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Muti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling Wu, Ling ; Nguyen, Van Dung ; 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 ▲] Detailed reference viewed: 57 (18 ULg)Prediction of macroscopic mechanical properties of a polycrystalline microbeam subjected to material uncertainties Lucas, Vincent ; Wu, Ling ; Arnst, Maarten et al in Cunha, Álvaro; Caetano, Elsa; Ribeiro, Pedro (Eds.) et al Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 (2014, June) The first resonance frequency is a key performance characteristic of MEMS vibrometers. In batch fabrication, this first resonance frequency can exhibit scatter owing to various sources of manufacturing ... [more ▼] The first resonance frequency is a key performance characteristic of MEMS vibrometers. In batch fabrication, this first resonance frequency can exhibit scatter owing to various sources of manufacturing variability involved in the fabrication process. The aim of this work is to develop a stochastic multiscale model for predicting the first resonance frequency of MEMS microbeams constituted of polycrystals while accounting for the uncertainties in the microstructure due to the grain orientations. At the finest scale, we model the microstructure of polycrystaline materials using a random Voronoï tessellation, each grain being assigned a random orientation. Then, we apply a computational homogenization procedure on statistical volume elements to obtain a stochastic characterization of the elasticity tensor at the second scale of interest, the meso-scale. In the future, using a stochastic finite element method, we will propagate these meso-scale uncertainties to the first resonance frequency at the coarser scale. [less ▲] Detailed reference viewed: 117 (45 ULg)Computational homogenization of cellular materials Nguyen, Van Dung ; Noels, Ludovic 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 ▲] Detailed reference viewed: 266 (149 ULg)Muti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling Wu, Ling ; Nguyen, Van Dung ; 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 ▲] Detailed reference viewed: 84 (13 ULg)Muti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling Noels, Ludovic ; Nguyen, Van Dung ; Wu, Ling 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 ▲] Detailed reference viewed: 61 (5 ULg)Quasicontinuum study of the shear behavior of defective tilt grain boundaries in Cu Péron-Lührs, Vincent ; ; Noels, Ludovic 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 ▲] Detailed reference viewed: 120 (31 ULg)Homogenization with propagation of instabilities through the different scales Noels, Ludovic ; Wu, Ling ; Nguyen, Van Dung 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 ▲] Detailed reference viewed: 51 (6 ULg)A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites Wu, Ling ; Noels, Ludovic ; 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 ▲] Detailed reference viewed: 133 (65 ULg)Probabilistic model for MEMS micro-beam resonance frequency made of polycrystalline linear anisotropic material Lucas, Vincent ; Wu, Ling ; Arnst, Maarten 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 ▲] Detailed reference viewed: 103 (33 ULg)A micro-meso model to predict van der Walls and capillary induced stiction in micro-structures Hoang Truong, Vinh ; Noels, Ludovic ; Wu, Ling 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 ▲] Detailed reference viewed: 89 (30 ULg)Non-Local Incremental-Secant Mean-Field-Homogenization of Damage-Enhanced Elasto-Plastic Composites Wu, Ling ; Noels, Ludovic ; 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 ▲] Detailed reference viewed: 39 (3 ULg)An implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage Wu, Ling ; Noels, Ludovic ; 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 ▲] Detailed reference viewed: 99 (30 ULg)Multi-scale studies of foamed materials Nguyen, Van Dung ; Noels, Ludovic 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 ▲] Detailed reference viewed: 53 (16 ULg)A two-scale model predicting the mechanical behavior of nanocrystalline solids Péron-Lührs, Vincent ; ; 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 ▲] Detailed reference viewed: 125 (30 ULg)Fifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) Béchet, Eric ; ; Geuzaine, Christophe et al in International Journal of Computational & Applied Mathematics (2013), 246 Detailed reference viewed: 167 (37 ULg)An Energy-Based Variational Model of Ferromagnetic Hysteresis for Finite Element Computations François-Lavet, Vincent ; ; Stainier, Laurent 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 ▲] Detailed reference viewed: 268 (48 ULg)Multiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous Galerkin formulation Nguyen, Van Dung ; Becker, Gauthier ; Noels, Ludovic 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 ▲] Detailed reference viewed: 295 (135 ULg)A micro-model of the intra-laminar fracture in fiber-reinforced composites based on a discontinuous Galerkin/extrinsic cohesive law method Wu, Ling ; ; 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 ▲] Detailed reference viewed: 85 (4 ULg)Non-local multiscale analyzes of composite laminates based on a damage-enhanced mean–field homogenization formulation Wu, Ling ; Noels, Ludovic ; 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 ▲] Detailed reference viewed: 53 (2 ULg)An incremental-secant mean-field homogenization scheme for elasto-plastic and damage-enhanced elasto-plastic composite materials Wu, Ling ; Noels, Ludovic ; 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 ▲] Detailed reference viewed: 56 (10 ULg) |
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