References of "Noels, Ludovic"
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See detailA tutorial on Bayesian inference to identify material parameters in solid mechanics
Rappel, Hussein; Beex, Lars A A; Hale, Jake S et al

in Archives of Computational Methods in Engineering (in press)

The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already ... [more ▼]

The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress-strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress-strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions. [less ▲]

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See detailBayesian Identification of Mean-Field Homogenization model parameters and uncertain matrix behavior in non-aligned short fiber composites
Mahamedou, Mohamed; Zulueta Uriondo, Kepa; Chung, Chi Nghia et al

in Composite Structures (2019), 220

We present a stochastic approach combining Bayesian Inference (BI) with homogenization theories in order to identify, on the one hand, the parameters inherent to the model assumptions and, on the other ... [more ▼]

We present a stochastic approach combining Bayesian Inference (BI) with homogenization theories in order to identify, on the one hand, the parameters inherent to the model assumptions and, on the other hand, the composite material constituents behaviors, including their variability. In particular, we characterize the model parameters of a Mean-Field Homogenization (MFH) model and the elastic matrix behavior, including the inherent dispersion in its Young's modulus, of non-aligned Short Fibers Reinforced Polymer (SFRP) composites. The inference is achieved by considering as observations experimental tests conducted at the SFRP composite coupons level. The inferred model and material law parameters can in turn be used in Mean-Field Homogenization (MFH)-based multi-scale simulations and can predict the confidence range of the composite material responses. [less ▲]

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See detailA micro-mechanical model of reinforced polymer failure with length scale effects and predictive capabilities. Validation on carbon fiber reinforced high-crosslinked RTM6 epoxy resin
Nguyen, Van Dung ULiege; Wu, Ling ULiege; Noels, Ludovic ULiege

in Mechanics of Materials (2019), 133

We propose a micro-mechanical numerical model able to predict the nonlinear behavior and failure of unidirectional fiber reinforced high-crosslinked epoxy subjected to transverse loading conditions ... [more ▼]

We propose a micro-mechanical numerical model able to predict the nonlinear behavior and failure of unidirectional fiber reinforced high-crosslinked epoxy subjected to transverse loading conditions. Statistical microstructural volume elements (SMVE) of a realistic composite material are generated from the statistical characterization of the fibers distribution and fiber radius estimated from SEM images of a similar material system. The fibers are assumed to be transversely hyperelastic isotropic and the matrix obeys a hyperelastic viscoelastic-viscoplastic constitutive model enhanced by a multi-mechanism nonlocal damage model. This polymer model captures the pressure dependency and strain rate effects. Besides, it also accounts for size effects through its internal length scales, allowing capturing, with the same unique set of parameters, the behaviors of the epoxy as pure material as well as matrix phase in composites, which are experimentally observed to be different. Additionally, since fiber/matrix interfaces of the considered composite material are categorized as strong ones, the true underlying failure mechanism is located in the matrix close to the fibers, and the interface does not need to be explicitly introduced in the model. The model prediction is found to be in good agreement with experimental results in terms of the global nonlinear stress-strain curves over various strain rates and pressure conditions, on the one hand for pure matrix samples, and on the other hand for the composite coupons, making the proposed framework a predictive virtual testing facility for material design. Finally, using this model, we study the localization behavior in order to characterize the post-failure behavior of the composite material: the cohesive strength is given by the stress-strain curve peak stress while the critical energy release rate is estimated by evaluating the dissipated energy accumulated during the post-peak localization stage. Finally, different SMVE realizations are considered allowing assessing the discrepancy in the failure characteristics of composites. [less ▲]

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See detailAn inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites
Wu, Ling ULiege; Nguyen, Van Dung ULiege; Adam, Laurent et al

in Computer Methods in Applied Mechanics and Engineering (2019), 348

An inverse Mean-Field Homogenization (MFH) process is developed to improve the computational efficiency of non-linear stochastic multiscale analyzes by relying on a micro-mechanics model. First full-field ... [more ▼]

An inverse Mean-Field Homogenization (MFH) process is developed to improve the computational efficiency of non-linear stochastic multiscale analyzes by relying on a micro-mechanics model. First full-field simulations of composite Stochastic Volume Element (SVE) realizations are performed to characterize the homogenized stochastic behavior. The uncertainties observed in the non-linear homogenized response, which result from the uncertainties of their micro-structures, are then translated to an incrementalsecant MFH formulation by defining the MFH input parameters as random effective properties. These effective input parameters, which correspond to the micro-structure geometrical information and to the material phases model parameters, are identified by conducting an inverse analysis from the full-field homogenized responses. Compared to the direct finite element analyzes on SVEs, the resulting stochastic MFH process reduces not only the computational cost, but also the order of uncertain parameters in the composite micro-structures, leading to a stochastic Mean-Field Reduced Order Model (MF-ROM). A data-driven stochastic model is then built in order to generate the random effective properties under the form of a random field used as entry for the stochastic MF-ROM embedded in a Stochastic Finite Element Method (SFEM). The two cases of elastic Unidirectional (UD) fibers embedded in an elasto-plastic matrix and of elastic UD fibers embedded in a damage-enhanced elasto-plastic matrix are successively considered. In order to illustrate the capabilities of the method, the stochastic response of a ply is studied under transverse loading condition. [less ▲]

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See detailA finite strain incremental-secant homogenization model for elasto-plastic composites
El Ghezal, Marieme Imene; Wu, Ling ULiege; Noels, Ludovic ULiege et al

in Computer Methods in Applied Mechanics and Engineering (2019), 347

This paper presents a finite strain extension of the incremental-secant mean-field homogenization (MFH) formulation for two-phase elasto-plastic composites. The formulation of the local finite strain ... [more ▼]

This paper presents a finite strain extension of the incremental-secant mean-field homogenization (MFH) formulation for two-phase elasto-plastic composites. The formulation of the local finite strain elasto-plastic constitutive equations of each phase is based on a multiplicative decomposition of the deformation gradient as suggested by Simo in (Computer Methods in Applied Mechanics and Engineering, 99(1):61–112, 1992.). The latter has proposed algorithms which preserve the classical return mapping schemes of the infinitesimal theory by using principal Kirchhoff stresses and logarithmic eigenvalues of the left elastic Cauchy-Green strain. Relying on this property, we show that, by considering a quadratic logarithmic free energy and J2-flow theory at the local level, infinitesimal strain incremental-secant MFH is readily extended to finite strains. The proposed formulation and corresponding numerical algorithms are then presented. Finally, the predictions are illustrated with several numerical simulations which are verified against full-field finite element simulations of composite cells, demonstrating that the micro-mechanically based approach is able to predict the influence of the micro-structure and of its evolution on the macroscopic properties in a very cost-effective manner. [less ▲]

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See detail3D finite element formulation for mechanical-electrophysiological coupling in axonopathy
Kwong, Man Ting; Bianchi, Fabio; Malboubi, Majid et al

in Computer Methods in Applied Mechanics and Engineering (2019), 346

Traumatic injuries to the central nervous system (brain and spinal cord) have recently been put under the spotlight because of their devastating socio-economical cost. At the cellular scale, recent ... [more ▼]

Traumatic injuries to the central nervous system (brain and spinal cord) have recently been put under the spotlight because of their devastating socio-economical cost. At the cellular scale, recent research efforts have focused on primary injuries by making use of models aimed at simulating mechanical deformation induced axonal electrophysiological functional deficits. The overwhelming majority of these models only consider axonal stretching as a loading mode, while other modes of deformation such as crushing or mixed modes|highly relevant in spinal cord injury|are left unmodelled. To this end, we propose here a novel 3D finite element framework coupling mechanics and electrophysiology by considering the electrophysiological Hodgkin- Huxley and Cable Theory models as surface boundary conditions introduced directly in the weak form, hence eliminating the need to geometrically account for the membrane in its electrophysiological contribution. After validation against numerical and experimental results, the approach is leveraged to model an idealised axonal dislocation injury. The results show that the sole consideration of induced longitudinal stretch following transverse loading of a node of Ranvier is not necessarily enough to capture the extent of axonal electrophysiological deficit and that the non-axisymmetric loading of the node participates to a larger extent to the subsequent damage. On the contrary, a similar transverse loading of internodal regions was not shown to significantly worsen with the additional consideration of the non-axisymmetric loading mode. [less ▲]

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See detailDamage to crack transition for ductile materials using a cohesive-band /discontinuous Galerkin framework
Leclerc, Julien ULiege; Nguyen, Van Dung ULiege; Wu, Ling ULiege et al

Conference (2019, March 13)

Numerical predictions of the ductile failure process are still challenging. Indeed, such failure combines a diffuse damage stage followed by damage localisation and crack initiation/propagation. On the ... [more ▼]

Numerical predictions of the ductile failure process are still challenging. Indeed, such failure combines a diffuse damage stage followed by damage localisation and crack initiation/propagation. On the one hand, continuous damage models are suited for the diffuse damage stage but not for the description of physical discontinuities. On the other hand, discontinuous approaches, such as cohesive zone models, can reproduce crack initiation and propagation, but not the diffuse damage stage. In this work, we present a numerical scheme combining both approaches in a discontinuous Galerkin finite element framework. First, a non-local implicit damage model computes the initial diffuse damage stage beyond the softening point without mesh-dependency. Second, a crack is introduced using a cohesive band [1,2]. Contrarily to classical cohesive models, a 3D state is recreated at the crack interface by considering a small, but finite, fictitious cohesive thickness allowing a strain tensor to be evaluated from the cohesive jump and the neighbouring bulk deformation gradient. A stress tensor at the interface, from which the cohesive forces are deduced, is computed using an appropriate local damage law. The ductile failure is thus modelled by a combination of the Gurson and the Thomason evolution laws [3]. First, the initial diffuse void growth phase is modelled by the (non-local) Gurson model [4] accounting for shear effects [5]. Second, a crack is introduced when the coalescence is reached and the behaviour of the cohesive law is computed from the Thomason model [3]. The framework capabilities are demonstrated by reproducing the slanted and the cup-cone failure respectively of a plane strain specimen and a round bar. Ack.: The research has been funded by the Walloon Region under the agreement no.7581-MRIPF in the context of the 16th MECATECH call. REFERENCES [1] J.J.C. Remmers, R. de Borst., C.V. Verhoosel and A. Needleman. “The cohesive band model: a cohesive surface formulation with stress triaxiality”, Int. J. Fract. 181 (2013). [2] J. Leclerc, L. Wu, V.D. Nguyen and L. Noels, “Cohesive band model: a cohesive model with triaxiality for crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework”, Int. J. for Num. Methods in Eng. (2018) [3] A.A. Benzerga, J.-B. Leblond, A. Needleman, V. Tvergaard. Ductile failure modelling. Int J Fract 201 (2016). [4] F. Reusch, B. Svendsen and D. Klingbeil. A non-local extension of Gurson-based ductile damage modelling. Comp. Mat. Sci. 26 (2003). [5] K. Nahshon and J.W. Hutchinson, “Modification of the Gurson Model for shear failure”, European Journal of Mechanics A/Solids 27 (2008). [less ▲]

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See detailIdentifying elastoplastic parameters with Bayes’ theorem considering output error, input error and model uncertainty
Rappel, Hussein ULiege; Beex, Lars A A; Noels, Ludovic ULiege et al

in Probabilistic Engineering Mechanics (2019), 55

We discuss Bayesian inference for the identification of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors ... [more ▼]

We discuss Bayesian inference for the identification of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in the strain measurements. Since a difference between the model and the experimental data may still be present if the data is not contaminated by noise, we also incorporate the possible error of the model itself. The three formulations to describe model uncertainty in this contribution are: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. Our results show that incorporating model uncertainty often, but not always, improves the results. If the error in the strain is considered as well, the results improve even more. [less ▲]

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See detailA micro-mechanics-based inverse study for stochastic order reduction of elastic UD-fiber reinforced composites analyzes
Wu, Ling ULiege; Adam, Laurent; Noels, Ludovic ULiege

in International Journal for Numerical Methods in Engineering (2018), 115(12), 1430-1456

This research develops a stochastic mean-field-homogenization (MFH) process that is used as Reduced Order Model (ROM) to carry out a statistical multiscale analysis on unidirectional (UD) fiber reinforced ... [more ▼]

This research develops a stochastic mean-field-homogenization (MFH) process that is used as Reduced Order Model (ROM) to carry out a statistical multiscale analysis on unidirectional (UD) fiber reinforced composites. First full-field simulations of UD Stochastic Volume Elements (SVEs), whose statistical description is obtained from SEM images, are conducted to define statistical meso-scale apparent properties. A stochastic Mori-Tanaka MFH model is then developed through an inverse stochastic identification process performed on the apparent elastic properties obtained by full-field simulations. As a result, a random vector of the effective elastic properties of phases and micro-structure information of the Mori-Tanaka model is inferred. In order to conduct Stochastic Finite Element Method (SFEM) analyzes, a generator of this random vector is then constructed using the copula method, allowing predicting the statistical response of a composite ply under bending. The statistical dependence of the random vector entries is shown to be respected by the generator. Although this work is limited to the elastic response, we believe that the stochastic Mori-Tanaka model can be extended to nonlinear behaviors in order to conduct efficient stochastic multiscale simulations. [less ▲]

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See detailA stochastic Mean-Field Reduced Order Model of Unidirectional Composites
Wu, Ling ULiege; Noels, Ludovic ULiege

Scientific conference (2018, September 07)

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See detailGeneration and Analysis of open foam RVEs with sharp edges using Distance fields and Level sets
Kilingar, Nanda Gopala ULiege; Noels, Ludovic ULiege; Massart, Thierry Jacques et al

Conference (2018, August 07)

A methodology to generate Representative Volume Elements (RVEs) for open-foam cellular materials based on distance and level set functions is explained. The main focus of this work is to properly ... [more ▼]

A methodology to generate Representative Volume Elements (RVEs) for open-foam cellular materials based on distance and level set functions is explained. The main focus of this work is to properly represent the geometry of the foam struts of the RVEs that are resultants of the solidification phase during manufacturing. The distance functions are defined based on the work of Sonon[1], where an arbitrary shape packing generation algorithm is introduced based on distance functions. Combinations of these functions are used to generate tessellations and extract open-foam structures with variations in the strut morphology according to the foam the RVE is being compared with, for example, the shape of cross-sections of the struts and their variation along the axis of the struts. The generated morphologies have been compared with real foam samples from existing literature to verify statistically the morphological properties like face-to-cell ratio, edge-to-face ratio and strut length distribution among others. The correlation of these properties on the initial conditions like sphere packing fraction, sphere volume distribution and periodicity of the RVEs have also been studied and are found to be in good match. Steep discontinuities in the distance functions derivatives result in the generation of jagged sharp edges, due to the use of discrete level set functions. Thus a modification in this extraction was deemed necessary and a procedure to extract geometries from multiple level set functions to reproduce such sharp edges of the struts has been incorporated in the current work. The individual cells are extracted as inclusion surfaces based on said combination of the distance functions and their modifications. The sharp edges are computed from the intersection of these inclusion surfaces. The resulting geometry can then be meshed using size functions based on curvature and narrowness and a mesh optimization inspired from [2]. The methodology to produce high quality meshes based on [3] will be outlined. The resulting FE models are easily exported for a multi-scale study to understand the effects of a elastic-plastic test by upscaling to assess the practical applications of these models by comparing with experimental data of physical samples. [less ▲]

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See detailA Damage to Crack Transition Framework for Ductile Materials Accounting for Stress Triaxiality
Leclerc, Julien ULiege; Wu, Ling ULiege; Nguyen, Van Dung ULiege et al

Conference (2018, July 25)

Predicting the entire ductile failure process is still a challenge task since it involves different processes: damage first diffuses before localizing, eventually leading to a micro-crack initiation and ... [more ▼]

Predicting the entire ductile failure process is still a challenge task since it involves different processes: damage first diffuses before localizing, eventually leading to a micro-crack initiation and propagation. On the one hand, discontinuous approaches can describe localised processes such as crack propagation but fail in capturing diffuse damage evolution. On the other hand, continuous approaches such as continuum damage models are suited for diffuse damage modelling, but cannot represent properly physical discontinuities. In this work both approaches are combined in a hybrid implicit non-local damage model combined with an extrinsic cohesive law in a discontinuous Galerkin finite element framework [1]. The implicit non-local damage model reproduces the initial diffuse damage stage without mesh-dependency. Upon transition at void coalescence or intensive plastic localisation, a crack is introduced using a cohesive band model. Contrarily to cohesive elements, cohesive band models capture in-plane stretch effects, and thus account for stress triaxiality [2]. Indeed, by considering a band of small but finite thickness ahead of the crack surface, the strain field inside this band is evaluated from the neighbouring strains and from the cohesive jump [2]. Then, an appropriate damage model is used to compute the stress-state inside the band and the cohesive traction forces on the crack lips. The approach is first applied in the case of elastic damage for which the band thickness is evaluated to ensure the energetic consistency of the damage to crack transition with respect to purely non-local continuum damage mechanics [1]. Then, the scheme is formulated to the case of a non-local porous-plastic damage Gurson model. In particular, the law governing void growth accounts for shear effects, while the void coalescence mechanism, hence the damage to crack transition criterion, is predicted using the Thomason model [3]. References: [1] Leclerc J., Wu L., Nguyen V.D., Noels L. Cohesive band model: a cohesive model with triaxiality for crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Int. J. for Num. Methods in Eng. (2017): In press. [2] Remmers J. J. C., de Borst R., Verhoosel C. V., Needleman A. The cohesive band model: a cohesive surface formulation with stress triaxiality. Int. J. Fract. 181 (2013). [3] Benzerga A.A., Leblond J.-B., Needleman A., Tvergaard V. Ductile failure modelling. Int J Fract 201 (2016). [less ▲]

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See detailA probabilistic Mean-Field-Homogenization approach applied to study unidirectional composite structures
Wu, Ling ULiege; Adam, Laurent; Noels, Ludovic ULiege

Conference (2018, July 25)

In order to account for micro-structural geometrical and material properties in an accurate way, homogenization-based multiscale approaches have been widely developed. However, most of the approaches ... [more ▼]

In order to account for micro-structural geometrical and material properties in an accurate way, homogenization-based multiscale approaches have been widely developed. However, most of the approaches assume the existence of a statistically Representative Volume Element (RVE), which does not always exist for composite materials due to the existing micro-structural uncertainties, in particular when studying the onset of failure. In this work we develop a stochastic multi-scale approach for unidirectional composite materials in order to predict scatter at the structural behavior. First Stochastic Volume Elements (SVE) [1] are built from experimental measurements. Toward this end, statistical functions of the fibers features are extracted from SEM images to generate statistical functions of the micro-structure. The dependent variables are then represented using the copula framework, allowing generating micro-structures, which respect the statistical information, using a fiber additive process [2]. Probabilistic meso-scale stochastic behaviors are then extracted from direct numerical simulations of the generated SVEs, defining random fields of homogenized properties [3]. Finally, in order to provide an efficient way of generating meso-scale random fields, while keeping information, such as stress/strain fields, at the micro-scale during the resolution of macro-scale stochastic finite element, a probabilistic Mean-Field-Homogenization (MFH) method is developed. To this end, the phase parameters of the MFH are seen as random fields defined by inverse stochastic identification of the stochastic homogenized properties obtained through the stochastic direct simulations of the SVEs. As a result, non-deterministic macro-scale behaviors can be studied while having access to the micro-scale different phases stress-strain evolution, allowing to predict composite failure in a probabilistic way. [1] M. Ostoja-Starzewski, X. Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering 168 (14) (1999) 35 - 49, [2] L. Wu, C.N. Chung, Z. Major, L. Adam, L. Noels. From SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites. Submitted to Composite Structures. [3] V. Lucas, J.-C. Golinval, S. Paquay, V.-D. Nguyen, L. Noels, L. Wu, A stochastic computational multiscale approach; Application to MEMS resonators, Computer Methods in Applied Mechanics and Engineering 294 (2015) 141 - 167 [less ▲]

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See detailNon-local damage to crack transition framework for ductile failure based on a cohesive band model
Nguyen, Van Dung ULiege; Leclerc, Julien ULiege; Wu, Ling ULiege et al

Conference (2018, July 02)

A damage process starts with a diffuse stage followed by a localized stage in which the initiation and propagation of cracks can occur. To model this whole failure process, on the one hand, continuous ... [more ▼]

A damage process starts with a diffuse stage followed by a localized stage in which the initiation and propagation of cracks can occur. To model this whole failure process, on the one hand, continuous approaches formulated under the framework of continuum damage models succeed in capturing the material degradation but are unable to represent properly physical discontinuities. On the other hand, discontinuous approaches describe the failure process such as cracks by propagating field discontinuities. However, they usually do not capture the diffuse damage evolution and in-plane stretch effects which are the consequences of stress triaxiality and must be taken into account for accurate ductile failure simulations. Clearly both described approaches cannot separately represent the whole ductile failure process with accuracy. In this work, the advantages of these two approaches are combined in a single one, so-called non-local damage to crack transition. The non-local porous-plastic damage Gurson model [1] is used to reproduce the initial diffuse damage stage without mesh-dependency. In particular, the law governing void growth accounts for large shear effects [2], while the void coalescence mechanism, hence the damage to crack transition criterion is predicted using the Thomason model [3]. At the transition point, a crack is initiated using a cohesive band model represented by a cohesive law including in-plane stretch effects [4]. By assuming that all the damaging process is concentrated within a band of small but finite thickness, the deformation state inside this band is obtained from the one of neighboring material points and from the displacement jump. Then, the underlying constitutive law is still used to compute the stress state from which the cohesive traction across the cohesive band is estimated. This combined framework is implemented in a discontinuous Galerkin/ extrinsic cohesive zone method finite element framework, which has successfully been applied for elastic-damage problems in which the band thickness was evaluated to ensure the energetic consistency of the damage to crack transition with respect to purely non-local continuum damage mechanics [5]. The proposed framework is shown to capture the damage diffuse stage as well as crack initiation and propagation of the whole ductile failure process. [1] Reusch F., Svendsen B., and Klingbeil D., A non-local extension of Gurson-based ductile damage modelling, Comp. Mat. Sci., 26, (2013). [2] Nahshon K., Hutchinson J. W., Modification of the Gurson Model for shear failure, Eur. J. Mech. A Solids, 27, (2008). [3] Benzerga A.A., Leblond J.-B., Needleman A., Tvergaard V., Ductile failure modelling, Int. J. Fract., 201, (2016). [4] Remmers J. J. C., de Borst R., Verhoosel C. V., Needleman A., The cohesive band model: a cohesive surface formulation with stress triaxiality, Int. J. Fract., 181, (2013). [5] Leclerc J., Wu L., Nguyen V.D., Noels L., A damage to crack transition model accounting for stress triaxiality formulated in a hybrid non-local implicit discontinuous Galerkin - cohesive band model framework, Int. J. for Num. Methods in Eng., 113 (3), (2018) [less ▲]

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See detailA stochastic Mean Field Homogenization model of Unidirectional composite materials
Wu, Ling ULiege; Noels, Ludovic ULiege

Scientific conference (2018, June 22)

Homogenization-based multiscale approaches have been widely developed in order to account for micro-structural geometrical and material properties in an accurate way. However, most of the approaches ... [more ▼]

Homogenization-based multiscale approaches have been widely developed in order to account for micro-structural geometrical and material properties in an accurate way. However, most of the approaches assume the existence of a statistically Representative Volume Element (RVE), which does not always exist for composite materials due to the existing micro-structural uncertainties, in particular when studying the onset of failure. To address this lack of representativity, a stochastic multi-scale approach for unidirectional composite materials is developed with the aim of predicting scatter in the structural behavior. The first step consists in building Stochastic Volume Elements (SVE) [1] from experimental measurements. Toward this end, statistical functions of the fibers features are extracted from SEM images to generate statistical functions of the micro-structure. The dependent variables are then represented using the copula framework, allowing generating micro-structures respecting the statistical information using a fiber additive process [2]. Probabilistic meso-scale stochastic behaviors are then extracted from direct numerical simulations of the generated SVEs, defining random fields of homogenized properties [2]. Finally, in order to provide an efficient way of generating meso-scale random fields, while keeping information such as stress/strain fields at the micro-scale during the resolution of macro-scale stochastic finite element, a probabilistic Mean-Field-Homogenization (MFH) method is developed, first in the linear range [3] and then in the non-linear one. To this end, the phase parameters of the MFH are seen as random fields defined by inverse stochastic identification of the stochastic homogenized properties obtained through the stochastic direct simulations of the SVEs. The resulting micro-mechanics-based reduced order model allows studying composite failure in a probabilistic way. [1] M. Ostoja-Starzewski, X. Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering 168 (14) (1999) 35 - 49, [2] L. Wu, C.N. Chung, Z. Major, L. Adam, L. Noels. From SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites. Submitted to Composite Structures. [3] L. Wu, L. Adam, L. Noels, A micro-mechanics-based inverse study for stochastic order reduction of elastic UD-fiber reinforced composites analyzes, International Journal for Numerical Methods in Engineering (2018) [less ▲]

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See detailAn implicit non-local damage to crack transition framework for ductile materials involving a cohesive band model
Leclerc, Julien ULiege; Wu, Ling ULiege; Nguyen, Van Dung ULiege et al

Conference (2018, May 31)

Accurate numerical predictions of the entire ductile failure process is still challenging. There are two main philosophies to model the process consisting in an initial diffuse stage followed by localised ... [more ▼]

Accurate numerical predictions of the entire ductile failure process is still challenging. There are two main philosophies to model the process consisting in an initial diffuse stage followed by localised crack initiations and propagations. On the one hand, discontinuous approaches are adapted to localised processes as crack propagation but fail in capturing diffuse damage evolution. Moreover, they do not usually capture stress triaxiality effects, required for accurate ductile failure simulations. On the other hand, continuum damage models are suited for diffuse damage modelling but are unable to represent properly physical discontinuities. In order to describe the entire ductile failure process, the numerical scheme proposed here combines both approaches through a mesh-independent implicit non-local damage model combined with a cohesive band model, an extrinsic cohesive law, in a discontinuous Galerkin finite element framework. By assuming that all the damaging process is concentrated inside a band of small but finite thickness ahead of the crack surface, the cohesive forces are computed from neighbouring strains and the cohesive jump using an appropriate damage model. By this way, this approach naturally incorporates stress triaxiality effects. It has successfully been applied in the case of elastic damage for which the band thickness was evaluated to ensure the energetic consistency of the damage to crack transition with respect to purely non-local continuum damage mechanics [1]. In the present work, the scheme is extended to the case of non-local porous-plastic damage Gurson model accounting for large shear effects. A crack is introduced at the transition corresponding to intensive plastic localisation or void coalescence predicted by the Thomason model. [1] Leclerc J., Cohesive band model: a cohesive model with triaxiality for crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Int. J. Num. Meth. Eng. (2017). [less ▲]

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See detailComputational Fracture Mechanics
Noels, Ludovic ULiege

Conference (2018, May 17)

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See detailA stochastic 3-scale method for polycrystalline materials
Noels, Ludovic ULiege

Scientific conference (2018, April 03)

The purpose of this work is to upscale material uncertainties in the context of thermo-elastic response of polycrystalline structures using a stochastic multi-scale approach defined as follows 1 ... [more ▼]

The purpose of this work is to upscale material uncertainties in the context of thermo-elastic response of polycrystalline structures using a stochastic multi-scale approach defined as follows 1. Stochastic volume elements (SVEs) [1] are built using Voronoi tessellations and experimental measurements of the grain size, orientation, and surface roughness [2]; 2. Mesoscopic apparent thermo-elastic properties are extracted using a coupled homogenization theory [3, 4] applied on the generated SVEs; 3. A stochastic model of the homogenized properties extracted using a moving window technique is then constructed in order to generate spatially correlated meso-scale random fields; 4. The random fields are then used as input for stochastic finite elements. As a result, the probabilistic distribution of micro-resonator properties is studied for two-fold applications: 1. A stochastic thermo-elastic homogenization is coupled to thermoelastic 3D models of the micro-resonator in order to extract the probabilistic distribution of the quality factor of micro-resonators [5]; 2. A stochastic second-order mechanical homogenization is coupled to a plate model of the micro-resonator in order to extract the effect of the surface roughness of the polycrystalline structures [2]. [1] Ostoja-Starzewski, M., Wang, X. Stochastic finite elements as a bridge between random material microstructure and global response. Comput. Meth. in Appl. Mech. and Eng. (1999) 168: 35-49. [2] Lucas, V., Golinval, J.-C., Voicu, R., Danila, M., Gravila, R., Muller, R., Dinescu, A., Noels, L., Wu, L. Propagation of material and surface profile uncertainties on MEMS micro-resonators using a stochastic second-order computational multi-scale approach. Int. J. for Num. Meth. in Eng. (2017). [3] Temizer, I., Wriggers, P. Homogenization in finite thermoelasticity. J. of the Mech. and Phys. of Sol. (2011) 59, 344{372. [4] Nguyen, V. D., Wu, L., Noels, L. Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method. Computat. Mech. (2017) 59, 483-505. [5] Wu, L., Lucas, V., Nguyen, V. D., Golinval, J.-C., Paquay, S., Noels, L. A Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators. Comput. Meth. in Appl. Mech. and Eng. (2016) 310, 802-839. [less ▲]

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See detailFrom SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites
Wu, Ling ULiege; Chung, Chi Nghia; Major, Zoltan et al

in Composite Structures (2018), 189C

In this work, the elastic response of unidirectional fiber (UD) reinforced composites is studied in a stochastic multiscale way. First, the micro-structure of UD carbon fiber reinforced composites is ... [more ▼]

In this work, the elastic response of unidirectional fiber (UD) reinforced composites is studied in a stochastic multiscale way. First, the micro-structure of UD carbon fiber reinforced composites is statistically studied based on SEM images of its cross-section and an algorithm to generate numerical micro-structures with an equivalent random distribution of fibers is developed. In particular, based on the images spatial analysis, the empirical statistical descriptors are considered as dependent variables and represented using the copula framework, allowing generating micro-structure realizations used as Stochastic Volume Elements (SVEs). Second, a stochastic scale transition is conducted through the homogenization of SVEs. With a view to the use of the resulting meso-scale random field in structural stochastic analyzes, the homogenization is performed in two steps in order to respect the statistical content from the micro-meter-long SVEs to the millimeter-long structural finite elements. To this end, the computational homogenization is applied in a hierarchy model: i) Micro-structure generator produces Small SVEs (SSVEs) which are homogenized; ii) Big SVEs (BSVEs) are constructed from the SSVEs. Finally, it is shown on simple illustrative examples that the scatter of the (homogenized) stress distribution in a composite ply can be simulated by means of the developed methodology. [less ▲]

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See detailStochastic multiscale model of MEMS stiction accounting for high order statistical moments of non-Gaussian contacting surfaces
Hoang Truong, Vinh ULiege; Wu, Ling ULiege; Golinval, Jean-Claude ULiege et al

in IEEE/ASME Journal of Microelectromechanical Systems (2018), 27(2), 137-155

Stiction is a failure mode of microelectromechanical systems (MEMS) involving permanent adhesion of moving surfaces. Models of stiction typically describe the adhesion as a multiple asperity adhesive ... [more ▼]

Stiction is a failure mode of microelectromechanical systems (MEMS) involving permanent adhesion of moving surfaces. Models of stiction typically describe the adhesion as a multiple asperity adhesive contact between random rough surfaces, and they thus require a sufficiently accurate statistical representation of the surface, which may be non-Gaussian. If the stiction is caused primarily by multiple asperity adhesive contact in only a small portion of the apparent area of the contacting surfaces, the number of adhesive contacts between asperities may not be sufficiently statistically significant for a homogenized model to be representative. In [Hoang et al., A computational stochastic multiscale methodology for MEMS structures involving adhesive contact, Tribology International, 110:401-425, 2017], the authors have proposed a probabilistic multiscale model of multiple asperity adhesive contact that can capture the uncertainty in stiction behavior. Whereas the previous paper considered Gaussian random rough surfaces, the aim of the present paper is to extend this probabilistic multiscale model to non-Gaussian random rough surfaces whose probabilistic representation accounts for the high order statistical moments of the surface height. The probabilistic multiscale model thus obtained is validated by means of a comparison with experimental data of stiction tests of cantilever beams reported in the literature. [less ▲]

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