely periodic structure to the occurrence of arbitrarily located perturbations. A strategy is finally proposed for improving the robustness of periodic structures. It involves artificially adding several “controlled” perturbations for lowering the sensitivity of the dynamic response to the occurrence of other uncontrolled perturbations. © 2016 Elsevier B.V.


Suresh K.S.,Indian Institute of Science | Geetha M.,Vellore Institute of Technology | Richard C.,CNRS Mechanics and Rheology Laboratory | Landoulsi J.,University Pierre and Marie Curie | And 3 more authors.
Materials Science and Engineering C | Year: 2012

We report investigations on the texture, corrosion and wear behavior of ultra-fine grained (UFG) Ti-13Nb-Zr alloy, processed by equal channel angular extrusion (ECAE) technique, for biomedical applications. The microstructure obtained was characterized by X-ray line profile analysis, scanning electron microscope (SEM) and electron back scattered diffraction (EBSD). We focus on the corrosion resistance and the fretting behavior, the main considerations for such biomaterials, in simulated body fluid. To this end, potentiodynamic polarization tests were carried out to evaluate the corrosion behavior of the UFG alloy in Hanks solution at 37°C. The fretting wear behavior was carried out against bearing steel in the same conditions. The roughness of the samples was also measured to examine the effect of topography on the wear behavior of the samples. Our results showed that the ECAE process increases noticeably the performance of the alloy as orthopedic implant. Although no significant difference was observed in the fretting wear behavior, the corrosion resistance of the UFG alloy was found to be higher than the non-treated material. © 2012 Elsevier B.V. All rights reserved.


Nait-Abdelaziz M.,University of Lille Nord de France | Nait-Abdelaziz M.,Lille Laboratory of Mechanics | Zairi F.,University of Lille Nord de France | Zairi F.,Lille Laboratory of Mechanics | And 4 more authors.
Mechanics of Materials | Year: 2012

Using the fracture mechanics framework, a fracture criterion based upon the intrinsic defect concept was developed to predict the failure of rubber parts under biaxial monotonic loading. This fracture criterion requires as input data the fracture toughness of the material in terms of critical value of the J integral, the constitutive law of the material and the breaking stretch of a smooth specimen under uniaxial tension. To develop this criterion a generalized expression of the J integral under biaxial loading is proposed on the basis of finite element calculations on a RVE containing a small circular defect. The estimated failure elongations were found in very nice agreement with experimental data on two kinds of rubber materials. Moreover, we have also shown that this criterion could be extended to the failure analysis of thermoplastic polymers. © 2012 Elsevier Ltd. All rights reserved.


Delattre A.,Airbus | Lejeunes S.,Aix - Marseille University | Lacroix F.,CNRS Mechanics and Rheology Laboratory | Meo S.,CNRS Mechanics and Rheology Laboratory
International Journal of Solids and Structures | Year: 2016

This work focuses on the characterization and the modeling of the complex dynamical behavior of a butadiene rubber filled with carbon black. This material is used in helicopter rotors and submitted to severe operating conditions. In particular the effects of the environmental temperature, of the amplitudes and frequencies of cyclic loading are studied. A new constitutive model that takes into account the Payne effect, the frequency, temperature and pre-loading dependencies is proposed. A specific material parameter fitting strategy is also introduced. © 2016 Elsevier Ltd.


Silva P.B.,University of Campinas | Mencik J.-M.,CNRS Mechanics and Rheology Laboratory | de Franca Arruda J.R.,University of Campinas
International Journal for Numerical Methods in Engineering | Year: 2015

The wave finite element (WFE) method is used for assessing the harmonic response of coupled mechanical systems that involve one-dimensional periodic structures and coupling elastic junctions. The periodic structures under concern are composed of complex heterogeneous substructures like those encountered in real engineering applications. A strategy is proposed that uses the concept of numerical wave modes to express the dynamic stiffness matrix (DSM), or the receptance matrix (RM), of each periodic structure. Also, the Craig-Bampton (CB) method is used to model each coupling junction by means of static modes and fixed-interface modes. An efficient WFE-based criterion is considered to select the junction modes that are of primary importance. The consideration of several periodic structures and coupling junctions is achieved through classic finite element (FE) assembly procedures, or domain decomposition techniques. Numerical experiments are carried out to highlight the relevance of the WFE-based DSM and RM approaches in terms of accuracy and computational savings, in comparison with the conventional FE and CB methods. The following test cases are considered: a 2D frame structure under plane stresses and a 3D aircraft fuselage-like structure involving stiffened cylindrical shells. © 2015 John Wiley & Sons, Ltd.


Le Quilliec G.,CNRS Mechanics and Rheology Laboratory | Raghavan B.,CNRS Civil and Mechanical Engineering Laboratory | Breitkopf P.,CNRS Roberval Laboratory (Mechanical Research Unit)
Computer Methods in Applied Mechanics and Engineering | Year: 2015

The parameters of a stamping process include the geometry of the tools, the shape of the initial sheet blank, the material constitutive law and the process parameters. When designing the overall process, one has to also take into account the springback effect that appears when the tools are removed and additional surfaces are cut-off. The goal then is to obtain a final shape as close as possible to the desired shape, while satisfying the admissibility constraints on the variable parameters as well as the feasibility constraints frequently expressed in the form of forming limit diagrams. In the present paper we represent the post-springback shape by a level set function. Then, rather than rely on arbitrarily selected case-dependent measurement locations as in the NUMISHEET benchmark problems, we build a reduced order "shape space" where this level set evolves, by extending our recent shape manifold approach to the problem of springback assessment for 3D shapes. Next, we propose an optimization algorithm designed to minimize the gap between the post-springback and the desired final shapes. The required level set functions are generated from a corresponding set of springback shapes predicted by Finite Element simulations. Using our approach, we determine the minimal number of parameters needed in order to uniquely characterize the final formed shape regardless of complexity. Finally, we demonstrate the approach using an industrial test-case: springback assessment of the deep drawing operation of an automotive strut tower. © 2014 Elsevier B.V.


Mencik J.-M.,CNRS Mechanics and Rheology Laboratory
Computational Mechanics | Year: 2014

The wave finite element (WFE) method is investigated to describe the harmonic forced response of one-dimensional periodic structures like those composed of complex substructures and encountered in engineering applications. The dynamic behavior of these periodic structures is analyzed over wide frequency bands where complex spatial dynamics, inside the substructures, are likely to occur. Within the WFE framework, the dynamic behavior of periodic structures is described in terms of numerical wave modes. Their computation follows from the consideration of the finite element model of a substructure that involves a large number of internal degrees of freedom. Some rules of thumb of the WFE method are highlighted and discussed to circumvent numerical issues like ill-conditioning and instabilities. It is shown for instance that an exact analytic relation needs to be considered to enforce the coherence between positive-going and negative-going wave modes. Besides, a strategy is proposed to interpolate the frequency response functions of periodic structures at a reduced number of discrete frequencies. This strategy is proposed to tackle the problem of large CPU times involved when the wave modes are to be computed many times. An error indicator is formulated which provides a good estimation of the level of accuracy of the interpolated solutions at intermediate points. Adaptive refinement is carried out to ensure that this error indicator remains below a certain tolerance threshold. Numerical experiments highlight the relevance of the proposed approaches. © 2014 Springer-Verlag Berlin Heidelberg.

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