Publications of Ling Wu
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See detailTensile failure model of carbon fibre in unidirectionally reinforced epoxy composites with mean-field homogenisation
Wu, Ling ULiege; Maillard, Etienne; Noels, Ludovic ULiege

in Composite Structures (2021), 273

This paper presents an extension of the so-called incremental-secant mean-field homogenisation (MFH) formulation accounting for fibre bundle failure and matrix cracking in Unidirectional (UD) composites ... [more ▼]

This paper presents an extension of the so-called incremental-secant mean-field homogenisation (MFH) formulation accounting for fibre bundle failure and matrix cracking in Unidirectional (UD) composites. First a model for fibre bundle failure is developed bth failure probability of the carbon fibre described by a Weibull distribution. This fibre bundle failure model is then framed in a damage model of embedded bundles in a matrix by considering an exponential relation to describe the longitudinal stress build-up profile experimentally observed during failure of embedded fibre bundles. Cracking of the matrix in UD composites is accounted for through an anisotropic non-local damage model, which allows capturing the so-called 0∘ splits experimentally observed during the longitudinal tension of UD plies. A Mean Field Homogenisation (MFH) model is then extended to account for these damage models as component behaviours of the 2-phase composite material. A finite element multi-scale simulation of a notched laminate shows that the intra-laminar failure modes observed by an in situ experiment reported in the literature are well captured by the damage variables related to the matrix and fibre bundle failure processes. Inter-laminar failure is also captured by an extrinsic cohesive law introduced between the plies. [less ▲]

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See detailMicro-mechanics and data-driven based reduced order models for multi-scale analyses of woven composites
Wu, Ling ULiege; Adam, Laurent; Noels, Ludovic ULiege

in Composite Structures (2021), 270

Order reduction of woven composite materials is based on the definition of short fibres reinforced matrix material pseudo-grains completed by pure matrix parts. The former ones model the curved yarns ... [more ▼]

Order reduction of woven composite materials is based on the definition of short fibres reinforced matrix material pseudo-grains completed by pure matrix parts. The former ones model the curved yarns, which are assimilated to continuous fibre reinforced matrix materials, in woven composites, and the latter ones model the matrix response. The homogenisation is achieved by recursively using micro-mechanics models, such as mean-field homogenisation and Voigt’s rule of mixture, and on the laminate theory. The pseudo-grains number and micro-structural features such as orientation, aspect ratio and volume fraction are considered as the Reduced Order Model (ROM) parameters and are identified following the approach of Deep Material Network (DMN): a set of homogenised elasticity tensors evaluated by computational homogenisation of woven unit-cells is used as training data in order to identify the topological parameters of the ROM. Once the topological parameters are identified, the proposed ROM can be used to conduct nonlinear analyses of woven composites. The accuracy and efficiency of the proposed ROM have been verified by comparing the predictions with direct numerical simulations on two different woven unit cells. [less ▲]

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See detailNeural network-based surrogate model for multi-scale analyses
Noels, Ludovic ULiege; Wu, Ling ULiege

Scientific conference (2021, February 08)

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See detailA recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths
Wu, Ling ULiege; Nguyen, Van Dung ULiege; Kilingar, Nanda Gopala ULiege et al

in Computer Methods in Applied Mechanics and Engineering (2020), 369

An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyzes in solid mechanics. The design and training methodologies of ... [more ▼]

An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyzes in solid mechanics. The design and training methodologies of the NNW are developed in order to allow accounting for history-dependent material behaviors. On the one hand, a Recurrent Neural Network (RNN) using a Gated Recurrent Unit (GRU) is constructed, which allows mimicking the internal variables required to account for history-dependent behaviors since the RNN is self-equipped with hidden variables that have the ability of tracking loading history. On the other hand, in order to achieve accuracy under multi-dimensional non-proportional loading conditions, training of the RNN is achieved using sequential data. In particular the sequential training data are collected from finite element simulations on an elasto-plastic composite RVE subjected to random loading paths. The random loading paths are generated in a way similar to a random walking in stochastic process and allows generating data for a wide range of strain-stress states and state evolution. The accuracy and efficiency of the RNN-based surrogate model is tested on the structural analysis of an open-hole sample subjected to several loading/unloading cycles. It is shown that a similar accuracy as with a FE2 multi-scale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude. [less ▲]

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See detailBayesian inference of non-linear multiscale model parameters accelerated by a Deep Neural Network
Wu, Ling ULiege; Zulueta Uriondo, Kepa; Major, Zoltan et al

in Computer Methods in Applied Mechanics and Engineering (2020), 360

We develop a Bayesian Inference (BI) of a non-linear multiscale model and material parameters using experimental composite coupons tests as observation data. In particular we consider non-aligned Short ... [more ▼]

We develop a Bayesian Inference (BI) of a non-linear multiscale model and material parameters using experimental composite coupons tests as observation data. In particular we consider non-aligned Short Fibers Reinforced Polymer (SFRP) as a composite material system and Mean-Field Homogenization (MFH) as a multiscale model. Although MFH is computationally efficient, when considering non-aligned inclusions, the evaluation cost of a non-linear response for a given set of model and material parameters remains too prohibitive to be coupled with the sampling process required by the BI. Therefore, a Neural-Network-type (NNW) is first trained using the MFH model, and is then used as a surrogate model during the BI process, making the identification process affordable. [less ▲]

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See detailA stochastic Mean-Field-Homogenization-based micro-mechanical model of unidirectional composites failure
Wu, Ling ULiege; Calleja, Juan Manuel ULiege; Nguyen, Van Dung ULiege et al

Conference (2019, December 20)

Homogenization approaches are commonly developed in order to account for micro-structural geometrical and material properties in the framework of multiscale analyses. Although most of the approaches ... [more ▼]

Homogenization approaches are commonly developed in order to account for micro-structural geometrical and material properties in the framework of multiscale analyses. Although most of the approaches postulate the existence of a statistically Representative Volume Element (RVE), such representativity is not always ensured, in particular when studying the failure of composite materials, because of the existing micro-structural uncertainties. In this work we develop a stochastic multi-scale approach for unidirectional composite materials in order to predict the scatter existing at the structural behaviour. Statistical characteristics of the micro-structure are first extracted from SEM images in order to build a Stochastic Volume Elements (SVE) generator [1], allowing the extraction of probabilistic meso-scale stochastic behaviours from direct numerical simulations. Finally, a probabilistic Mean-Field-Homogenization (MFH) method is developed [2,3] such that the phase parameters of the MFH are defined as random fields identified from the stochastic homogenized behaviours obtained through the direct simulations of the SVEs. As a result, non-deterministic macro-scale behaviours can be studied, allowing to predict composite failure in a probabilistic way. [1] L. Wu, C. N. Chung, Z. Major, L. Adam, and L. Noels. "From SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites." Composite Structures 189C (2018): 206-227. [2] L. Wu, L. Adam, and 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 115, no. 12 (2018): 1430-1456. [3] L. Wu, V. D. Nguyen, L. Adam, and L. Noels. "An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites." Computer Methods in Applied Mechanics and Engineering (2019). [less ▲]

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See detailQuasi-static crush modelling of carbon/epoxy composites with discontinuous Galerkin/anisotropic extrinsic cohesive law method
Liu, Xing; Wu, Ling ULiege; Van Hemelrijck, Danny et al

in Composite Structures (2019), 230

Carbon/epoxy composites demonstrate significant promising improvements of weight to performance in the automotive industry. However, the design of carbon/epoxy composite components for crashworthiness ... [more ▼]

Carbon/epoxy composites demonstrate significant promising improvements of weight to performance in the automotive industry. However, the design of carbon/epoxy composite components for crashworthiness remains challenging and normally requires laborious and repeated experimental work. This study adopts a predictive crush model of carbon/epoxy composites, which can partially replace the experimental work. The discontinuous Galerkin (DG) method with extrinsic cohesive laws is employed to simulate the failure patterns in the composite structures. The application of DG distinguishes the fracture model from the conventional approach where preset cohesive elements are used on the location where cracks are expected. The mixed mode cohesive laws are used to simulate the delamination between each layer. To capture different crack propagations in different layups, the anisotropic cohesive law is used to simulate the intralaminar crack propagation in composites. To verify the adopted model, circular composite tube specimens with different layups have been simulated and compared with tests under quasi-static crush loadings. The comparisons of numerical results with experimental data show that the DG crush model can reproduce the experimental results with relatively high accuracy. [less ▲]

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See detailA Bayesian framework to identify random parameter fields based on the copula theorem and Gaussian fields: Application to polycrystalline materials
Hussein, Rappel; Wu, Ling ULiege; Noels, Ludovic ULiege et al

in Journal of Applied Mechanics (2019), 86(12), 121009

For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application ... [more ▼]

For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application approaches the length scale of the micro-structure however, spatially fluctuating parameter fields (which vary from one realization of the field to another) can be incorporated to make the model capture the stochasticity of the underlying micro-structure. Randomly fluctuating parameter fields are often described as Gaussian fields. Gaussian fields however assume that the probability density function of a material parameter at a given location is a univariate Gaussian distribution. This entails for instance that negative parameter values can be realized, whereas most material parameters have physical bounds (e.g. the Young’s modulus cannot be negative). In this contribution, randomly fluctuating parameter fields are therefore described using the copula theorem and Gaussian fields, which allow different types of univariate marginal distributions to be incorporated, but with the same correlation structure as Gaussian fields. It is convenient to keep the Gaussian correlation structure, as it allows us to draw samples from Gaussian fields and transform them into the new random fields. The benefit of this approach is that any type of univariate marginal distribution can be incorporated. If the selected univariate marginal distribution has bounds, unphysical material parameter values will never be realized. We then use Bayesian inference to identify the distribution parameters (which govern the random field). Bayesian inference regards the parameters that are to be identified as random variables and requires a user- defined prior distribution of the parameters to which the observations are inferred. For the homogenized Young’s modulus of a columnar polycrystalline material of interest in this study, the results show that with a relatively wide prior (i.e. a prior distribution without strong assumptions), a single specimen is sufficient to accurately recover the distribution parameter values. [less ▲]

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See detailAn inverse Mean-Field-Homogenization-based micro-mechanical model for stochastic multiscale simulations of unidirectional composites
Wu, Ling ULiege; Calleja, Juan Manuel ULiege; Nguyen, Van Dung ULiege et al

Conference (2019, October 03)

Homogenization approaches have been widely developed in order to account for micro-structural geometrical and material properties in the framework of multiscale analyses. Most of the approaches postulate ... [more ▼]

Homogenization approaches have been widely developed in order to account for micro-structural geometrical and material properties in the framework of multiscale analyses. Most of the approaches postulate the existence of a statistically Representative Volume Element (RVE). However, such representativity is not always ensured, in particular when studying the failure of composite materials, because of the existing micro-structural uncertainties. In this work we develop a stochastic multi-scale approach for unidirectional composite materials in order to predict the scatter existing at the structural behaviour. Statistical characteristics of the micro-structure are first extracted from SEM images in order to build a Stochastic Volume Elements (SVE) [1] generator [2]. Probabilistic meso-scale stochastic behaviours are then extracted from direct numerical simulations of the generated SVEs. Finally, in order to provide an efficient way of exploiting the meso-scale random fields, while keeping information such as stress/strain history at the micro-scale during the resolution of macro-scale stochastic finite element, a probabilistic Mean-Field-Homogenization (MFH) method is developed [3,4]. To this end, the phase parameters of the MFH are defined as random fields, which are identified from the stochastic homogenized behaviours obtained through the stochastic direct simulations of the SVEs. As a result, non-deterministic macro-scale behaviours can be studied while having access to the micro-scale different phase 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, and L. Noels. "From SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites." Composite Structures 189C (2018): 206-227. [3] L. Wu, L. Adam, and 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 115, no. 12 (2018): 1430-1456. [4] L. Wu, V. D. Nguyen, L. Adam, and L. Noels. "An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites." Computer Methods in Applied Mechanics and Engineering 348 (2019): 97-138. [less ▲]

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See detailNumerical Evaluation of Interaction Tensors in Heterogeneous Materials
Spilker, Kevin ULiege; Noels, Ludovic ULiege; Wu, Ling ULiege

Conference (2019, September 16)

Two-scale simulations for multiscale modeling purposes require the solution of boundary value problems for each macroscopic material point. Each macroscopic point contains a representative volume element ... [more ▼]

Two-scale simulations for multiscale modeling purposes require the solution of boundary value problems for each macroscopic material point. Each macroscopic point contains a representative volume element (RVE) that exhibits the micro-structure of the material, constituted by microscopic points. When dealing with complex heterogeneous micro-structures, the computational effort to solve the boundary problems for all macroscopic points is immense. In order to make multiscale simulations utilizable for a wider range of purposes, a reduction of the computational complexity is indispensable. A reduction of the systems internal variables can be achieved by a decomposition of the full RVE into several subdomains, where constitutive equations need to be solved for all subdomains instead of for all microscopic points. In this work, the Transformation Field Analysis (TFA) strategy [1] will be implemented, assuming uniform stress and strain fields within the subdomains. The strain inside the subdomains is affected by the present eigenstrains in all other subdomains. This requires the determination of strain concentration tensors and eigenstrain – strain interaction tensors. The computation of these quantities and the domain decomposition of the RVE can be performed once for all by FE simulations in the so-called “off-line” stage. In order to achieve a reasonable decomposition into subdomains, strain concentration tensors of all microscopic points inside the RVE, representing their mechanical behavior, are computed by the application of various boundary conditions on the RVE. Subsequently, the microscopic points are decomposed into subdomains by a clustering method based on the similarity of their mechanical behavior. The applied clustering approach for the domain decomposition may allow both for a high reduction of computational costs for the simulations and settle shortcomings due to not well captured plastic strain fields of the original TFA method. The constitutive relations for the single clusters rely on interaction effects between the clusters. Interaction tensors can be evaluated in the “off-line” stage by analytical or numerical approaches. Analytical approaches include homogenized overall properties of the RVE, being not representative in cases of the presence of dominant heterogeneous microstructures. In this work, the eigenstrain – strain interaction tensors for the TFA approach are determined numerically by off-line FE simulations. Eigenstrains are applied on each single cluster, and a comparison with the resulting strain in all clusters allows for the complete characterization of the interaction tensors. References [1] Dvorak J. Transformation Field Analysis of Inelastic Composite Materials. Proceedings: Mathematical and Physical Sciences 1992; 437:311–327. [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 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 detailEvaluation of microdamage initiation in Z-pinned laminates by means of automated RVE computations
Pierreux, Gerrit; Wu, Ling ULiege; Van Hemelrijck, Danny et al

in Composite Structures (2018), 206

Z-pinning was originally designed to improve the delamination toughness and the impact resistance of composite laminates. However, there is extensive experimental evidence that this improvement is ... [more ▼]

Z-pinning was originally designed to improve the delamination toughness and the impact resistance of composite laminates. However, there is extensive experimental evidence that this improvement is accompanied by a reduction of the in-plane properties. The main mechanisms responsible for this deterioration are the local change in fiber content, fiber distortion, and the inclusion of resin-rich regions near the Z-pin. The shape of these geometrical features strongly depends on the laminate stacking sequence and on pin parameters such as pin diameter, pin content, and initial pin inclination angle. Their shape complexity challenges analytical modelling approaches which are currently used to generate RVE geometries for simulations. A computational approach is presented to generate such geometrical models. Resin-rich regions are modelled by initially straight discretized lines which are gradually shaped by a set of geometrical operations mimicking pin insertion, pin rotation and fiber deflection. Fiber distortion is modelled in a post-processing stage in cross-sections accounting for the preservation of the amount of fibers. These models are then transformed into finite element mechanical models in order to investigate how local fiber volume fraction changes, fiber misalignment, or distortions in reinforcement due to pin rotation, affect the global stiffness and local stress concentrations. [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 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 ▲]

Detailed reference viewed: 107 (1 ULiège)