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See detailElastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework
Wu, Ling ULg; Becker, Gauthier ULg; Noels, Ludovic ULg

in Computer Methods in Applied Mechanics & Engineering (2014), 279

One current challenge related to computational fracture mechanics is the modeling of ductile fracture and in particular the damage to crack transition. On the one hand, continuum damage models, especially ... [more ▼]

One current challenge related to computational fracture mechanics is the modeling of ductile fracture and in particular the damage to crack transition. On the one hand, continuum damage models, especially in their non-local formulation which avoids the loss of solution uniqueness, can capture the material degradation process up to the localization of the damage, but are unable to represent a discontinuity in the structure. On the other hand cohesive zone methods can represent the process zone at the crack tip governing the crack propagation, but cannot account for the diffuse material damaging process. In this paper we propose to combine, in a small deformations setting, a non-local elastic damage model with a cohesive zone model. This combination is formulated within a discontinuous Galerkin nite element discretization. Indeed this DG weak formulation can easily be developed in a non-local implicit form and naturally embeds interface elements that can be used to integrate the traction separation law of the cohesive zone model. The method remains thus consistent and computationally e cient as compared to other cohesive element approaches. The effects of the damage to crack transition and of the mesh discretization are respectively studied on the compact tension specimen and on the double-notched specimen, demonstrating the efficiency and accuracy of the method. [less ▲]

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See detailStreamable Laguerre-Voronoi Tessellation Model for Tomographic Images
Leblanc, Christophe ULg; Nguyen, Van Dung ULg; Wan, Fangyi et al

Conference (2014, July 25)

Introduction. Nowadays, the interest in foam materials is growing in several engineering fields [1]. Foams can exhibit a nonlinear mechanical behavior [2], which is highly depen- dent on their ... [more ▼]

Introduction. Nowadays, the interest in foam materials is growing in several engineering fields [1]. Foams can exhibit a nonlinear mechanical behavior [2], which is highly depen- dent on their microstructure [3]. Thus designing foams with specific mechanical properties can be very challenging. The present contribution is part of the ARC-Bridging project [4], whose objective is to predict the mechanical behavior of complex microstructured mate- rials via numerical simulations. A possible classification of foam models into two groups is: random models and deterministic models [5]. The random models frequently require statistical estimations of their parameters [6], whereas the deterministic models generally require numerically expensive image analyse. Indeed, classical analysis steps involve a distance tranform, a watershed and, optionally, a h-minima transform [5, p. 22], which can be computationally demanding [7, 8, 9]. Contribution. In the present Laguerre–Voronoi tessellation model, the image analysis part neither involes the watershed transform, nor the h-minima transform. Instead, fol- lowing the original idea of A.M. Lopez-Reina et E. Béchet [10], these two transforms are respectively replaced by a Hessian-based removal of spurious extrema and a clustering of the remaining maxima. This substitution allows the processing of large 3D-images by slices, i.e. “streaming”. The only limitation is enforced by the distance transform: the “feature” voxel of a given voxel should belong to the same slice. For foam images, this condition is fulfilled as long as the slice’s thickness is larger than the maximal foam cell’s size. Conclusion and perspectives. The aim of this contribution is to provide an efficient tessellation model for tomographic images of foams. From input tomographic images, this model provides a geometry model which will be used as an input for finite element simulations under the ARC-Briding project [4]. Simulation results will be compared with experimental measures. [less ▲]

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See detailMultiscale Computational Modeling of Deformation Mechanics andIntergranular Fracture in Nanocrystalline Copper
Péron-Lührs, Vincent ULg; Sansoz, Frédéric; Jérusalem, Antoine et al

in Computational Materials Science (2014), 90

The material description is based on two constitutive elements, the grains (or bulk crystals) and the grainboundaries (GBs), both having their behavior determined atomistically using the quasicontinuum ... [more ▼]

The material description is based on two constitutive elements, the grains (or bulk crystals) and the grainboundaries (GBs), both having their behavior determined atomistically using the quasicontinuum (QC) method by simulating the plastic deformation of [110] tilt crystalline interfaces undergoing simple shear, tension and nano-indentation. Unlike our previous work [V. Péron-Lührs et al., JMPS, 2013] however, the GB thickness is here calibrated in the model, providing more accurate insight into the GB widths according to the interface misorientation angle. In this contribution, the new two-scale model is also validated against fullyatomistic NC simulations tests for two low-angle and high-angle textures and two grain sizes. A simplified strategy aimed at predicting the mechanical behavior of more general textures without the need to run more QC simulations is also proposed, demonstrating significant reduction in computational cost compared to full atomistic simulations. Finally, by studying the response of dogbone samples made of NC copper, we show in this paper that such a two-scale model is able to quantitatively capture the differences in mechanical behavior of NC metals as a function of the texture and grain size, as well as to accurately predict the processes of inter-granular fracture for different GB character distributions. This two-scale method is found to be an effective alternative to other atomistic methods for the prediction of plasticity and fracture in NC materials with a substantial number of 2-D grains such as columnar-grained thin films for micro-scale electro-mechanical devices. [less ▲]

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See detailA probabilistic model of the adhesive contact forces between rough surfaces in the MEMS stiction context
Hoang Truong, Vinh ULg; Wu, Ling ULg; Arnst, Maarten ULg et al

Conference (2014, June 26)

Stiction is a common failure mechanism in microelectromechanical systems (MEMS) in which two interacting bodies permanently adhere together. This problem is due to the comparability of adhesive surface ... [more ▼]

Stiction is a common failure mechanism in microelectromechanical systems (MEMS) in which two interacting bodies permanently adhere together. This problem is due to the comparability of adhesive surface forces (e.g. Van der Waals forces, capillary forces) and body forces in the MEMS context. To predict the adhesive contact forces coupled with stiction phenomenon, the combination of the Nayak statistical approach with the asperity-based theories is a common solution. However, this method contains some limitations due to the underlying assumptions: infinite size of the interacting rough surfaces and negligibility of asperity interactions. Furthermore, the Nayak solution suffers from a considerable dependency on the choice of the minimum wave length considered in the surface representation, which remains diXcult to select. The main goal of our research is to propose an improved method (i) which accounts for the Vnite size of the interacting surfaces, (ii) accounts for the uncertainties related to these surface topologies, (iii) in which the minimum wave length selection is physically based, and (iv) in which the validity of the asperity-based theories is demonstrated. From the topology measurements of MEMS samples, an analysis of the power spectral density function is carried out to determine the minimum relevant wave length for the problem of interest (here capillary stiction). We also show that at this scale of interest the asperity-based theories remain valid for polysilicon materials. Moreover, instead of considering inVnite surfaces as in the Nayak approach, a set of surfaces, whose sizes are representative of the MEMS structure, is generated based on the approximated power spectral density analysis and using the Monte Carlo method. From this description of the contacting surfaces, the adhesive contact forces can be evaluated by applying the asperity contact theories, leading to a probabilistic distribution of the adhesive contact forces. In addition, as the contact forces are rooted from the micro-scale adhesive forces, while their consequence, stiction, happens at the macro-scale of the considered device, the multi-scale nature of the phenomenon is accounted for. To predict this macro-scale behavior in a probabilistic form, the uncertainty quantiVcation process is coupled with a multiscale analysis. [less ▲]

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See detailMuti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling
Wu, Ling ULg; Nguyen, Van Dung ULg; Adam, Laurent et al

Conference (2014, June 06)

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic ... [more ▼]

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailComputational homogenization of cellular materials
Nguyen, Van Dung ULg; Noels, Ludovic ULg

in International Journal of Solids and Structures (2014), 51(11-12), 2183-2203

In this work we propose to study the behavior of cellular materials using a second–order multi–scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin ... [more ▼]

In this work we propose to study the behavior of cellular materials using a second–order multi–scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin components, such as cell walls or cell struts, can occur. Even if the behavior of the materials of which the micro–structure is made remains elliptic, the homogenized behavior can lose its ellipticity. In that case, a localization band is formed and propagates at the macro–scale. When the localization occurs, the assumption of local action in the standard approach, for which the stress state on a material point depends only on the strain state at that point, is no–longer suitable, which motivates the use of the second-order multi–scale computational homogenization scheme. At the macro–scale of this scheme, the discontinuous Galerkin method is chosen to solve the Mindlin strain gradient continuum. At the microscopic scale, the classical finite element resolutions of representative volume elements are considered. Since the meshes generated from cellular materials exhibit voids on the boundaries and are not conforming in general, the periodic boundary conditions are reformulated and are enforced by a polynomial interpolation method. With the presence of instability phenomena at both scales, the arc–length path following technique is adopted to solve both macroscopic and microscopic problems. [less ▲]

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See detailMuti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling
Wu, Ling ULg; Nguyen, Van Dung ULg; Doghri, Issam et al

Scientific conference (2014, April 28)

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses ... [more ▼]

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses should also be computed within a nested scheme. This is particularly true when non-linear behaviours are modelled, or when the failure and post failure analyses are sought. In this work, multi-scale methods with strain softening are developed in the contexts of damage modelling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailMuti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling
Noels, Ludovic ULg; Nguyen, Van Dung ULg; Wu, Ling ULg et al

Scientific conference (2014, April 14)

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses ... [more ▼]

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses should also be computed within a nested scheme. This is particularly true when non-linear behaviours are modelled, or when the failure and post failure analyses are sought. In this work, multi-scale methods with strain softening are developed in the contexts of damage modelling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailQuasicontinuum study of the shear behavior of defective tilt grain boundaries in Cu
Péron-Lührs, Vincent ULg; Sansoz, Frédéric; Noels, Ludovic ULg

in Acta Materialia (2014), 64

Atomistic simulations using the quasicontinuum method are used to study the role of vacancy defects and angström-scale voids on the mechanical behavior of five tilt bicrystals containing grain boundaries ... [more ▼]

Atomistic simulations using the quasicontinuum method are used to study the role of vacancy defects and angström-scale voids on the mechanical behavior of five tilt bicrystals containing grain boundaries (GBs) that have been predicted to exhibit characteristic deformation processes of nanocrystalline and nanotwinned metals: GB-mediated dislocation emission, interface sliding, and shear-coupled GB migration. We demonstrate that such nanoscale defects have a profound impact on interfacial shear strength and underlying deformation mechanisms in copper GBs due to void-induced local stresses. In asymmetric high and low angle GBs, we find that voids become preferential sites for dislocation nucleation when the void size exceeds 4 Å. In symmetric 9(221) GBs prone to sliding, voids are shown to shield the local shear stress, which considerably reduces the extent of atom shuffling at the interface. In symmetric Sigma5(210) and Sigma27(115) GBs, we find that the effect of voids on shear-coupled GB migration depends on the GB tilt direction considered, as well as on the size and number of voids. Remarkably, large voids can completely abate the GB migration process in Sigma 27(115) GBs. For all GB types, the interfacial shear strength is shown to decrease linearly as the volume fraction of voids at the interface increases; however, this study also suggests that this decrease is much more pronounced in GBs deforming by sliding than by dislocation nucleation or migration, owing to larger void-induced stresses. [less ▲]

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See detailHomogenization with propagation of instabilities through the different scales
Noels, Ludovic ULg; Wu, Ling ULg; Nguyen, Van Dung ULg et al

Scientific conference (2014, January 31)

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic ... [more ▼]

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailProbabilistic model for MEMS micro-beam resonance frequency made of polycrystalline linear anisotropic material
Lucas, Vincent ULg; Wu, Ling ULg; Arnst, Maarten ULg et al

Conference (2013, December)

In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction cannot be deterministic: there is a scatter in the ... [more ▼]

In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction cannot be deterministic: there is a scatter in the reached value resulting from the uncertainties involved in the manufacturing process. The purpose of this work is to take into account these uncertainties of the microstructure and to propagate them up to the micro-beam resonance frequency. The objective is a non-deterministic model that can be used since the design stage. Towards this end a 3-scales stochastic model predicting the resonance frequency of a micro-beam made of a polycrystalline linear anisotropic material is described. Uncertainties are related to the sizes and orientations of the grains. The first part of the problem is a homogenization procedure performed on a volume which is not representative, due to the small scale of the problem inherent in MEMS. The method is thus non-deterministic and a meso-scale probabilistic elasticity tensor is predicted. This stage is followed by a perturbation stochastic finite element procedure to propagate the meso-scale uncertainties to the macro-scale, leading to a probabilistic model of the resonance frequency of the MEMS. [less ▲]

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See detailA micro-meso model to predict van der Walls and capillary induced stiction in micro-structures
Hoang Truong, Vinh ULg; Noels, Ludovic ULg; Wu, Ling ULg

Conference (2013, December)

Undesirable stiction in MEMS results from the contact between surfaces and is due to the adhesive van der Waal and/or capillary forces, which become important for micro-structures. In this work, a micro ... [more ▼]

Undesirable stiction in MEMS results from the contact between surfaces and is due to the adhesive van der Waal and/or capillary forces, which become important for micro-structures. In this work, a micro-macro multi-scale approach is developed in order to predict possible stiction in MEMS structures At the lower scale, the unloading adhesive contact-distance curves of two interacting rough surfaces are established based on Maugis’ model extended herein to account simultaneously for the van der Waals and the capillary forces. The resulting unloading adhesive contact-distance curves are dependent on the material and surface properties -such as elastic modulus, surface energy- on the rough surfaces’ topography parameters -the standard deviation of asperities heights and the asperities’ density- and on the humidity level. At the higher scale, a beam finite element analysis is considered to determine the residual configuration due to the adhesive forces once contact happened. Toward this end, the adhesive contact-distance curve computed previously is integrated on the surface of the finite elements as a contact law. [less ▲]

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See detailNon-Local Incremental-Secant Mean-Field-Homogenization of Damage-Enhanced Elasto-Plastic Composites
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

Conference (2013, December)

An anisotropic gradient–enhanced continuum damage model is herein embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly ... [more ▼]

An anisotropic gradient–enhanced continuum damage model is herein embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. [less ▲]

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See detailA combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

in International Journal of Plasticity (2013), 51

This paper presents an incremental secant mean-fi eld homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached ... [more ▼]

This paper presents an incremental secant mean-fi eld homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached in the elasto-plastic phases upon a fi ctitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using secant tensors, which are naturally isotropic and enable to de fine the Linear-Comparison-Composite. The method, which remains simple in its formulation, is valid for general non-monotonic and non-proportional loading. It is applied on various problems involving elastic, elasto-plastic and perfectly-plastic phases, to demonstrate its accuracy compared to other existing MFH methods. [less ▲]

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See detailAn implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

in International Journal of Solids and Structures (2013), 50(24), 38433860

This paper presents an incremental-secant mean- field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the ... [more ▼]

This paper presents an incremental-secant mean- field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the proposed method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme. When strain softening of materials is involved, classical fi nite element formulations lose solution uniqueness and face the strain localization problem. To avoid this issue the model is formulated in a so-called implicit gradient-enhanced approach, with a view toward macro-scale simulations. The method is then used to predict the behavior of composites whose matrix phases exhibit strain softening, and is shown to be accurate compared to unit cell simulations and experimental results. Then the convergence of the method upon strain softening, with respect to the mesh size, is demonstrated on a notched composite ply. Finally, applications consisting in a stacking plate, successively without and with a hole, are given as illustrations of the possibility of the method to be used in a multiscale framework. [less ▲]

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See detailMulti-scale studies of foamed materials
Nguyen, Van Dung ULg; Noels, Ludovic ULg

Conference (2013, September)

We propose a multi-scale study to predict micro-buckling that could happen in foamed materials. At the macroscopic scale, when localization occurs, the characteristic size of macroscopic deformation is ... [more ▼]

We propose a multi-scale study to predict micro-buckling that could happen in foamed materials. At the macroscopic scale, when localization occurs, the characteristic size of macroscopic deformation is the same order of the microscopic size. The assumption of material action in standard multi-scale computational homogenization approach where the stress only depends on the strain at this point is no-longer suitable, which motivates the uses of the second-order scheme. In this work, an implementation of the second-order continuum based on a discontinuous Galerkin approximation is shown to be particularly efficient to constrain weakly the continuities of the displacement field and of its gradient. At the microscopic scale, classical finite element resolutions of RVEs are considered. To enforce the periodic boundary condition of this micro problem, we propose an efficient method, which is based on the polynomial interpolation, and allows applying the periodic boundary condition without requiring conformal meshes. The micro-macro transition follows the second-order computational homogenization scheme. With the proposed framework it is shown that, during the macroscopic loading, the micro- buckling of the thin components of the foamed structure (cell walls and edges) can occur even if the tangent modulus of micro-material is still elliptic since the homogenized tangent modulus at macro-scale can lose its ellipticity. In that case, the localization occurs at macro- scale and can be captured by the model. [less ▲]

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See detailA two-scale model predicting the mechanical behavior of nanocrystalline solids
Péron-Lührs, Vincent ULg; Jérusalem, Antoine; Sansoz, Frédéric et al

in Journal of the Mechanics & Physics of Solids (2013), 61(9), 1895-1914

Polycrystalline materials, with nanosized grains (<100 nm), exhibit superior strength exceeding those of their coarse-grained counterparts. With such small grains, the deformation mechanisms taking place ... [more ▼]

Polycrystalline materials, with nanosized grains (<100 nm), exhibit superior strength exceeding those of their coarse-grained counterparts. With such small grains, the deformation mechanisms taking place at grain boundaries (GBs) become dominant compared to the intragranular crystal plasticity. Recent studies have revealed that the deformation mechanisms are influenced by the GB network. For instance, a high yield stress in nanostructured metals can be obtained by choosing the relevant grain boundary character distribution (GBCD). In this paper we present an original numerical multiscale approach to predict the mechanical behavior of nanostructured metals according to their GBCD composed of either high angle (HA) GBs (HAB) or low angle (LA) GBs (LAB). Molecular simulations using the quasicontinuum method (QC) are performed to obtain the mechanical response at the nanoscale of GB undergoing simple shear (GB sliding behavior) and tensile loads (GB opening behavior). To simulate the grain behavior, a mechanical model of dislocation motions through a forest dislocation is calibrated using a nanoindentation simulation performed with QC. These QC results are then used in a finite element code (direct numerical simulation-DNS) as a GB constitutive model and as a grain constitutive model. This two-scale framework does not suffer from length scale limitations conventionally encountered when considering the two scales separately. [less ▲]

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See detailFifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011)
Béchet, Eric ULg; Dick, Erik; Geuzaine, Christophe ULg et al

in International Journal of Computational & Applied Mathematics (2013), 246

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See detailAn Energy-Based Variational Model of Ferromagnetic Hysteresis for Finite Element Computations
François-Lavet, Vincent; Henrotte, François; Stainier, Laurent ULg et al

in Journal of Computational & Applied Mathematics (2013), 246

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic ... [more ▼]

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. [less ▲]

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See detailMultiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous Galerkin formulation
Nguyen, Van Dung ULg; Becker, Gauthier ULg; Noels, Ludovic ULg

in Computer Methods in Applied Mechanics & Engineering (2013), 260

When considering problems of dimensions close to the characteristic length of the material, the size e ects can not be neglected and the classical (so–called first–order) multiscale computational ... [more ▼]

When considering problems of dimensions close to the characteristic length of the material, the size e ects can not be neglected and the classical (so–called first–order) multiscale computational homogenization scheme (FMCH) looses accuracy, motivating the use of a second–order multiscale computational homogenization (SMCH) scheme. This second–order scheme uses the classical continuum at the micro–scale while considering second–order continuum at the macro–scale. Although the theoretical background of the second–order continuum is increasing, the implementation into a finite element code is not straightforward because of the lack of high–order continuity of the shape functions. In this work, we propose a SMCH scheme relying on the discontinuous Galerkin (DG) method at the macro–scale, which simplifies the implementation of the method. Indeed, the DG method is a generalization of weak formulations allowing for inter-element discontinuities either at the C0 level or at the C1 level, and it can thus be used to constrain weakly the C1 continuity at the macro–scale. The C0 continuity can be either weakly constrained by using the DG method or strongly constrained by using usual C0 displacement–based finite elements. Therefore, two formulations can be used at the macro–scale: (i) the full–discontinuous Galerkin formulation (FDG) with weak C0 and C1 continuity enforcements, and (ii) the enriched discontinuous Galerkin formulation (EDG) with high–order term enrichment into the conventional C0 finite element framework. The micro–problem is formulated in terms of standard equilibrium and periodic boundary conditions. A parallel implementation in three dimensions for non–linear finite deformation problems is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward and e cient way. [less ▲]

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