LMT-Cachan

    PANETIER, J., LADEVEZE, P., CHAMOIN, L.    "Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM"    Int. Jnl. Numer. Meth. Eng., Vol. 81, pp. 671-700, 2010. DOI

Contributions to the global error estimate for the adjoint problem solved using XFEM and a mesh consisting of 1071 elements.

Abstract: In this work, we analyze a method which leads to strict and high-quality local error bounds in the context of fracture mechanics. We investigate in particular the capability of this method to evaluate the discretization error for quantities of interest computed using the eXtended Finite Element Method (XFEM). The goal-oriented error estimation method we are focusing on uses the concept of Constitutive Relation Error (CRE) along with classical extraction techniques. The main innovation in this paper resides in the methodology employed to construct admissible fields in the XFEM framework, which involves enrichments with singular and level set basis functions. We show that this construction can be performed through a generalization of the classical procedure used for the standard finite element method. Thus, the resulting goal-oriented error estimation method leads to relevant and very accurate information on quantities of interest which are specific of fracture mechanics, such as mixed-mode stress intensity factors. The technical aspects and the effectiveness of the method are illustrated through two-dimensional numerical examples.

    ALLIX, O., KERFRIDEN, P. GOSSELET, P.    "On the control of the load increments for a proper description of multiple delamination in a domain decomposition framework."    Int. J. Num. Meth. Eng., accepted for publication draft PDF

Damage state in the interfaces of the holed plate at the beginning of a global instability in the case of a coarse time grid (Case 1), and in a converged case (Case 2). A Fixed arc-length is prescribed in both cases. In the first case, the damage in the [−45 +45] interface is underestimated.

Abstract: In quasi-static nonlinear time-dependent analysis, the choice of the time discretization is a complex issue. The most basic strategy consists in determining a value of the load increment that ensures the convergence of the solution with respect to time on the base of preliminary simulations. In more advanced applications, the load increments can be controlled for instance by prescribing the number of iterations of the nonlinear resolution procedure, or by using an arc-length algorithm. These techniques usually introduce a parameter whose correct value is not easy to obtain. In this paper, an alternative procedure is proposed. It is based on the continuous control of the residual of the reference problem over time, whose measure is easy to interpret. This idea is applied in the framework of a multiscale domain decomposition strategy in order to perform 3D delamination analysis.

    ZHANG, J., AIMEDIEU, P., HILD, F., ROUX, S., ZHANG, T.    "Complexity of shear localization in a Zr-based bulk metallic glass"    Scripta Materialia , Vol. 61, pp. 1145-1148, 2009. DOI

a) Three IR camera images after shear band slips during the experimental test. Note that the left image shows a partial slip or rotation, while the right one displays a kink (shown with an arrow) that can be interpreted as the mobilization of two slip planes. b) (Left) Three consecutive incremental strain maps obtained from DIC showing multiple slip systems being simultaneously active. (Right) Strain map prior to failure where A shows a branching point and B shows a kink produced by the intersection of two slip bands. The colour bar indicates the apparent strain level computed over 35 µm wide elements.

Abstract: The compressive behaviour of a Zr-based metallic glass was studied in situ through optical and infrared imaging. Results show that localization bands are more complex than simple planes, and interactions between different slip systems are an essential ingredient to understanding slip arrest and hence the ultimate strain such materials sustain. Roughness, which is responsible for both the damage and arrest mechanisms, is argued to be another key feature that enhances the ultimate macroscopic shear strain.

    ROUX, S., RETHORE, J., HILD, F.    "Digital image correlation and fracture: An advanced technique for estimating stress intensity factors of 2D and 3D cracks"    Journal of Physics D: Applied Physics, Vol. 42, pp. 214004 (21 p.), 2009. DOI

a) Reference (load 5N) and deformed (load 100 N) 3D images of a cracked sample. The load is applied along the longitudinal direction (normal to the crack). b)Geometry of the crack surface (left). Displacement component (expressed in voxels) along the loading direction obtained from DVC using an enriched kinematics (right). The volume shown here lies strictly inside the sample to avoid edge effects. The voxel size is 3.5μm.

Abstract: Digital image correlation is a measurement technique that allows one to retrieve displacement fields ‘separating’ two digital images of the same sample at different stages of loading. Because of its remarkable sensitivity, it is possible to not only detect cracks with sub-pixel opening, which would not be visible but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from the atomistic to the geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three-dimensional cracks based on x-ray Computed micro-tomographic images (see figure).

    TRUMEL, H., HILD, F., ROY, G., PELLEGRINI, Y.-P., DENOUAL, C.    "On probabilistic aspects in the dynamic degradation of ductile materials"    Journal of the Mechanics and Physics of Solids, Vol. 57, pp. 1980-1998, 2009. DOI

Example of a 5mm thick tantalum sample damaged by a symmetric impact at 270 m/s by a CuC2 flyer plate (the shock wave traveled from top to bottom); zone I: uniaxially loaded, zone II: biaxially loaded, zone III: rapidly unloaded. Only the left half of the target is shown. The right edge of the image is close to the symmetry axis.

Abstract: Dynamic loadings produce high stress waves leading to the spallation of ductile materials such as aluminum, copper, magnesium or tantalum (see figure). The main mechanism used herein to explain the change of the number of cavities with the stress rate is nucleation inhibition, as induced by the growth of already nucleated cavities. The dependence of the spall strength and critical time with the loading rate is investigated in the framework of a probabilistic model. The present approach, which explains previous experimental findings on the strain-rate dependence of the spall strength, is applied to analyze experimental data on tantalum.

    BORNERT, M., BREMAND, F., DOUMALIN, P., DUPRE, J.-C., FAZZINI, M., GREDIAC, M., HILD, F., ROUX, S., MISTOU, S., MOLIMARD, J., ORTEU, J.-J., ROBERT, L., SURREL, Y., VACHER, P., WATTRISSE, B.    "Assessment of Digital Image Correlation Measurement Errors: Methodology and Results"    Experimental Mechanics, Accepted for publication. Vol. 49, pp. 353-370, 2009. DOI

Influence of the first and second displacement gradients on the local standard deviation.

Abstract: Optical full-field measurement methods such as Digital Image Correlation (DIC) are increasingly used in the field of experimental mechanics, but they still suffer from a lack of information about their metrological performances. To assess the performance of DIC techniques and give some practical rules for users, a collaborative work has been carried out by the Workgroup “Metrology” of the French CNRS research network 2519 “MCIMS (Mesures de Champs et Identification en Mécanique des Solides / Full-field measurement and identification in solid mechanics, http://www.ifma.fr/lami/gdr2519.)”. A methodology is proposed to assess the metrological performances of the image processing algorithms that constitute their main component, the knowledge of which being required for a global assessment of the whole measurement system. The study is based on displacement error assessment from synthetic speckle images. Series of synthetic reference and deformed images with random patterns have been generated, assuming a sinusoidal displacement field with various frequencies and amplitudes. Displacements are evaluated by several DIC packages based on various formulations and used in the French community. Evaluated displacements are compared with the exact imposed values and errors are statistically analyzed. Results show general trends rather independent of the implementations but strongly correlated with the assumptions of the underlying algorithms. Various error regimes are identified, for which the dependence of the uncertainty with the parameters of the algorithms, such as subset size, gray level interpolation or shape functions, is discussed.

    BENOIT, A., GUERARD, S., GILLET, B., GUILLOT, G., HILD, F., MITTON, D., PERIE, J.-N., ROUX, S.    "3D analysis from micro-MRI during in situ compression on cancellous bone"    Journal of Biomechanics , Vol. 42, pp. 2381-2386. DOI

Cuts along two planes containing the longitudinal axis of the region of interest. The gray level picture and the longitudinal strain fields corresponding to the two loading steps are shown.

Abstract: A mini-compression jig was built to perform in situ tests on bovine trabecular bone monitored by micro-MRI. The MRI antenna provided an isotropic resolution of 78 mm that allows for a volume correlation method to be used. Three-dimensional displacement fields are then evaluated within the bone sample during the compression test. The performances of the correlation method are evaluated and discussed to validate the technique on trabecular bone. By considering correlation residuals and estimates of acquisition noise, the measured results are shown to be trustworthy. By analyzing average strain levels for different interrogation volumes along the loading direction, it is shown that the sample size is less than that of a representative volume element. This study shows the feasibility of the 3D-displacement and strain field analyses from micro-MRI images. Other biological tissues could be considered in future work.

    CAIGNOT, A., LADEVEZE, P., NERON, D., DURAND, J.-F.    "Virtual testing for the prediction of damping in joints"    Engineering Computations, Accepted for publication.

The dissipation and slippage map.

Abstract: The purpose of this work is to propose a strategy for the prediction of damping in the joints which are present in the ARIANE 5 space launcher. Our approach is based on the use of the LArge Time INcrement (LATIN) method to test the behavior of the joints under alternating loading virtually, then calculate the dissipations due to friction. The damping thus predicted is compared to experimental results, and the approach appears promising. Then, several parametric studies are performed in order to analyze the influence of various parameters, such as the friction coefficient or the pretension in the bolts.

    LIMODIN, N., RETHORE, J., BUFFIERE, J.-Y., GRAVOUIL, A., HILD, F., ROUX, S.    "Crack closure and stress intensity factor measurements in nodular graphite cast iron using three-dimensional correlation of laboratory X-ray microtomography images"    Acta Materialia, Vol. 57(14), pp. 4090-4101, 2009. DOI

SIF values along the crack front for (a) mode I, (b) mode II and (c) mode III. Measured (‘‘FF”) values of SIF (symbols) are compared with computed (‘‘E”) values (lines). The hatched area in (a) corresponds to the Kop range obtained from literature data.

Abstract: Three-dimensional (3-D) tomographic images of a nodular graphite cast iron obtained using a laboratory X-ray source were used to analyze the opening of a fatigue crack during in situ mechanical loading. Direct image analysis and digital image correlation are utilized to obtain the 3-D morphology and front location of the crack, as well as the displacement fields in the bulk of the specimen. From digital image correlation results it is possible to extract the crack opening displacement (COD) map in the whole sample cross-section and to compute stress intensity factors (SIFs) all along the crack front, even for COD values that are less than the image resolution. The comparison of COD maps with local values of the SIF enabled for an estimation of the opening SIF (Kop) equal to 6 MPa m1/2.

    GUIMARD, J.-M., ALLIX, O., PERCHNIK, N., THEVENET, P.    "Characterization and modeling of rate effects in the dynamic propagation of mode-II delamination in composite laminates"    International Journal of Fracture, online. DOI

Numerical results for the extent of the process zone versus crack velocity: effect of the rate dependence

Abstract: This paper addresses the question of rate effects in the propagation of delamination cracks in Composite Fiber-Reinforced Plastics (CFRPs). In order to make use of a simple loading device, a mode-II case is used as the basis of the experimental study. The position of the crack is recorded quantitatively by means of a high-speed camera and dedicated image processing techniques. The delamination process is modeled by means of an interfacial Continuum Damage Model (CDM), similar to Cohesive Zone Model (CZM) approaches. In order to make suitable comparison between test and explicit finite element simulation of the test, criterai of proper temporal and spatial discretization have been derived. They ensure a fine description of the process zone and a proper description of the degradation evolution of the interface. Using such simulations and direct comparisons with the tests results, it is shown that the experimentalresults cannot be reproduced numerically without introducing rate effects. Then, it is proposed and identified by means of comparison between experiments and numerical simulation a bounded-damage-rate interfacial model. The main consequence of the proposed rate-dependent model is that it introduces a maximum crack velocity which is a function of the maximum damage rate. The dependence of the critical energy release rate on the crack’s velocity is analyzed, which leads to the identification of an equivalent rate-dependent fracture mechanics criterion.

    GUIMARD, J.-M., ALLIX, O., PERCHNIK, N., THEVENET, P.    "Energetic analysis of fragmentation mechanisms and dynamic delamination modelling in CFRP composites"    Computers and Structures, Vol. 87 (15-16), pages 1022-1032. DOI

(a) Identification of peak loads repartition law (Weibul normal), and (b) Identification of dissipated energy repartition law (Weibul normal) for Ti300.

Abstract: this paper deals with the understanding and the numerical simulation of complex dissipative phenomena involved in composite absorbers for two main degradation modes: the fragmentation and the delamination modes. Fragmentation is the last step of degradation in pure compression leading to total failure of a laminate and for CFRP it is mainly initiated by a microbuckling mechanism, which is dependant on the microstructural imperfections. The dissipated energies associated to the fragment creation are evaluated through micromodelling approaches and contrary to expectations, these energies seem to be insensitive to microscopic parameters. A Weibull density knowledge on peak load and dissipated energy is also proposed. On the other hand, computation control on the delamination process has been investigated. Numerical sensitivities are justified thanks to analytical approaches and physical based mesh criteria are proposed for classical propagation tests. Some quasi-static experiments have been performed and good accuracy is obtained with the model. All these results give perspectives to implement delamination and fragmentation interactions at mesoscale within an absorber-like configuration.

    KASSIOTIS, M., COLLIAT, J.-B., IBRAHIMBEGOVIC, A., MATTHIES, H. G.    "Multiscale in time and stability analysis of operator split solution procedures applied to thermomechanical problems"    Engineering Computations, Vol. 26(1-2), pages 205-223. DOI

Abstract: Purpose: The purpose of this paper is to study the partitioned solution procedure for thermomechanical coupling, where each sub-problem is solved by a separate time integration scheme. Design/methodology/approach: In particular, the solution which guarantees that the coupling condition will preserve the stability of computations for the coupled problem is studied. The consideration is further generalized for the case where each sub-problem will possess its particular time scale which requires different time step to he selected for each sub-problem. Findings: Several numerical simulations are presented to illustrate very satisfying performance of the proposed solution procedure and confirm the theoretical speed-up of computations which follow from the adequate choice of the time step for each sub-problem. Originality/value: The paper confirms that one can make the most appropriate selection of the time step and carry out the separate computations for each sub-problem, and then enforce the coupling which will preserve the stability of computations with such,in operator split procedure.

This picture shows coupling algorithm by Gauss-Seidel method on the same window with small time steps for mechanics (system 1) and large time steps for heat transfer (system 2).

    NIEKAMP, R., MARKOVIC, D., IBRAHIMBEGOVIC, A., MATTHIES, H. G., TAYLOR, R. L.    "Multi-scale modelling of heterogeneous structures with inelastic constitutive behavior - Part II - software coupling implementation aspects"    Engineering Computations, Vol. 26(1-2), pages 6-28. DOI

Abstract: Purpose: The purpose of this paper is to consider the computational tools fur solving a strongly coupled multi-scale problem in the context of inelastic structural mechanics. Design/methodology/approach: In trying to maintain the highest level of generality, the finite clement method is employed for representing the microstructure: at this fine scale and computing the solution. The main focus of this work is the implementation procedure which crucially relies on a novel software product developed by the first author in terms of component template library (CTL). Findings: The paper confirms that trills that one can produce very powerful Computational tools by software coupling technology described herein, which allow; the class of complex problems one can successfully tackle nowadays to be extended significantly. Originality/value: This paper elaborates upon a nets multi-scale solution strategy suitable for highly non-linear inelastic problems.

This picture shows the coupling algorithm by Gauss-Seidel method on the same window with small time steps for mechanics (system 1) and large time steps for heat transfer (system 2)

    IBRAHIMBEGOVIC, A., HERVE, G., VILLON, P.    "Nonlinear impact dynamics and field transfer suitable for parametric design studies"    Engineering Computations, Vol. 26(1-2), pages 185-204. DOI

Abstract: Purpose: The purpose of this paper is to provide the methodology for structural design of complex massive structures under impact by a large airplane. Design/methodology/approach: Using case studies, the issues related to multi-scale modelling of inelastic damage mechanisms for massive structures are discussed, as well as the issues pertaining to the time integration schemes in presence of different scales in time variation of different sub-problems, brought by a particular nature of loading with a very short duration) and finally the issues related to model reduction seeking to provide an efficient and yet sufficiently reliable basis for parametric studies which are an indispensable part. of a design procedure. Findings: Several numerical simulations are presented in order to further illustrate the approaches proposed herein. Concluding remarks are stated regarding the current and future research in this domain. Originality/value: Proposed design procedure for complex massive engineering structures under impact by a large airplane provides on one side a very reliable representation of inelastic damage mechanisms and external loading represented by the solution of the corresponding contact/impact problem, and on the other side a very efficient basis obtained by model reduction for performing the parametric design studies.

This picture shows the analysis-design procedure based on split between local phase and global phase.

    MARKOVIC, D., IBRAHIMBEGOVIC, A., PARK, K. C.    "Partitioning based reduced order modelling approach for transient analyses of large structures"    Engineering Computations, Vol. 26(1-2), pages 46-68. DOI

Abstract: Purpose: The purpose of this piper is to describe reduced order modelling based on dynamic flexibility approximation and applied to transient analyses. Design/methodology/approach: This work is based oil a recently proposed flexibility-based component modes synthesis (CMS) approach which was shown to he very efficient for solving large eigenvalue problems. The model reduction approach is based oil partionning via the localized Lagrange multipliers method, which makes it very appropriate late to handle coupled problems. Findings: In particular, it is demonstrated in this paper how the utilised model reduction method and efficielltly coupled to a full finite element model. The performance of the method is investigated on numerical examples of plate and 3D problems. Originality/value: The proposed, flexibility-based CMS approach call be used as a very efficient tool for complex engineering structures under dynamic load where these mode superposition method applies. The efficiency of the computations is brought about by the model reduction.

This picture shows the substructuring by the method of localized Lagrange multipliers.

    GOSSELET, P., RIXEN, D., REY, C.    "A domain decomposition strategy to efficiently solve structures containing repeated patterns"    International Journal for Numerical Methods in Engineering, Vol. 78(7), pages 828-842. DOI

Abstract: This paper presents a strategy for the computation of structures with repeated patterns based on domain decomposition and block-Krylov solvers. It can be seen as a special variant of the FETI method. We propose using the presence of repeated domains in the problem to compute the solution by minimizing the interface error on several directions simultaneously. The method not only drastically decreases the size of the problems to solve but also accelerates the convergence of interface problem for nearly no additional computational cost and minimizes expensive memory accesses. The numerical performances are illustrated on some thermal and elastic academic problems.

This picture shows an example of structure the method is dedicated to.

    BRANCHERIE, D., IBRAHIMBEGOVIC, A.    "Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures: Part I: theoretical formulation and numerical implementation"    Engineering Computations, Vol. 26(1-2), pages 100-127. DOI

Abstract: Purpose: The purpose of this paper is to present a finite element model capable of describing both the diffuse damage mechanism which develops first during the loading of massive brittle structures and the failure process, essentially due to the propagation of a macro-crack responsible for the softening behaviour of the structure. The theoretical developments for such a model are presented, considering an isotropic damage model for the continuum and a Coulomb-type criterion for the localized part. Design/methodology/approach: This is achieved by activating subsequently diffuse and localized damage mechanisms. Localized phenomena are taken into account by meanns of the introduction of a displacement discontinuity at the element level. Finding: It was found that, with such an approach, the final crack direction is predicted quite well, in fact much better than the prediction made by the fracture mechanics type of models considering combination of only elastic response and softening. Originality/value: The presented model has the potential to describe complex damage phenomena in a cyclic and/or non-proportional loading program, such as crack closing and re-opning, cohesive resistance deterioration due to tangential sliding by using only a few parameters compared to the traditonal models for cyclic loading.

This picture shows the load-displacement diagram for structured and unstructured meshes.

    KUCEROVA, A., BRANCHERIE, D., IBRAHIMBEGOVIC, A., ZEMAN, J., BITTNAR, Z.    "Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures Part II: identification from tests under heterogeneous stress field"    Engineering Computations, Vol. 26(1-2), pages 128-144. DOI

Abstract: Purpose: The purpose of this paper is too discuss the identification of the model parameters for constitutive model capable of representing the failure of massive structure. from two kinds of experiments, a uniaxial tensile test annd a three-point bending test. Design/methodology/approach: A detailed development of the ingredients for constitutive model for failure of massive structures are presented in Part I of this paper. The salient feature of the model is in its ability to correctly represent two different failure mechanisms for massive structures. the diffuse damage in so-called fracture process zone with microcracks and localized damage in a macrocrak. The identification of such model parameters is best performed from thhe tests under heterogeneous stress field. Two kinds of tests are used the simple tension test and the three-point bending test. The former allows us illustrate the non-homogeneity of the strain field at failure enve under homogeneous stress, whereas the latter provides a very good illustration for the proposed inverse optimization proble for which the specimanis subjected to a heterogeneous stress field. Findings: Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology for identifying the corresponding material parameters of the constitutive model for failure of massive structures. Originality/value: The paper confirms that one can make a very good use of the proposed identification procedure for estimating the corresponding parameters of damage model for localized failure of massive structure, and the advantages to using the experimental results obtained by testing under heterogeneous stress field.

This picture shows the definition of cost function for different phases of response in parameter identification.

    HAUTEFEUILLE, M., MELNYK, S., COLLIAT, J.-B., IBRAHIMBEGOVIC, A.    "Failure model for heterogeneous structures using structured meshes and accounting for probability aspects"    Engineering Computations, Vol. 26(1-2), pages 166-184. DOI

Abstract: Purpose: The purpose of this paper is to discuss the inelastic behavior of heterogeneous structures within the framework of finite element modelling, by taking into the related probabilistic aspects of heterogeneities. Design/methodology/approach: The paper shows how to construct the structured FF mesh representation lot the failure modelling for such structures, by using a building-block of a constant stress element which can contain two different phases and phase interface. All the modifications Which are needed to enforce for such an element ill order to for inelastic behavior in each phase and the corresponding inelastic failure modes at the phase interface are presented. Findings: It is demonstrated by numerical examples that the proposed structured FE mesh approach is much more efficient from the non-structured mesh representation. This feature is of Special interest for probabilistic analysis, where a large amount of computation is needed ill order to provide the corresponding statistics. One such case of probabilistic analysis is considered in this work where. the geometry of the phase interface is obtained is the result of the Gibbs random process. Originality/value: The paper confirms, that one can make the most appropriate interpretation of the heterogeneous structure properties by taking into account the fine details of the internal structure, along, with the related probabilistic aspects with the proper source of randomness, such as the one addressed herein in terms of porosity.

This picture shows the definition of cost function for different phases of response in parameter identification.

    BOHINC, U., IBRAHIMBEGOVIC, A., BRANK, B.    "Model adaptivity for finite element analysis of thin or thick plates based on equilibrated boundary stress resultants"    Engineering Computations, Vol. 26(1-2), pages 66-69. DOI

Abstract: Purpose: The purpose of this paper is to address error-controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable plate model (among available hierarchical plate models) for each particular FE of the selected mesh, that is provided as the final output of the mesh, adaptivity procedure. Design/methodology/approach: The model adaptivity procedure can be seen as an appropriate extension to model adaptivity for linear elastic plates of so-called equilibrated boundary traction approach error estimates, previously proposed for 2D/3D linear elasticity. Model error indicator is based on a posteriori element-wise computation of improved (continuous) equilibrated boundary stress resultants, and on a set of hierarchical plate models, The paper illustrates the details of proposed model adaptivity procedure for choosing between two most frequently used plate models: the one of Kirchhoff and the other of Reissner-Mindlin. The implementation details are provided for a particular case of the discrete Kirchhoff quadrilateral four-node plate FE and the Corresponding Reissner-Mindlin quadrilateral with the same number of nodes. The key feature for those elements that they both provide the same quality of the discretization space (and thus the same discretization error) is the one which justifies uncoupling of the proposed model adaptivity from the mesh adaptivity. Findings: Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology in guiding the final choice of the optimal model and mesh in analysis of complex plate structures. Originality/value: The paper confirms that: one call make an automatic selection of the most appropriate plate model for thin and thick plates on the basis of proposed model adaptivity procedure.

    HILD, F., MAIRE, E., ROUX, S., WITZ, J.-F.    "Three-dimensional analysis of a compression test on stone wool"    Acta Materialia, Vol. 57(11), pages 3310-3320. DOI

The figure shows 3D isosurface to highlight the regions where the measured compression strain is the highest (a), and where the gray level of the reconstructed images are low, i.e. with the smaller density (b). The strains were obtained by using the sample in its first deformed state, and the gray level for the sample in its initial state (i.e. before deformation).

Abstract: A full three-dimensional (3D) study of a compression test on a sample made of stone wool is presented. The analysis combines different tools, namely X-ray microtomography of an in situ experiment, image acquisition and treatment, and volume correlation. This set of tools allows for the measurement of 3D displacement fields and enables Poisson’s ratio of this type of material to be evaluated. The strain fields are used to analyze localization phenomena. The uncertainty of the analysis is evaluated by actually moving the sample in its undeformed and deformed states, qualifying both image acquisition and correlation steps.

    KERFRIDEN, P., ALLIX, O., GOSSELET, P.    "A three-scale domain decomposition method for the 3D analysis of debonding in laminates"    Computational Mechanics, Vol. 44(3), pages 343-362. DOI

Abstract: The prediction of the quasi-static response of industrial laminate structures requires to use fine descriptions of the material, especially when debonding is involved. Even when modeled at the mesoscale, the computation of these structures results in very large numerical problems. In this paper, the exact mesoscale solution is sought using parallel iterative solvers. The LaTIn-based mixed domain decomposition method makes it very easy to handle the complex description of the structure; moreover the provided multiscale features enable us to deal with numerical difficulties at their natural scale; we present the various enhancements we developed to ensure the scalability of the method. An extension of the method designed to handle instabilities is also presented.

This picture shows the damage map in the 0/90 interfaces of a four-plies holed plate laminated composite test case (stacking sequence [0 90]_s, 3.10^6 degrees of freedom, computation performed using 10 CPU), under traction. The global behavior of the structure is also represented.

    AMIOT, F., KANOUFI, F., HILD, F., ROGER, J. P.    "Charge redistribution in electrochemically actuated mechanical sensors"    Sensors and Actuators A, Vol. 152, pages 88-95. DOI

The picture is a schematic view of the imaging set-up and typical interference pattern. The shear direction is parallel to the cantilever direction, and the shear distance d is almost equal to the cantilever length. The axis system is shifted for the sake of clarity and the origin is set at point O.

Abstract: Many proofs of concept studies have established the mechanical sensitivity of functionalized microcantilevers to a large spectrum of target molecules. However, moving to real-life applications also requires the monitored mechanical effect to be highly specific. Moving towards more specificity in cantileverbased sensing, monitoring the mechanical response of electrochemically actuated microcantilevers is then thought to provide a fast, reliable and complementary experimental information to the long-time cantilever bending measurement for the detection of target molecules. Full-field measurements (see figure) are therefore used to investigate the way the electro-elastic coupling is altered when a microcantilever undergoes decane-thiol adsorption. The proposed technique reveals that the latter results in a charge density redistribution along the cantilever in addition to the local surface passivation. Focusing on the cantilever tip displacement under electrochemical actuation, this redistribution partially compensates the electro-elastic coupling alteration due to the surface passivation, therefore possibly yielding an ambiguous detection result. This effect should be taken into account for the optimal design of specific electrochemically actuated mechanical sensors.

    TRICONNET, K. DERRIEN, K., HILD, F., BAPTISTE, D.    "Parameter choice for optimized digital image correlation"    Optics and Lasers in Engineering, Vol. 47, pages 728-737. DOI

Abstract: Digital image correlation is a photomechanical technique utilized to measure displacement fields. Although the method has been used successfully in a variety of applications, there is a need for guidelines to choose correlation parameters and for an understanding of their link with the analyzed texture and their effect on the uncertainty of measured quantities. In this paper, two criteria are proposed from a texture study to evaluate the best compromise between measurement uncertainty and spatial resolution prior to any mechanical test. These criteria are then validated on a priori uncertainty evaluations with different textures, and on a real experiment when comparing image correlation results with strain gauge data (see figure).

The picture shows comparison between experimentally determined and a priori evaluated standard strain uncertainties as functions of the zone of interest (ZOI) size. The solid and dashed lines represent power law fits.

    HILD, F., ROUX, S., GRAS, R., GUERRERO, N., MARANTE, M. E., FLOREZ-LOPEZ, J.    "Displacement measurement technique for beam kinematics"    Optics and Lasers in Engineering, Vol. 47, pages 495-503. DOI

Abstract: It is proposed to develop a digital image correlation procedure that is suitable for beams whose kinematics is described by an Euler-Bernoulli hypothesis. As a direct output, the degrees of freedom corresponding to flexural and axial loads are directly measured. The performance of the correlation algorithm is evaluated by using a picture of a cantilever beam experiment. One load level is analyzed with the present algorithm. The latter is validated by comparing the displacement field with that given by a finite element based correlation algorithm. It is also shown that a locally buckled zone (see figure) is detectable with the present procedure.

The picture shows a cantilever beam in its reference (a) and deformed (b) state. The picture resolution is 3888 x 2592 pixels with an 8-bit digitization.

    ROUX, S., HILD, S.    "Self-consistent scheme for toughness homogenization"    International Journal of Fracture, Vol. 154, pages 159-166. DOI

Abstract: Considering a semi-infinite planar crack propagating along a plane where the local toughness is a random field, the addressed problem is to compute the effective (or homogeneous and macroscopic) toughness. After a brief introduction to the two regimes—strong and weak pinning—that are expected depending on the system size, a self-consistent homogenization scheme is introduced (see figure). It is shown that this scheme allows one to predict not only the mean value but also the standard deviation and even the complete probability distribution function of the toughness. A discussion about the quality of this prediction as compared with direct numerical simulations is proposed.

Illustration of the self-consistent prescription. The full problem (left) is replaced by a homogenized version outside the strip. Imposing that the front remains flat determines the effective macroscopic toughness

    GENDRE, L., ALLIX, O., GOSSELET, P., COMTE, F.    "Non-intrusive and exact global/local techniques for structural problems with local plasticity"    Computational Mechanics, In Press. DOI

Abstract: This paper introduces a computational strategy to solve structural problems featuring nonlinear phenomena that occur within a small area, while the rest of the structure retains a linear elastic behavior. Two finite element models are defined: a global linear model of the whole structure, and a local nonlinear "submodel" meant to replace the global model in the nonlinear area. An iterative coupling technique is then used to perform this replacement in an exact but non-intrusive way, which means the model data sets are never modified and the computations can be carried out with standard finite element software. Several ways of exchanging data between the models are discussed and their convergence properties are investigated on two examples.

The figure shows a 3D global/local test case provided by Snecma. The global model (blue and grey) is linear elastic and the local model (green) is elastic-plastic.

    VIVIER, G., TRUMEL, H., HILD, F.    "On the stored and dissipated energies in heterogeneous rate-independent systems: theory and simple examples"    Continuum Mechanics and Thermodynamics, Vol. 20 (7), pages 411-427. DOI

Abstract: The aim of the present work is to determine the amount of dissipated and stored energies in structures containing frictional cracks and elasto-plastic zones. The proposed theory combines micromechanical and thermodynamic tools to calculate both energies. Using simple examples, it is shown (see figures) that the Taylor-Quinney coefficient is not a constant, and can be much less than the values usually considered (i.e. close to unity).

The picture shows the Taylor-Quinney coefficient for elasto-plastic (a) and frictional (b) composite structures.

    PERIE, J.-N., LECLERC, H., ROUX, S., HILD, F.    "Digital image correlation and biaxial test on composite material for anisotropic damage law identification"    International Journal of Solids and Structures, Vol. 46, pages 2388-2396. DOI

Abstract: The purpose of the work is to extend the use of non-conventional tests and full field measurements to the identification of an anisotropic damage law. A Digital Image Correlation technique based on a finite element discretization is used to extract planar displacement fields. The reconditioned Equilibrium Gap Method is then used to retrieve a damage law that accounts for shear softening, a specific form suited to the present application (Figure a). The identification is shown to reduce to a linear system. The example of a biaxial shear test performed on a cruciform specimen is considered. The approach is first qualified by using displacement fields resulting from a non-linear computation with a known damage law. A good agreement is observed between the prescribed and identified laws for distinct parameter settings, even when significant noise is added to the displacement fields. The reconstructed displacement fields coincide perfectly with the measurements. The complete scheme is finally tested considering images taken during an experiment performed on a carbon/carbon composite. The identified damage pattern (Figure b) and the corresponding damage values are similar to post-processed maps using classically identified parameters. The reconstructed displacement field accounts for 95% of the fluctuations observed in the measurements (Figure c).

The picture shows the comparison between measured and reconstructed displacements (expressed in pixels), and corresponding differences for the last loading level..

    LADEVEZE, P., WAEYTENS, J.    "Model verification in dynamics through strict upper error bounds"    Comput. Methods Appl. Mech. Engrg. (2009), 2009. DOI

Abstract: This paper describes new strict error bounds of calculated outputs of interest in linear dynamics. All sources of errors, including modeling errors, are taken into account, which makes such error bounds suitable tools for analyzing various approximations in dynamics. Small-displacement problems are included through the classical thermodynamics framework involving internal state variables. Preliminary numerical illustrations are given.

This picture shows the dissipation error of the adjoint problem in each element at a time step.

    LAVERNHE-TAILLARD, K., CALLOCH, S., ARBAB-CHIRANI, S., LEXCELLENT, C.    "Multiaxial shape memory effect and superelasticity"    Strain, Vol. 45 (1), pages 77-84. DOI

Abstract: The specific behaviour of shape memory alloys (SMA) is due to a martensitic transformation [Shape Memory Materials. Cambridge University press, Cambridge]. This transformation consists mainly in a shear without volume change and is activated either by stress or temperature. The superelastic behaviour and the one-way shape memory effect are both due to the partition between austenite and martensite. The superelastic effect is obtained for fully austenitic SMA: loaded up to 5% strain, a sample recovers its initial shape after unloading with a hysteretic loop. The one-way shape memory effect is obtained when a martensitic SMA, plastically deformed, recovers its initial shape by simple heating. Superelasticity and one-way shape memory effect are useful for several three-dimensional applications. Despite all these phenomena are well known and modelled in 1D, the 3D behaviour, and especially the one-way shape memory effect, remains quite unexplored [Mater. Sci. Res. Int., 1 (1995) 260]. Actually, the development of complex 3D applications requires time-consuming iterations and expensive prototypes. Predictive phenomenological models are consequently crucial objectives for the design and dimensioning of SMA structures. Therefore, a series of 2D proportional and non-proportional, isothermal and non-isothermal tests have been performed. This database will be used to build a phenomenological model within the framework of irreversible processes.

The picture shows a comparison of one-way shape memory effect under pure tension and compression.

    ALLIX, O.    "Some remarks on identification strategies for constitutive behavior"    EUROMECH Solid Mechanics Fellow 2006 Paper.

Abstract: Most often, identification is viewed as an ill-posed data fitting problem. The optimum set of parameters is deduced from a direct comparison between numerical experiments and actual tests, and the ill-posed nature of the problem leads to the use of a regularization technique. When the data are highly scattered, one uses filtering techniques, among which the most widely known is that proposed by Kalman and its numerous variations. Here, our ob jective is to discuss the potential of a somewhat different approach inspired by verification and validation concepts and techniques.

The picture shows the cost function for various perturbation levels.

    CLUZEL, C., BARANGER, E., LADEVEZE, P., MOURET, A.    "Mechanical behaviour and lifetime modelling of self-healing ceramic-matrix composites subjected to thermomechanical loading in air"    Composites: Part A, In Press. DOI

Abstract: The simulation of the behaviour and lifetime of composites with self-healing ceramic matrix requires the coupling of models issued from both mechanics and chemistry. The mechanical macromodel is based on a partitioning of damage according to the various degradation mechanisms. Analysis windows on the microscale enable the reconstruction of the crack network indicators and of the opening states of the cracks as functions of the loading. The self-healing mechanism is modelled by creating an oxide plug in an open crack and simulating the diffusion of oxygen through its evolving geometry. An evolution law for fibre strength as a function of oxygen concentration provides an illustration of the influence of complex thermomechanical loading on the composite’s lifetime.

Schematic description of an inter-yarn crack filled by an oxide plug.

    PEBREL, J., REY, C., GOSSELET, P.    "A nonlinear dual-domain decomposition method: application to structural problems with damage"    International Journal for Multiscale Computational Engineering, Vol. 6 (3), pages 251-262.

Abstract: A dual-domain decomposition method dedicated to nonlinear problems is presented. The decomposition is introduced in the nonlinear formulation, and the nonlinear problem is first condensed on the interface then solved by a Newton-type method. Considering the specificities of the introduced operators, the algorithm can be interpreted as a local/global strategy with global Newton-type iterations and nonlinear relocalizations per subdomain. Such a strategy is particularly interesting in cases where the nonlinearity is localized. First results are presented on structural problems with damage.

The picture shows the damage map computed with after a 6-sd decomposition.

    BOUCARD, P.-A., BUYTET, S., GUIDAULT, P.-A.    "A multiscale strategy for structural optimization"    International Journal for Numerical Methods in Engineering, In Press. DOI

Abstract: This paper presents a multiscale strategy dedicated to structural optimization. The applications concern the study of geometric details (such as holes, surface profiles, etc) within the structures with frictional contacts. The first characteristic of the method is that it uses a micro-macro approach. This approach is based on a domain decomposition into substructures and interfaces, which involves the resolution of independent micro problems in each substructure and transfers macro information only through the interfaces. The second characteristic is the use of a multiresolution strategy in order to reduce the computation cost for problems with evolving design parameters. The last characteristic is the capability to model the geometry of details without remeshing thanks to two features: the use of a local enrichment method , and the use of level set functions to easily modify the boundary of the detail during the optimization process.

The picture shows the objective function f versus number of optimization iterations.

    PROMMA, N., RAKA, B., GREDIAC, M., TOUSSAINT, E., LE CAM, J.-B., BALANDRAUD, F., HILD, F.    "Some remarks on identification strategies for constitutive behavior"    International Journal of Solids and Structures, Vol. 46, pages 698-715. DOI

Abstract: This paper deals with the identification of constitutive parameters of a Mooney model suitable for hyperelastic materials. These parameters are retrieved from a multiaxial mechanical test that gives rise to heterogeneous stress / strain fields. Since no analytical relationship is available between measurements and unknown parameters, a suitable tool, namely the virtual fields method, is developed in case of large deformations and used to identify these unknowns. Several results obtained with numerical simulations and experiments (see figure) performed on rubber specimens illustrate the approach.

The picture shows a biaxial experiment on a rubber-like material. Digital Image Correlation was used to measure displacement fields.

    RETHORE, J., BESNARD, G., VIVIER, G., HILD, F., ROUX, S.    "Experimental investigation of localized phenomena using digital image correlation"    Philosophical Magazine, Vol. 88 (28-29), pages 3339-3355. DOI

Abstract: This paper is dedicated to the use of enriched discretization schemes in the context of digital image correlation. The aim is to capture and evaluate strong or weak discontinuities of a displacement field directly from digital images. An analysis of different enrichment performances is provided. Two examples of strain localization illustrate the discussion. The first one deals with the analysis of a strong discontinuity in an energetic material, and the second one with a weak discontinuity associated with a Portevin-Le Chatelier band in an aluminum alloy (see figure).

The picture shows normal ε_nn, shear ε_nt and tangent ε_tt strain fields (x 10-3) obtained using a Q4 approach with 16-pixel elements (a, b, c) and the regularized enriched approach (X-Q4r) with 128-pixel elements (d, e, f ).

    NGUYEN, H.-M., ALLIX, O., FEISSEL, P.    "A robust identification strategy for rate-dependent models in dynamics"    Inverse Problems, Vol. 24. DOI

Abstract: The motivation of the paper is to develop a method allowing us to make use, in the context of identification, of highly perturbed tests leading to non-reliable measurements. Such tests are not seldom especially when dealing with structural fracture in dynamics. We follow here the concept of the modified constitutive relation error (MCRE) [1] where error on the model and error on the experimental data are both introduced. A first paper was devoted to the extension of the MCRE method to transient elasticity [2]. This paper is devoted to the extension to nonlinear constitutive relations, in particular viscoplasticity and damage. The MCRE formulation in transient dynamics leads to the solving of a coupled direct and adjoint nonlinear problem, which implies dedicated methods, which is the core of this paper. This has led us to define a particular MCRE formulation well suited for numerical treatment and to develop an extension of the LATIN method [3] to ill-posed problems. Once the difficulties have been resolved and the formulation implemented in the one-dimensional case, the proposed identification strategy appears to be very robust with respect to perturbed measurements in the absence of a priori knowledge, even in the case of localization and rupture.

The picture shows the cost functions for various measurement perturbations levels (visco-plastic case).

    BRANK, B., IBRAHIMBEGOVIC, A., BOHINC, U.    "On prediction of 3d stress state in elastic shell by higher-order shell formulations"    CMES - Computer Modeling in Engineering & Sciences, Vol. 33 (1), pages 85-108. Journal WebPage

Abstract: In this work we study the accuracy of modem higher-order shell finite element formulations in computation of 3d stress state in elastic shells. In that sense we compare three higher-order shell models: (i) with seven dislacement-like kinematic parameters, and (ii, iii) with six displacement-like kinematic parameters plus one strain-like kinematic parameter introduced by two different versions of enhanced assumed strain (EAS) concept. The finite element approximations of all shell models are based on 4-node quadrilateral elements. Geometrically nonlinear and consistently linearized forms of considered formulations are given. Several numerical examples are presented, where computed stresses are compared with analytical solutions. It was found that through-the-thickness variation of some (non-dominant) stress tensor components, including through-the-thickness normal stress, may be computed very inaccurately. The reliable representation for those stresses can be interpreted only if the "layer-wise" averaging or the through-the-thickness averaging is performed.

The picture shows a 3d representation of plate displacements for version 1 (magnified 120 times) for mesh 20x4 elements.

    DORIVAL, O., ROUCH, P., ALLIX, O.    "A substructured Trefftz method for updating joint models in the medium-frequency range"    Computaional Mechanics, Vol. 42 (3), pages 381-394. DOI

Abstract: The response of a structure to medium-frequency vibrations is highly dependent on several phenomena. One of these, the behavior of joints between substructures, is essential because it controls the distribution of the power injected into the structure and governs most of the dissipative effects. This paper introduces a new method for the identification of joint parameters from experimental vibration data, inspired by previous works on finite element model updating using the error in the constitutive relation. Since such numerical techniques are not suitable for the medium-frequency range, in which the finite element mesh must be refined, our work uses the numerical framework of the variational theory of complex rays, which is a Trefftz approach entirely dedicated to the calculation of medium-frequency vibrations at very low cost. The main scope of this paper is the presentation of the formulation and its validation against actual and numerically-simulated experimental results.

The picture shows a the experimental displacement field at 550 Hz.

    BRANCHERIE, D., VILLON, P., IBRAHIMBEGOVIC, A.    "On a consistent field transfer in non linear inelastic analysis and ultimate load computation"    Computational Mechanics, Vol. 42 (2), pages 213-226. DOI

Abstract: In this work we propose a field transfer operator for remeshing carried out in the course of incremental analysis of a non linear inelastic behavior. The proposed procedure is geared towards the ultimate load computation of a complex structure, where we choose the appropriate mesh grading for each different phase of