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Zhu Q.-Z.,University Paris Est Creteil | Zhu Q.-Z.,Lille Laboratory of Mechanics
International Journal for Numerical Methods in Engineering | Year: 2012

This paper presents mathematical derivation of enrichment functions in the extended finite element method for numerical modeling of strong and weak discontinuities. The proposed approach consists in combining the level set method with characteristic functions as well as domain decomposition and reproduction technique. We start with the simple case of a triangular linear element cut by one interface across which displacement field suffers a jump. The main steps towards the derivation of enrichment functions are as follows: (1) extension of the subfields separated by the interface to the whole element domain and definition of complementary nodal variables; (2) construction of characteristic functions for describing the geometry and physical field; (3) determination of the sets of basic nodal variables; (4) domain decompositions according to Step 3 and then reproduction of the physical field in terms of characteristic functions and nodal variables; and (5) comparison of the piecewise interpolations formulated at Steps 3 and 4 with the standard extended finite element method form, which yields enrichment functions. In this process, the physical meanings of both the basic and complementary nodal variables are clarified, which helps to impose Dirichlet boundary conditions. Enrichment functions for weak discontinuities are constructed from deeper insights into the structure of the functions for strong discontinuities. Relationships between the two classes of functions are naturally established. Improvements upon basic enrichment functions for weak discontinuities are performed so as to achieve satisfactory convergence and accuracy. From numerical viewpoints, a simple and efficient treatment on the issue of blending elements is also proposed with implementation details. For validation purposes, applications of the derived functions to heterogeneous problems with imperfect interfaces are presented. © 2012 John Wiley & Sons, Ltd.

Cenerario N.,Lille Laboratory of Mechanics | Delot T.,Lille Laboratory of Mechanics | Ilarri S.,University of Zaragoza
IEEE Transactions on Intelligent Transportation Systems | Year: 2011

This paper focuses on intelligent transportation systems and, more precisely, on intervehicle ad hoc networks. A vehicular ad hoc network (VANET) is a highly dynamic network as the vehicles communicate using short-range wireless communications and can move very quickly. Thus, for example, we can only rely on short interactions between vehicles to exchange information about relevant events. In this paper, we describe in detail a dissemination protocol that vehicles can use to share information by using vehicle-to-vehicle communications. The dissemination approach considers the relevance of the data, represented by what we call encounter probability, to decide when a rediffusion is needed. The protocol is able to disseminate data about any type of event in the network (e.g., available parking spaces, accidents or obstacles in the road, information about moving objects such as emergency vehicles that should get the right of way, etc.) by setting appropriate weights for the different factors that affect the computation of the encounter probability. An extensive experimental evaluation with different types of events shows the interest of the proposal: The vehicles receive the relevant messages in time, and the network overload is limited. © 2006 IEEE.

Zhu Q.Z.,Lille Laboratory of Mechanics | Shao J.F.,Lille Laboratory of Mechanics | Mainguy M.,Total S.A.
International Journal of Plasticity | Year: 2010

This paper is devoted to the formulation of a micromechanics-based constitutive model for granular materials under relatively low confining pressure. The constitutive formulation is performed within the general framework of homogenization for granular materials. However, new rigorous stress localization laws are proposed. Some local constitutive relations are established under the consideration of irreversible thermodynamics. Macroscopic plastic deformation is obtained by considering local plastic sliding in a limit number of families of contact planes. The plastic sliding at each contact plane is described by a non-associated plastic flow rule, taking into account pressure sensitivity and normal dilatancy. Nonlinear elastic deformation related to progressive compaction of contacts is also taken into account. Material softening is described by involving damage process related to degradation of microstructure fabric. The proposed model is applied to some typical granular materials (sands). The numerical predictions are compared with experimental data. © 2009 Elsevier Ltd. All rights reserved.

Pastor F.,Lille Laboratory of Mechanics | Kondo D.,University Pierre and Marie Curie
European Journal of Mechanics, A/Solids | Year: 2013

Several extensions of the Gurson model have been proposed such as to account for void shape effects (e.g. Gologanu, M., Leblond, J., 1993. Approximate models for ductile metals containing non-spherical voids e case of axisymmetric prolate ellipsoidal cavities. Journal of the Mechanics and Physics of Solids 41 (11), 1723e1754; Gologanu, M., Leblond, J., Perrin, G., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids e case of axisymmetric oblate ellipsoidal cavities. Journal of Engineering Materials and Technology 116, 290e297; Gologanu, M., Leblond, J., Perrin, G., Devaux, J., 1997. Recent extensions of Gurson's model for porous ductile metals. In: Suquet, P. (Ed.), Continuum Micromechanics, Springer Verlag; Garajeu, M., Suquet, P., 1997. Effective properties of porous ideally plastic or viscoplastic materials containing rigid particles. Journal of the Mechanics and Physics of Solids 45, 873e902 and more recently by Monchiet, V., Charkaluk, E., Kondo, D., 2007. An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields. Comptes Rendus Mécanique 335, 32e41). The main goal of this study is to assess the latter models by establishing relevant numerical LA-type lower and upper bounds to the exact solutions for 3D stress and strain conditions. Numerical limit analysis techniques are extended to the case of spheroid cavities under various 3D loading conditions. First numerical tests for the hollow sphere (Gurson) model were performed to verify the computational efficiency of the new codes. A second series of tests, performed for uniform strain rate boundary conditions and axisymmetric loadings, allowed to assess the criteria proposed by Gologanu et al. in the case of prolate voids as well as oblate ones. It is shown that the 1997-Gologanu et al. criterion appears to be very accurate for the above boundary conditions. For the assessment of a recent criterion derived by Monchiet et al. (2007), we performed other computations corresponding to uniform stress boundary conditions for both oblate and prolate cavities. It is shown that the Monchiet et al. (2007) criterion appears to be an estimate which may be improved. However, this criterion is very accurate when compared to the numerical results with strain rate boundary conditions. Finally a first attempt with 3D-loadings seems to confirm the above conclusions. © 2012 Elsevier Masson SAS. All rights reserved.

Liu J.,Lille Laboratory of Mechanics | Qi T.,Southwest Jiaotong University | Wu Z.,Southwest Jiaotong University
Tunnelling and Underground Space Technology | Year: 2012

Using expanding excavation based on shield tunnel can be regarded as a new approach to construct a metro station, especially when traditional methods cannot be implemented. This paper focuses on the ground movement property caused by shield tunneling and expanding construction. Ground movement property and construction influence scope, which happens during the construction process, are obtained by large numbers of numerical calculations and monitoring measurements. Results show that expanding excavation is the main factor which affects ground movement, and its influence will increase as the stability of surrounding rock deteriorates. Besides, horizontal displacement and vertical displacement (uneven settlement) are the two important factors which lead to building deformation and cracks; therefore, more attention should be given to these areas where the maximum displacement may occur during the construction process. Analysis of the two parameters, length to diameter ratio and depth to diameter ratio, indicates their relationship with safety of tunnel and building. Influence degree and scope of ground settlement are obtained due to change of the two parameters. The practical importance of this analysis is that we can judge whether building and tunnel are in a dangerous zone and thereby adopt relevant pre-reinforcements to ensure their safety. Later with the comparison of numerical simulation and in-situ data, we verify the accuracy of simulation. © 2011 Elsevier Ltd.

Drai A.,Lille Laboratory of Mechanics | Drai A.,Normal Superior School of Technical Education Oran | Aour B.,Normal Superior School of Technical Education Oran
Engineering Structures | Year: 2013

High pressure torsion (HPT) is an effective tool to modify microstructures via severe plastic deformation. In order to optimize the process conditions and then to control the change in microstructure, the estimation of the plastic strain achieved in the processed material is of utmost importance. Noting that the key parameters of HPT process are essentially the imposed pressure and the number of revolutions applied to the samples. The goal of this work is to numerically investigate the effects of these parameters on the plastic strain homogeneity during HPT of a typical semicrystalline polymer (high-density polyethylene: HDPE). To this end, compressive tests at different strain rates were used to estimate the material parameters of a phenomenological elastic-viscoplastic model. Then, the HPT process was analyzed by 3-dimensional finite element method to highlight the distribution of the plastic strain, the equivalent plastic strain rate and the mean normal stresses. It was found that the optimal strain homogeneity was obtained by a weak vertical displacement and a high torsion angle. © 2012 Elsevier Ltd.

Parsa S.,Wesleyan University | Calzavarini E.,Lille Laboratory of Mechanics | Toschi F.,TU Eindhoven | Voth G.A.,Wesleyan University
Physical Review Letters | Year: 2012

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape. © 2012 American Physical Society.

Pavlov V.I.,Lille Laboratory of Mechanics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012

We analytically study the evolution of gravitational instability of self-gravitating dark matter within the framework of a nonrelativistic "hydrodynamical" model of the Universe, valid for scales that are small compared to the Hubble scale and for distances far away from black holes. We propose a particular form for parametrization of the particle distribution function via macroscopic quantities, such that the initial dispersion of microscopic velocities is not neglected, but plays a determinant role. Thus our model may be called a modified cold dark matter model. We found an analytical solution which indicates that a spontaneous spatially localized fluctuation of velocity generates density perturbations relative to initially unperturbed background. For the instability to arise, we do not need to assume any initial density (metric) fluctuations. The evolving perturbation is hydrodynamically unstable in the self-gravitating expanding Universe and can produce both-regions where no dark matter accumulates and halolike regions where dark matter does accumulate. The perturbation region boundary propagates as a shock wave with a speed that is time varying, until eventually reaching its steady state. We also derive an explicit analytical expression for the correlation function R(x 1-x 2) of density fluctuations, which can be compared by experimentalists with data from astrophysical observations. © 2012 American Physical Society.

Jiang T.,Multiscale Design Systems, LLC | Shao J.F.,Lille Laboratory of Mechanics
Computers and Geotechnics | Year: 2012

Micromechanical analysis based on the fast Fourier transform (FFT) is presented as applied to the nonlinear behavior of porous geomaterials. In this micromechanical model, a simple classical constitutive model is employed for the solid phase, such that the distinct mechanical properties of porous geomaterials can be subsequently and satisfactorily predicted without the use of additional parameters. Furthermore, the FFT-based model automatically satisfies the periodic boundary condition of the micromechanics scheme. The efficacy of the model is shown by applications to Lixhe chalk and Vosges sandstone. © 2012 Elsevier Ltd.

Bikong C.,Lille Laboratory of Mechanics | Hoxha D.,University of Orléans | Shao J.F.,Lille Laboratory of Mechanics
International Journal of Plasticity | Year: 2015

In this paper, a micro-macro model is proposed for the time-dependent behavior of clayey rocks. Two material scales are considered. At the mesoscopic scale, the studied material is represented by a three-phase composite. Quartz and calcite grains are embedded inside the clay matrix. At the microscopic scale, the clay matrix is characterized by a cracked elastic solid. The creep deformation is assumed to be induced by the time-dependent propagation of anisotropic microcracks inside the clay matrix. A two-step homogenization procedure is proposed. The effective elastic properties of the cracked clay matrix are first determined using an Eshelby solution based homogenization method. Two different homogenization schemes are used respectively with and without taking into account crack interactions. Then the macroscopic mechanical properties of heterogeneous clayey rocks are determined by the second homogenization step using the Mori Tanaka Scheme. A sensitivity study is performed in order to evaluate macroscopic consequences of the microscopic time-dependent propagation law of microcracks. Finally, comparisons between numerical results and experimental data from creep tests are presented. © 2015 Elsevier Ltd. All rights reserved.

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