Homogenization of fibre reinforced composite with gradient enhanced damage model Wu, Ling ; Noels, Ludovic ; et al in Hogge, Michel; Van Keer, Roger; Dick, Erik (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November) Classical finite element simulations face the problems of losing uniqueness and strain localization when the strain softening of materials is involved. Thus, when using continuum damage model or ... [more ▼] Classical finite element simulations face the problems of losing uniqueness and strain localization when the strain softening of materials is involved. Thus, when using continuum damage model or plasticity softening model, numerical convergence will not be obtained with the refinement of the finite element discretization when strain localization occurs. Gradient-enhanced softening and non-local continua models have been proposed by several researchers in order to solve this problem. In such approaches, high-order spatial gradients of state variables are incorporated in the macroscopic constitutive equations. However, when dealing with complex heterogeneous materials, a direct simulation of the macroscopic structures is unreachable, motivating the development of non-local homogenization schemes. In this work, a non-local homogenization procedure is proposed for fiber reinforced materials. In this approach, the fiber is assumed to remain linear elastic while the matrix material is modeled as elasto-plastic coupled with a damage law described by a non-local constitutive model. Toward this end, the mean-field homogenization is based on the knowledge of the macroscopic deformation tensors, internal variables and their gradients, which are applied to a micro- structural representative volume element (RVE). Macro-stress is then obtained from a homogenization process. [less ▲] Detailed reference viewed: 75 (9 ULg)Influence of the elasto-plastic adhesive contact on Micro-Switches Wu, Ling ; Golinval, Jean-Claude ; Noels, Ludovic in Hogge, Michel; Van Keer, Roger; Dick, Erik (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November) Undesirable stiction, which results from contact between surfaces, is a major failure mode in micro,electro-mechanical systems (MEMS). In previous works, a statistical rough surfaces interaction,model ... [more ▼] Undesirable stiction, which results from contact between surfaces, is a major failure mode in micro,electro-mechanical systems (MEMS). In previous works, a statistical rough surfaces interaction,model, based on Maugis and Kim formulations has been presented to estimate the adhesive forces in MEMS switches. In this model, only elastic adhesive contact has been considered. However, during the impact between rough surfaces, at pull-in process for example, plastic deformations of the rough surfaces cannot be always neglected especially for the MEMS with metallic contact surfaces. In the present work, a new micro-model predicting the adhesive-contact force on a single elasticplastic asperity interacting with a rigid plane is presented. This model will be used later on for the interaction between two elastic-plastic rough surfaces. 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. [less ▲] Detailed reference viewed: 59 (5 ULg)A two-scale model predicting the mechanical sliding and opening behavior of grain boundaries in nanocrystalline solids Péron-Lührs, Vincent ; ; et al in Hogge, Michel; Van Keer, Roger; Dick, Erik (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November) In polycrystalline materials with nanosized grains smaller than 100 nm, the deformation mechanisms taking place at grain boundaries (GBs) become dominant compared to intragranular crystal plasticity ... [more ▼] In polycrystalline materials with nanosized grains smaller than 100 nm, the deformation mechanisms taking place at grain boundaries (GBs) become dominant compared to intragranular crystal plasticity. Recent studies have revealed that more accurate mechanical properties can be obtained by choosing the relevant GB character distribution (GBCD). We use here a numerical multiscale approach (an extension of a previous work [1]) to predict the mechanical behavior of nanostructured metals according to their GBCD composed of either high angle GBs (HAB) or low angle GBs (LAB). The quasicontinuum method (QC) is used to obtain the GB mechanical response at the nanoscale under simple shear (sliding part) and tensile load (opening part). These QC results are then used in a finite element code (direct numerical simulation-DNS) as GB constitutive models. This two-scale framework does not suffer from length scales limitations conventionally encountered when considering the two scales separately. [less ▲] Detailed reference viewed: 124 (30 ULg)Full discontinuous Galerkin formulation of shell in large deformations with fracture mechanic applications Becker, Gauthier ; Noels, Ludovic Different methods have been developed to model tearing prediction, as e.g., the combination between the cohesive principle and the finite element method. Unfortunately, this method has some well known ... [more ▼] Different methods have been developed to model tearing prediction, as e.g., the combination between the cohesive principle and the finite element method. Unfortunately, this method has some well known issues that can be fixed by recourse to discontinuous Galerkin formulation. Such a formulation allows to insert very easily an extrinsic cohesive element at onset of fracture without any mesh modification. This promising technique has been recently developed by the authors for linear shell. Although promising numerical results were obtained, it is difficult to compare the method with experiments due to the large plastic deformation present in material before the fracture apparition. Thus, the method is extent herein to elasto-plastic finite deformations. The simulations of some benchmarks prove the ability of this new framework to model accurately the continuum part of the deformation and the crack propagation. [less ▲] Detailed reference viewed: 79 (30 ULg)Vectorial Incremental Nonconservative Consistent Hysteresis model François-Lavet, Vincent ; ; Stainier, Laurent et al in Hogge, Michel; Van Keer, Roger; Malengier, Benny (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November) 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 ▲] Detailed reference viewed: 103 (14 ULg)Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) Hogge, Michel ; ; et al Book published by Université de Liège - Dépôt légal: D/2011/0480/31 (2011) Detailed reference viewed: 53 (7 ULg)Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation Nguyen, Van Dung ; Béchet, Eric ; Geuzaine, Christophe et al 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 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 the identical mesh condition on opposite RVE boundaries. [less ▲] Detailed reference viewed: 132 (64 ULg)A one Field Full Discontinuous Galerkin Method for Kirchhoff-Love Shells Applied to Fracture Mechanics Becker, Gauthier ; Geuzaine, Christophe ; Noels, Ludovic in Computer Methods in Applied Mechanics & Engineering (2011), 200(45-46), 3223-3241 In order to model fracture, the cohesive zone method can be coupled in a very efficient way with the Finite Element method. Nevertheless, there are some drawbacks with the classical insertion of cohesive ... [more ▼] In order to model fracture, the cohesive zone method can be coupled in a very efficient way with the Finite Element method. Nevertheless, there are some drawbacks with the classical insertion of cohesive elements. It is well known that, on one the hand, if these elements are present before fracture there is a modification of the structure stiffness, and that, on the other hand, their insertion during the simulation requires very complex implementation, especially with parallel codes. These drawbacks can be avoided by combining the cohesive method with the use of a discontinuous Galerkin formulation. In such a formulation, all the elements are discontinuous and the continuity is weakly ensured in a stable and consistent way by inserting extra terms on the boundary of elements. The recourse to interface elements allows to substitute them by cohesive elements at the onset of fracture. The purpose of this paper is to develop this formulation for Kirchhoff-Love plates and shells. It is achieved by the establishment of a full DG formulation of shell combined with a cohesive model, which is adapted to the special thickness discretization of shell formulation. In fact, this cohesive model is applied on resulting reduced stresses which are the basis of thin structures formulations. Finally, numerical examples demonstrate the efficiency of the method. [less ▲] Detailed reference viewed: 184 (66 ULg)Projects in Fracture Simulations Noels, Ludovic ; ; Wu, Ling et al Scientific conference (2011, September) Detailed reference viewed: 12 (7 ULg)A Micro-Macroapproach to Predict Stiction due to Surface Contact in Microelectromechanical Systems Wu, Ling ; Noels, Ludovic ; et al in IEEE/ASME Journal of Microelectromechanical Systems (2011), 20(4), 976-990 Stiction, which results from contact between surfaces, is a major failure mode in micro electro-mechanical systems (MEMS). Indeed microscopic structures tend to adhere to each other when their surfaces ... [more ▼] Stiction, which results from contact between surfaces, is a major failure mode in micro electro-mechanical systems (MEMS). Indeed microscopic structures tend to adhere to each other when their surfaces enter into contact and when the restoring forces are unable to overcome the interfacial forces. Since incidental contacts cannot be completely excluded and since contacts between moving parts can be part of the normal operation of some types of MEMS, stiction prediction is an important consideration when designing micro and nano-devices. In this paper a micro-macro multi-scale approach is developed in order to predict possible stiction. At the lower scale, the unloading adhesive contact-distance curves of two interacting rough surfaces are established based on a previously presented model [L. Wu et al., J. Appl. Phys. 106, 113502, 2009]. In this model, dry conditions are assumed and only the van der Waals forces as adhesion source are accounted for. The resulting unloading adhesive contact-distance curves are dependant on the material and on surface properties, such as, elastic modulus, surface energy and on the rough surfaces topography parameters; the standard deviation of asperity heights and the asperities density. At the higher scale, a finite element analysis is considered to determine the residual cantilever beam 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. Effects of design parameters can then be studied for given material and surface properties. [less ▲] Detailed reference viewed: 211 (94 ULg)Multi‐scale modelling of fibre reinforced composite with non‐local damage variable Wu, Ling ; Noels, Ludovic ; et al Conference (2011, July) Classical finite element simulations face the problems of losing uniqueness and strain localization when the strain softening of materials is involved. Thus, when using continuum damage model or ... [more ▼] Classical finite element simulations face the problems of losing uniqueness and strain localization when the strain softening of materials is involved. Thus, when using continuum damage model or plasticity softening model, numerical convergence will not be obtained with the refinement of the finite element discretization when strain localization occurs. Gradient-enhanced softening and non-local continua models have been proposed by several researchers in order to solve this problem. In such approaches, the spatial gradients of state variables are incorporated in the macroscopic constitutive equation [1, 2]. However, when dealing with complex heterogeneous materials, a direct simulation of the macroscopic structures is unreachable, motivating the development of non-local homogenization schemes [3]. In our work, a gradient-enhanced homogenization procedure is proposed for fiber reinforced materials. In the approach, the fiber is assumed to remain linear elastic while the matrix material is modeled as elasto-plastic [4] coupled with damage and is described by a non-local constitutive model [5]. Toward this end, the mean-field homogenization is based on the knowledge of the macroscopic deformation tensors, internal variables and their gradients, which are applied to a micro-structural representative volume element (RVE). Macro-stress is then obtained from a homogenization process. This procedure is applied to simulate damage process occurring in unidirectional carbon-fiber reinforced epoxy composites submitted to different loading histories. [less ▲] Detailed reference viewed: 62 (4 ULg)A shell fracture framework based on a full discontinuous Galerkin formulation combined with an extrinsic cohesive law Becker, Gauthier ; Noels, Ludovic Conference (2011, June 06) The cohesive method can be combined easily with Finite Element method to simulate a fracture problem which can contains fracture initiation and propagation. Nevertheless, the insertion of cohesive ... [more ▼] The cohesive method can be combined easily with Finite Element method to simulate a fracture problem which can contains fracture initiation and propagation. Nevertheless, the insertion of cohesive elements is not straightforward. Indeed, the two classical approaches suffer from severe limitations. On one hand, in the intrinsic approach, as the cohesive element is inserted at the beginning, this element has to model the continuum stage of deformation before fracture. This is ensured by an initial slope in the cohesive law which leads to a stiffness modification and to an alteration of propagation of wave. On the other hand, the introduction of the cohesive element during the simulation in extrinsic approach requests a dynamic modification of mesh. This operation is very difficult to implement especially in the case of a parallel implementation which is almost mandatory due to the very important number of degrees of freedom inherent to a fine mesh used to track the crack path. A solution to these limitations, pioneered by J. Mergheim and R. Radovitzky is to recourse to a discontinuous Galerkin formulation. Indeed this one used discontinuous test functions and integration at the interface of elements to discretize a structure with discontinuous elements. The integration on the boundary of elements allows ensuring weakly the continuity of displacements in a stable and consistent manner. As interface elements are present they can be easily substituted by cohesive elements when a fracture criterion is reached. The interest of the method has been recently proved by R. Radovitzky etal. for 3D elements and by the authors for Euler-Bernoulli beams. An extension of the formulation to Kirchhoff-Love shell is presented here. A novel extrinsic cohesive law is developed to model a through the thickness fracture. In fact, as in thin bodies formulation the thickness is not “discretized” this operation is not straightforward. Indeed, as the fracture occurs only in tension, in a pure bending case the position of neutral axis has to be move to propagate the fracture. To avoid this complicated step, it is suggested to integrate on the thickness the cohesive law which is then applies on resultant efforts. The coupling between the openings in displacement and rotation is performed in a way which guarantees a proper release of energy for any loading. Furthermore, the combination between fracture modes I and II is realized as suggested by M. Ortiz etal. Some numerical quasi-static and dynamic benchmarks are simulated to show the interest and the good performance of the presented framework. [less ▲] Detailed reference viewed: 19 (5 ULg)A fracture framework for Euler Bernoulli beams based on a full discontinuous Galerkin formulation/extrinsic cohesive law combination Becker, Gauthier ; Noels, Ludovic in International Journal for Numerical Methods in Engineering (2011), 85(10), 12271251 A new full Discontinuous Galerkin discretization of Euler Bernoulli beam is presented. The main interest of this framework is its ability to simulate fracture problems by inserting a cohesive zone model ... [more ▼] A new full Discontinuous Galerkin discretization of Euler Bernoulli beam is presented. The main interest of this framework is its ability to simulate fracture problems by inserting a cohesive zone model in the formulation. With a classical Continuous Galerkin method the use of the cohesive zone model is di cult because as insert a cohesive element between bulk elements is not straightforward. On one hand if the cohesive element is inserted at the beginning of the simulation there is a modification of the structure stiffness and on the other hand inserting the cohesive element during the simulation requires modification of the mesh during computation. These drawbacks are avoided with the presented formulation as the structure is discretized in a stable and consistent way with full discontinuous elements and inserting cohesive elements during the simulation becomes straightforward. A new cohesive law based on the resultant stresses (bending moment and membrane) of the thin structure discretization is also presented. This model allows propagating fracture while avoiding through-the-thickness integration of the cohesive law. Tests are performed to show that the proposed model releases, during the fracture process, an energy quantity equal to the fracture energy for any combination of tension-bending loadings. [less ▲] Detailed reference viewed: 183 (76 ULg)Finite Element Computation of Nonlinear Normal Modes Renson, Ludovic ; Deliège, Geoffrey ; Noels, Ludovic et al in Fifth International Conference on Advanced COmputational Methods in ENgineering (2011) Detailed reference viewed: 47 (8 ULg)Design of Microswitch Systems Avoiding Stiction due to Surface Contact Wu, Ling ; Noels, Ludovic ; et al in Proulx, Tom (Ed.) MEMS and Nanotechnology, Volume 2 (2011) Stiction which results from contact between surfaces is a major failure mode in micro electro-mechanical systems (MEMS). Increasing restoring forces using high spring constant allows avoiding stiction but ... [more ▼] Stiction which results from contact between surfaces is a major failure mode in micro electro-mechanical systems (MEMS). Increasing restoring forces using high spring constant allows avoiding stiction but leads to an increase of the actuation voltage so that the switch’s efficiency is threatened. A statistical rough surfaces interaction model, based on Maugis’ and Kim’s formulations is applied to estimate the adhesive forces in MEMS switches. Based on the knowledge of these forces, the proper design range of the equivalent spring constant, which is the main factor of restoring force in MEMS switches, can be determined. The upper limit of equivalent spring constant depends mainly on the expected actuator voltage and on the geometric parameters, such as initial gap size and thickness of dielectric layer. The lower limit is assessed on the value of adhesive forces between the two contacting rough surfaces. It mainly depends on the adhesive work of contact surfaces and on the surfaces’ roughness. In order to study more complicated structures, this framework will be used in a multiscale model: resulting unloading micro adhesive contact-distance curves of two rough surfaces will be used as contact forces in a finite-element model. In this paper the extraction of these curves for the particular case of gold to gold micro-switches is pursued. [less ▲] Detailed reference viewed: 94 (24 ULg)A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, Cohesive Element Method ; ; et al in Computer Methods in Applied Mechanics & Engineering (2011), 200(1-4), 326-344 A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discon- tinuous Galerkin (DG) formulation of the ... [more ▼] A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discon- tinuous Galerkin (DG) formulation of the continuum problem and Cohesive Zone Models (CZM) of fracture. Prior to fracture, the flux and stabilization terms aris- ing from the DG formulation at interelement boundaries are enforced via interface elements, much like in the conventional intrinsic cohesive element approach, albeit in a way that guarantees consistency and stability. Upon the onset of fracture, the traction-separation law (TSL) governing the fracture process becomes operative without the need to insert a new cohesive element. Upon crack closure, the rein- statement of the DG terms guarantee the proper description of compressive waves across closed crack surfaces. The main advantage of the method is that it avoids the need to propagate topo- logical changes in the mesh as cracks and fragments develop, which enables the indistinctive treatment of crack propagation across processor boundaries and, thus, the scalability in parallel computations. Another advantage of the method is that it preserves consistency and stability in the uncracked interfaces, thus avoiding issues with wave propagation typical of intrinsic cohesive element approaches. A simple problem of wave propagation in a bar leading to spall at its center is used to show that the method does not affect wave characteristics and as a consequence properly captures the spall process. We also demonstrate the ability of the method to capture intricate patterns of radial and conical cracks arising in the impact of ceramic plates which propagate in the mesh impassive to the presence of processor boundaries. [less ▲] Detailed reference viewed: 302 (66 ULg)Proceedings of the Fourth International Conference on Advanced Computational Methods in Engineering (ACOMEN 2008) Hogge, Michel ; ; et al in Journal of Computational & Applied Mathematics (2010), 234(7), Detailed reference viewed: 77 (31 ULg)A Full Discontinuous Galerkin Formulation Of Euler Bernoulli Beams In Linear Elasticity With Fractured Mechanic Applications Becker, Gauthier ; Noels, Ludovic Conference (2010, July 21) A full discontinuous Galerkin method is used to predict the fracture of beams thanks to insertion of an extrinsic cohesive element. In fact, The formulation developed originally by G. Wells etal. to ... [more ▼] A full discontinuous Galerkin method is used to predict the fracture of beams thanks to insertion of an extrinsic cohesive element. In fact, The formulation developed originally by G. Wells etal. to guarantee weakly the high order derivatives of plates with only displacement field unknown and extended by L. Noels etal. for shells is derived for beam with full discontinuous elements. This new formulation can be advantageously combined, as shown first by J. Mergheim etal. , with an extrinsic cohesive approach as there is no need to modify dynamically the mesh, which is the major drawback of this approach. The pre-fractured stage is modeled by full discontinuous elements in a manner which is proved stable and consistent and the fracture is modeled by a cohesive law applied on stress resultant an stress couple defined by J.C. Simo etal. The suggested study produces two type of results. On one hand, it is shown analytically and verified by numerical examples that the presented framework has got the properties of consistency and convergence expected for a numerical scheme. On the other hand, it is proved by some test cases that the energy released during fracture process is equal to the fracture energy except in the case where the difference of internal energy between not fractured and fractured configurations is bigger than the fracture energy. In this case, the fracture occurs in one time step. The presented work proposed a novel interesting manner to take into account fracture in thin bodies. The verification made on the particularized case of beams suggested great perspectives for plates and shells which allow to simulate more complex problems. [less ▲] Detailed reference viewed: 49 (8 ULg)Application of discontinuous Galerkin methods to shells and fracture of thin structures Noels, Ludovic Scientific conference (2010, January) Detailed reference viewed: 1 (0 ULg)Prediction of Stiction in Microswitch Systems Wu, Ling ; Rochus, Véronique ; Noels, Ludovic et al in EUROSIME 2010 (2010) Stiction is a major failure mode of MEMS as microscopic structures tend to adhere to each other when their surfaces enter into contact. Although increasing the restoring forces of switch devices could ... [more ▼] Stiction is a major failure mode of MEMS as microscopic structures tend to adhere to each other when their surfaces enter into contact. Although increasing the restoring forces of switch devices could overcome the stiction effect, this is not practical, as in turn, it also increases the actuation voltage. Therefore stiction prediction is important to be considered when designing micro- and nano- devices. In this paper, the numerical prediction of stiction for capacitive MEMS switches is considered. Toward this end, a micro-adhesive-contact law is derived from previous work and combined with a finite-element model. [less ▲] Detailed reference viewed: 134 (34 ULg) |
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