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See detailNon-local multiscale analyzes of composite laminates based on a damage-enhanced mean–field homogenization formulation
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

Conference (2013, June)

Properties of carbon fiber reinforced epoxy laminates are studied using an anisotropic gradient–enhanced continuum damage model embedded in a mean–field homogenization (MFH) procedure. The fibers are ... [more ▼]

Properties of carbon fiber reinforced epoxy laminates are studied using an anisotropic gradient–enhanced continuum damage model embedded in a mean–field homogenization (MFH) procedure. The fibers are assumed to remain elastic, and the matrix material obeys an elasto–plastic behavior enhanced by the proposed damage model. 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 and strain localization, which happens in classical finite element simulations when strain softening of materials is involved, is avoided. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions, accordingly to the conducted experimental results. [less ▲]

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See detailAn incremental-secant mean-field homogenization scheme for elasto-plastic and damage-enhanced elasto-plastic composite materials
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

Conference (2013, June)

This paper presents an incremental secant mean-field homogenization process for composite materials made of elasto–plastic constituents, which can exhibit damage. In this formulation, the residual stress ... [more ▼]

This paper presents an incremental secant mean-field homogenization process for composite materials made of elasto–plastic constituents, which can exhibit damage. In this formulation, 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 method, remains simple in its formulation, is applied on various problems involving elastic, elasto–plastic and perfectly–plastic phases, to demonstrate its accuracy compared to other existing MFH methods. The method is particularly attractive when the damaging process is accounted for in the matrix phase. Indeed, during the damaging process of one phase, the secant method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme, when compared to direct numerical simulations. [less ▲]

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See detailModeling of damage to crack transition using a coupled discontinuous Galerkin/cohesive extrinsic law framework
Wu, Ling ULg; Becker, Gauthier; Noels, Ludovic ULg

Conference (2013, June)

One current challenge related to computational fracture mechanics is the modelization of ductile fracture and in particular the damage to crack transition. In this paper we propose to achieve this goal by ... [more ▼]

One current challenge related to computational fracture mechanics is the modelization of ductile fracture and in particular the damage to crack transition. In this paper we propose to achieve this goal by combining 1. A non-local damage model 2. The hybrid discontinuous Galerkin (DG)/extrinsic cohesive law (ECL) formulation As classical damage models for finite element formulations lose the solution uniqueness and face the strain localization problem when strain softening of materials is involved, the damage model is herein formulated in a so-called implicit non-local approach, following the developments in [1]. In this formulation, a new non-local variable, the non-local accumulated plastic strain eg, representative of an internal variable and its derivatives, results from the resolution of a new boundary value problem. Besides the advantage of using C0 elements, although the elements have now one additional degree of freedom per node, this approach also possesses the feature of being fully non-local. The hybrid DG/ECL method was recently proposed [2] to circumvent the drawbacks of the cohesive element methods. Indeed, with this DG/ECL method, prior to fracture, the flux and stabilization terms arising from the DG formulation at interelement boundaries are enforced via interface elements in a way that guarantees consistency and stability, contrarily to traditional extrinsic cohesive zone methods. Upon the onset of fracture, the traction–separation law (TSL) governing the fracture process becomes operative without the need to modify the mesh topology as the the cohesive elements required to integrate the TSL are already present. This DG/ECL method has been shown to be an efficient numerical framework that can easily be implement in parallel with excellent scalability properties to model fragmentation, dynamic crack propagation in brittle and smallscale yielding materials, for 3D problems and for thin structures [3,4]. In this work, the DG/ECL method is extended to account for the damage process, as described in the non-local setting. One main advantage of the DG/ECL formulation is the existence of interface elements in which the damage model can be solved, the hydrostatic pressure can be resolved, and through which discontinuities can easily be introduced with a physically-based criterion. [less ▲]

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See detailA micro-model of the intra-laminar fracture in fiber-reinforced composites based on a discontinuous Galerkin/extrinsic cohesive law method
Wu, Ling ULg; Tjahjanto, Denny; Makradi, Ahmed et al

Conference (2013, June)

The hybrid discontinuous Galerkin (DG)/extrinsic cohesive law (ECL) method was recently proposed [1] to circumvent the drawbacks of the cohesive element methods. With the DG/ECL method, prior to fracture ... [more ▼]

The hybrid discontinuous Galerkin (DG)/extrinsic cohesive law (ECL) method was recently proposed [1] to circumvent the drawbacks of the cohesive element methods. With the DG/ECL method, prior to fracture, the flux and stabilization terms arising from the DG formulation at interelement boundaries are enforced via interface elements in a way that guarantees consistency and stability, contrarily to traditional extrinsic cohesive zone methods. At the onset of fracture, the traction–separation law (TSL) governing the fracture process becomes operative without the need to modify the mesh topology since the cohesive elements required to integrate the TSL are already present. This DG/ECL method has been shown to be an efficient numerical framework that can easily be implement in parallel with excellent scalability properties to model fragmentation, dynamic crack propagation in brittle and small-scale yielding materials, both for 3D problems and for thin structures [1, 2]. In this work, following the developments in [3], the DG/ECL method is extended to the study of composite materials failures at the micro-scale. The method is applied to study the transverse traction of composite materials in characteristic micro-volumes of different sizes. The method captures the debonding process, assimilated to a damaging process before the strain softening onset. It is shown that the density of dissipated energy resulting from the damage (debonding) remains the same for the different studied cell sizes. During the strain softening phase, a micro-crack initiates and propagates, in agreement with experimental observations. After strain softening onset, the extracted macroscale cohesive law, obtained by the method proposed in [4], is ultimately shown to converge for the different cell sizes. The predicted behaviors are then compared to experimental results obtained from laminate tests, and are found to be in good agreement. [less ▲]

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See detailA micro-meso-model of intra-laminar fracture in fiber-reinforced composites based on a Discontinuous Galerkin/Cohesive Zone Method
Wu, Ling ULg; Tjahjanto, Denny; Becker, Gauthier ULg et al

in Engineering Fracture Mechanics (2013), 104

The recently developed hybrid discontinuous Galerkin/extrinsic cohesive law framework is extended to the study of intra{laminar fracture of composite materials. Toward this end, micro-volumes of di erent ... [more ▼]

The recently developed hybrid discontinuous Galerkin/extrinsic cohesive law framework is extended to the study of intra{laminar fracture of composite materials. Toward this end, micro-volumes of di erent sizes are studied. The method captures the debonding process, which is herein proposed to be assimilated to a damaging process, before the strain softening onset, and the density of dissipated energy resulting from the damage (debonding) remains the same for the di erent studied cell sizes. Finally, during the strain softening phase a micro{crack initiates and propagates in agreement with experimental observations. We thus extract a resulting mesoscale cohesive law, which is independent on the cell sizes, using literature methods. [less ▲]

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See detailON THE MODELING OF ADHESIVE CONTACT AND STICTION FAILURE IN MICRO-SWITCHES
Wu, Ling ULg; Noels, Ludovic ULg; Golinval, Jean-Claude ULg

in Ouisse (FEMTO-ST – ENSMM, France); Deü (CNAM, FR), J.F. (Eds.) MEDYNA 2013 Proceedings (2013, April)

Undesirable stiction, which results from contact between surfaces, is a major failure mode in micro-switches. Indeed the adhesive forces can become so important that the two surfaces remain permanently ... [more ▼]

Undesirable stiction, which results from contact between surfaces, is a major failure mode in micro-switches. Indeed the adhesive forces can become so important that the two surfaces remain permanently glued, limiting the life-time of the MEMS. This is especially true when contact happens between surfaces where elasto-plastic asperities deform permanently until the surfaces reach plastic accommodation, increasing the surface forces. To predict this behavior, a micro adhesive-contact model is developed, which accounts for the surfaces topography evolutions during elasto-plastic contacts. This model can be used at a higher scale to study the MEMS behavior, and thus its life-time. For illustration purpose, an electrostatic-structural analysis is performed on a micro-switch. [less ▲]

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See detailMulti-scale modelling
Noels, Ludovic ULg; Becker, Gauthier; Mulay, Shantanu Shashikant ULg et al

Scientific conference (2013, March 11)

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See detailA full-discontinuous Galerkin formulation of non-linear Kirchhoff-Love shells: elasto-plastic finite deformations, parallel computation & fracture applications
Becker, Gauthier ULg; Noels, Ludovic ULg

in International Journal for Numerical Methods in Engineering (2013), 93(1), 80-117

Due to its ability to take into account discontinuities, the discontinuous Galerkin (DG) method presents some advantages for modeling crack initiations and propagations. This concept has been recently ... [more ▼]

Due to its ability to take into account discontinuities, the discontinuous Galerkin (DG) method presents some advantages for modeling crack initiations and propagations. This concept has been recently applied to 3D simulations and to elastic thin bodies. In this last case, the assumption of small elastic deformations before crack initiations or propagations reduces drastically the applicability of the framework to a reduced number of materials. To remove this limitation, a full-DG formulation of non-linear Kirchhoff-Love shells is presented and is used in combination with an elasto-plastic finite deformations model. The results obtained by this new formulation are in agreement with other continuum elasto-plastic shell formulations. Then this full-DG formulation of Kirchhoff-Love shells is coupled with the cohesive zone model to perform thin body fracture simulations. As this method allows considering elasto-plastic constitutive laws in combination with the cohesive model, accurate results compared to the experiments are found. In particular, the crack path and propagation rate of a blasted cylinder are shown to match experimental results. One of the main advantages of this framework is its ability to run in parallel with a high speed-up factor, allowing the simulation of ultra fine meshes. [less ▲]

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See detailA Micro Model for Elasto-Plastic Adhesive-Contact in Micro-Switches: Application to cyclic loading
Wu, Ling ULg; Golinval, Jean-Claude ULg; Noels, Ludovic ULg

in Tribology International (2013), 57

Stiction is a major failure mode in micro-electromechanical systems. In previous works, a statistical rough surfaces interaction model, for which only elastic adhesive contact has been considered, was ... [more ▼]

Stiction is a major failure mode in micro-electromechanical systems. In previous works, a statistical rough surfaces interaction model, for which only elastic adhesive contact has been considered, was developed for multiscale analyzes. However, during the impact between rough surfaces, plastic deformations of asperities cannot always be neglected. In the present work, the adhesion between rough surfaces is studied considering the elasto-plastic deformations of the asperities, and a model predicting the resulting micro adhesive-contact forces is derived. For illustration purpose, an electrostatic-structural analysis is performed on a micro-switch. To determine the degree of plasticity involved, the impact energy of the movable electrode at pull-in is estimated. Thus the maximal adhesive force evolution during cyclic loading is predicted using the developed model. [less ▲]

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See detailThe fracture studies of polycrystalline silicon based MEMS
Mulay, Shantanu Shashikant ULg; Becker, Gauthier; Vayrette, Renaud et al

in EUROSIME 2013 (2013)

The advantages of micro-electro-mechanical systems (MEMS), such as low power requirement, miniaturized sizes and costs reduction, have already made significant impact in many technological fields. MEMS ... [more ▼]

The advantages of micro-electro-mechanical systems (MEMS), such as low power requirement, miniaturized sizes and costs reduction, have already made significant impact in many technological fields. MEMS are now widely used as accelerometers, pressure sensors, and resonators etc. However, the determination of the mechanical properties of MEMS devices with high accuracy is still a challenging task due to their small dimensions and often anisotropic behaviour. This paper focuses on the modelling and simulation of the fracture of a key MEMS component, which is a polycrystalline silicon beam, by discontinuous Galerkin (DG) formulation combined with an extrinsic cohesive law (ECL) to describe the fracture process. As the beam is modelled by plane-stress 2D elements, an analytical equation to compute the effective fracture strength and the effective critical strain energy release rate in terms of the through-the-thickness fracture mode and of the orientation of the facet with respect to the crystal is also developed. At the end, a model is simulated, and the results are verified as per the physics of the problem and experiments. [less ▲]

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See detailNon-local Damage-Enhanced MFH for Multiscale Simulations of Composites
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

in Patterson, Eann; Backman, David; Cloud, Gary (Eds.) Composite Materials and Joining Technologies for Composites, Volume 7 (2013)

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix ... [more ▼]

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material obeys an elasto-plastic behavior enhanced by a damage model. As classical finite element simulations face the problems of losing uniqueness and strain localization when strain softening of materials is involved, we develop the mean-field homogenization in a non-local way. Toward this end we use the so-called non-local implicit approach, reformulated in an anisotropic way to describe the damage in the matrix. As a result we have a multi-scale model that can be used to study the damage process at the meso-scale, and in particular the damaging of plies in a composite stack, in an efficient comput0ational way. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions. [less ▲]

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See detailStiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts
Wu, Ling ULg; Golinval, Jean-Claude ULg; Noels, Ludovic ULg

in Shaw, Gordon; Prorok, Bart; Starman, LaVern (Eds.) MEMS and Nanotechnology, Volume 6 (2013)

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See detailThe fracture studies of polycrystalline silicon based MEMS
Mulay, Shantanu Shashikant ULg; Becker, Gauthier; Vayrette, Renaud et al

Scientific conference (2012, November 24)

The advantages of micro-electro-mechanical system (MEMS), such as low power requirement, miniature sizes and costs reduction, has already made significant impact in many technological fields. MEMS are now ... [more ▼]

The advantages of micro-electro-mechanical system (MEMS), such as low power requirement, miniature sizes and costs reduction, has already made significant impact in many technological fields. MEMS are now widely used as accelerometers, pressure sensors, and resonators. However, the determination of mechanical properties of MEMS devices with high accuracy is still a challenging task due to their miniature size. For example, the crystal size and orientation may have a significant effect on the fracture strength of MEMS microstructure. Among several important materials used for the development of MEMS devices, polycrystalline silicon plays a key role in various applications. Thus, an understanding of the relationship between poly-silicon manufacturing processes, and the resulting mechanical behaviour and durability of micro-fabricated structures is needed to allow rational design of MEMS devices. This work focuses on the modelling and simulation of the fracture of MEMS, made up of polycrystalline silicon, by discontinuous Galerkin (DG) formulation combined with an extrinsic cohesive law. The problem is solved as plane-stress type. All the elements are discontinuous in the DG method, and inter-element continuity is weakly enforced by having recourse to interface elements. When a fracture criterion is reached, an extrinsic cohesive law is activated on the already existing interface elements. The cracks can be initiated, merged or propagated, in this method. The fracture properties of material can be considered different along crystal interfaces and inside crystal bulk, and can account for crystal orientation. Moreover this method avoid drawbacks of usual cohesive method (no modification of the structure stiffness and no complex implementation in parallel) allowing for accurate large scale simulation. Polycrystalline silicon is an orthotropic material, i.e., it has different material properties, such as Young’s modulus, Poisson’s ratio, fracture strength, along different crystal lattice planes. These properties are also symmetric for a cubic crystal, i.e., the lattice planes perpendicular to each other have similar properties. This symmetric nature is well captured in the proposed work by a new formulation to compute effective fracture strength along any plane of interest based on the known values of the same along (1 0 0), (1 1 0), and (1 1 1) lattice planes. The effect of thickness of MEMS is also included by computing the effective stress on interface elements at different vertical angles. These formulations are analyzed by sample simulation results. The efficiency and accuracy of the method are assessed by experiments involving on-chip fracture tests, providing the fracture stress, and supplemented by the characterization of the test specimen. The characterization consists of the measurement of grain size and crystallographic orientation by electron back scattering diffraction, and the determination of crack path. An important point is the analysis of the competition between inter-granular versus trans-granular crack path with respect to the grain orientation. [less ▲]

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See detailStiction failure in microswitches due to elasto-plastic adhesive contact and cyclic loading
Wu, Ling ULg; Golinval, Jean-Claude ULg; Noels, Ludovic ULg

Scientific conference (2012, November 24)

Undesirable stiction, which results from contact between surfaces, is a major failure mode in micro-switches. This is especially true when contact happens between surfaces where elastoplastic asperities ... [more ▼]

Undesirable stiction, which results from contact between surfaces, is a major failure mode in micro-switches. This is especially true when contact happens between surfaces where elastoplastic asperities deform permanently until the surfaces reach plastic accommodation. Indeed before or at accommodation, the adhesive forces can become so important that the two surfaces remain permanently glued, limiting the life-time of the MEMS. To predict the behavior a micro adhesive-contact model is developed, which account for the surfaces topography evolutions during elasto-plastic contacts. This model can be used at a higher scale to study the MEMS behavior, and thus its life-time. The MEMS devices studied here are assumed to work in a dry environment. In these operating conditions only the Van der Waals forces have to be considered for adhesion. For illustration purpose, an electrostatic-structural analysis is performed on a micro-switch. To determine the degree of plasticity involved, the impact energy of the movable electrode at pull-in is estimated. Thus the maximal adhesive force is predicted using the developed model.Within this formalism, the cyclic loading and accommodation effects can be taken into account, as represented on the picture, which shows the non-dimensional force vs. separation distance of two rough surfaces after different cycle numbers. [less ▲]

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See detailValidation tests of the full-discontinuous Galerkin / extrinsic cohesive law framework of Kirchhoff-Love shells
Becker, Gauthier ULg; Noels, Ludovic ULg

in International Journal of Fracture (2012), 178(1), 299-322

Due to its ability to account for discontinuities, the discontinuous Galerkin (DG) method presents two main advantages for modeling crack initiations and propagation. On the one hand, it provides an easy ... [more ▼]

Due to its ability to account for discontinuities, the discontinuous Galerkin (DG) method presents two main advantages for modeling crack initiations and propagation. On the one hand, it provides an easy way to insert the cohesive elements during the simulation and therefore avoids the drawbacks inherent to the use of an extrinsic cohesive law. On the other hand, the capture of complex crack path requires very thin meshes and the recourse to a parallel implementation of DG formulations exhibits a high scalability of the resolution scheme. Recently, the authors developed such a DG-fracture framework for Kirchhoff-Love shells in the linear and non-linear ranges. They proved that this framework dissipates, during the fracture process, an amount of energy equal to the fracture energy of the material and that the model is able to propagate the crack with the right speed. In this paper, novel numerical benchmarks are presented to validate the method in various fracture conditions. The two first ones include an initial notch and study the fracture propagation under two different dynamic loadings (impact and blast). The two other ones focus on the fragmentation of initially unbroken specimens due to uniform expansion in order to demonstrate the ability of the new framework to model crack initiations. Results are in all cases in agreement with the ones reported in the literature. [less ▲]

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See detailFull discontinuous Galerkin formulation of shells in large deformations with parallel and fracture mechanics applications
Becker, Gauthier ULg; Noels, Ludovic ULg

Conference (2012, July 11)

Fracture mechanical problems can be solved by coupling the finite elements with a cohesive approach. Unfortunately, the classical cohesive methods suffer from severe limitations. Indeed, on one hand, the ... [more ▼]

Fracture mechanical problems can be solved by coupling the finite elements with a cohesive approach. Unfortunately, the classical cohesive methods suffer from severe limitations. Indeed, on one hand, the intrinsic approach, which inserts the cohesive elements at the beginning, has to model the prefracture stage. This requires an initial slope in the traction separation law that should tend toward infinity to avoid lack of consistency leading to obvious numerical problems. On the other hand, the extrinsic cohesive method inserts the cohesive elements during the simulation when a fracture criterion is reached. This insertion requires topological mesh modifications and therefore a very complicated implementation, especially in a parallel code. To overcome these limitations, new methods were developed and in particular, an approach based on discontinuous Galerkin formulation (DG) has been pioneered by R. Radovitzky (Radovitzky cmame2011). The use of the DG principle allows to formulate the problem with discontinuous elements and the continuity between them is ensured weakly by terms integrated on the elements interface . These interface elements can be easily replaced by a cohesive element during the simulation. We have recently developed this approach for shells (Becker cmame2011) to obtain a full DG method. Moreover, a new cohesive law based on the reduced stresses of the thin bodies formulation is developed to propagate a fracture through the thickness. This cohesive model dissipates the right amount of energy during crack phenomena. These developments are implemented in parallel and validated by the study the blast of a notched cylinder, for which experimental and numerical (by XFEM method) data are reported in the literature by R. Larsson (Larsson ijnme2011). Finally, as thin structures are often made of ductile materials, which show large deformations before fracture, the formulation is extended to the non linear case with hyperelastic material law. This one can take into account the damage and a criterion based on the work of Huespe (Huespe plasticity2009) is developed to localize the damage leading to the apparition and propagation of cracks. [less ▲]

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See detailMultiscale Simulations of Composites with Non-Local Damage-Enhanced Mean-Field Homogenization
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

Conference (2012, July)

The mean-field homogenization (MFH) approach is an attractive framework for multiscale methods, as it provides predictions of the macroscopic behavior of particle or fiber reinforced composites at a ... [more ▼]

The mean-field homogenization (MFH) approach is an attractive framework for multiscale methods, as it provides predictions of the macroscopic behavior of particle or fiber reinforced composites at a reasonable computational cost. Efficient MFH methods have been available for a long time for linear elastic problems, using for example the Mori-Tanaka scheme [2], but they can also be extended in the non-linear regime after linearization of the constitutive behavior at the current strain state, as for the incremental approach, e.g. [1]. In this work, the application of ductile-damage theories to a multiscale analysis of continuous fiber reinforced composites is considered. Toward this end, the incremental MFH approach is extended to account for the damage behavior happening in the matrix material at the microscale and to derive the effective properties of particle or fiber reinforced composites. However, capturing the degradation, damage or failure of material happening at the microscopic scale could lead to loss of uniqueness in the solution as the governing partial differential equations may lose ellipticity at a given level of loading corresponding to the strain-softening onset. Thus, in order to avoid the strain/damage localization caused by matrix material softening, the gradient-enhanced formulation [3] is adopted to describe the material behavior of the matrix during the homogenization process, as we have recently proposed [4]. As illustration, the behavior of a fiber re-enforced elasto-plastic matrix is considered. The properties of the matrix correspond to an elasto-plastic material experiencing damage, with a non-local form of Lemaitre Chaboche model. The fibers are assumed linear elastic, see [4] for details. A loading-unloading cycle is applied in the direction transverse to the fibers. A maximal deformation of 10 % is reached before the unloading proceeds to zero-transverse deformation. The effective behavior predicted by the MFH models is compared to the solutions obtained by finite element computations performed on a unit periodic cell and on RVE where the micro-structure is fully meshed. The results for three fiber volume ratios are presented in Fig. 1. For the three fiber volume ratios, the homogenized property is dominated by the properties of the matrix, with an obvious elasto-plastic behavior exhibiting softening. For vI = 15% and 30%, rather good predictions are given by the MFH model, with, as expected, higher macroscopic stress and damage predicted by the MFH due to the incremental formulation. However for vI = 50%, the MFH model overestimates the macroscopic stress considerably. This error comes from the assumption of Mori - Tanaka based MFH. As it is shown to be an efficient multi-scale approach, the developed gradient enhanced MFH formulation presented can now be used to model the behavior of composite laminates experiencing damage. [less ▲]

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See detailA one-field formulation of elasto-plastic shells with fracture applications
Becker, Gauthier; Noels, Ludovic ULg

Conference (2012, July)

The main feature of Discontinuous Galerkin (DG) methods is their ability to take into account discontinuities of the unknown field in the interior domain of studied problems. In such formulations the ... [more ▼]

The main feature of Discontinuous Galerkin (DG) methods is their ability to take into account discontinuities of the unknown field in the interior domain of studied problems. In such formulations the integration by parts is realized on the elements leading to boundary integral terms These terms between elements ensure the continuity and compatibility of the solution in a stable manner, which makes DG attractive to ensure weakly the C0 continuity and/or the C1 continuity. For non-linear Kirchhoff-Love shells, the C0/DG formulation - the C0 continuity is ensured as usual by considering continuous shape functions and the C1 continuity is weakly ensured by DG interface terms in a stable and consistent way - leads to a one-field formulation, where the displacements are the only unknowns of the problem [5]. DG methods have also an advantage when it comes to simulate fracture with a cohesive approach. Indeed, the classical cohesive methods suffer from severe limitations. The intrinsic approach, which inserts the cohesive elements at the beginning, requires an initial slope in the traction separation law and suffers from lack of consistency, while the extrinsic cohesive method, which inserts the cohesive elements during the simulation when a fracture criterion is reached, suffers from difficult parallel implementation due to the topological mesh modifications happening during the simulations. To overcome these limitations, new methods were developed and in particular, an approach based on a C0-discontinuous Galerkin formulation where continuity between elements is ensured weakly by the interface elements. These interface elements can be easily replaced by a cohesive element during the simulation, leading to an efficient fracture framework [4, 6]. We have recently extended this approach for linear shells [1] to obtain a full DG formulation of thin bodies, where discontinuities in the C0 and C1 fields are weakly enforced using consistent interface elements, and where the interface elements can be used to integrate the cohesive law when a fracture criterion is met. Moreover, a new cohesive law based on the reduced stresses of the thin bodies formulation is developed to propagate a fracture through the thickness. This cohesive model dissipates the right amount of energy during crack initiations and/or propagations. These developments are extended to non-linear elasto-plastic shells and are implemented in parallel, which allows to simulate complex fracture problems. As a validation example, the study of a blasted notched-cylinder is performed, for which experimental and numerical (by XFEM method) data are reported in the literature by [3]. Figure 1 illustrates the results obtained at different times. It can be seen that the simulation allows to model crack propagation, as well as the bifurcation happening when the crack reaches the top of the cylinder. Also, it appears that with the elasto-plastic framework, the crack speed numerically predicted matches the experimental measures [2]. [less ▲]

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See detailMulti-scale computational homogenization analysis of foams with micro-buckling
Nguyen, Van Dung ULg; Noels, Ludovic ULg

Conference (2012, July)

When studying the behavior of foams by multi-scale computational homogenization procedure, the micro-buckling may occur at the cell walls and edges and reduces the effective stiffness of the structures at ... [more ▼]

When studying the behavior of foams by multi-scale computational homogenization procedure, the micro-buckling may occur at the cell walls and edges and reduces the effective stiffness of the structures at macro-scale. This instability can be enhanced by plastic deformation at micro-scale. At sufficiently large value of macro-strain, even if the micro-tangent moduli of micro-material is still elliptic, the homogenized tangent moduli at macro-scale can lose its ellipticity that implies the localization occurs at macro-scale. When localization occurs, the characteristic size of macro- scopic 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. And the material behavior at given point depends also on the neighborhood of this point. To cover this problem, the second-order multi-scale computational homogenization is suitably used. At macroscopic problem, the high-order stress and the high-order strain are enhanced to the standard formulation by using the Discontinuous-Galerkin formulation while at the micro-scale, the standard continuum formulation is still used. By this procedure, the influence of micro-buckling of foams on structural behaviour is studied. [less ▲]

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See detailImposing periodic boundary condition on arbitrary meshes by polynomial interpolation
Nguyen, Van Dung ULg; Béchet, Eric ULg; Geuzaine, Christophe ULg et al

in Computational Materials Science (2012), 55

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with ... [more ▼]

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with appropriate boundary conditions, among which periodic boundary condition is the most efficient in terms of convergence rate. The classical method to impose the periodic boundary condition requires the identical meshes on opposite RVE boundaries. This condition is not always easy to satisfy for arbitrary meshes. This work develops a new method based on polynomial interpolation that avoids the need of matching mesh condition on opposite RVE boundaries. [less ▲]

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