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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 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)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: 52 (7 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: 134 (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: 90 (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: 100 (30 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: 88 (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: 57 (10 ULg)Modeling of damage to crack transition using a coupled discontinuous Galerkin/cohesive extrinsic law framework Wu, Ling ; ; Noels, Ludovic 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 ▲] Detailed reference viewed: 62 (5 ULg)A micro-meso-model of intra-laminar fracture in fiber-reinforced composites based on a Discontinuous Galerkin/Cohesive Zone Method Wu, Ling ; ; Becker, Gauthier 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 ▲] Detailed reference viewed: 152 (39 ULg)ON THE MODELING OF ADHESIVE CONTACT AND STICTION FAILURE IN MICRO-SWITCHES Wu, Ling ; Noels, Ludovic ; Golinval, Jean-Claude 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 ▲] Detailed reference viewed: 44 (8 ULg)Multi-scale modelling Noels, Ludovic ; ; Mulay, Shantanu Shashikant et al Scientific conference (2013, March 11) Detailed reference viewed: 39 (13 ULg)A Micro Model for Elasto-Plastic Adhesive-Contact in Micro-Switches: Application to cyclic loading Wu, Ling ; Golinval, Jean-Claude ; Noels, Ludovic 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 ▲] Detailed reference viewed: 101 (20 ULg)Non-local Damage-Enhanced MFH for Multiscale Simulations of Composites Wu, Ling ; Noels, Ludovic ; 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 ▲] Detailed reference viewed: 78 (19 ULg)Stiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts Wu, Ling ; Golinval, Jean-Claude ; Noels, Ludovic in Shaw, Gordon; Prorok, Bart; Starman, LaVern (Eds.) MEMS and Nanotechnology, Volume 6 (2013) Detailed reference viewed: 54 (9 ULg)Stiction failure in microswitches due to elasto-plastic adhesive contact and cyclic loading Wu, Ling ; Golinval, Jean-Claude ; Noels, Ludovic 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 ▲] Detailed reference viewed: 19 (1 ULg)A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models Wu, Ling ; Noels, Ludovic ; et al in Computer Methods in Applied Mechanics & Engineering (2012), 233-236 In this work, a gradient-enhanced 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 ... [more ▼] In this work, a gradient-enhanced 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). The macro-stress is then obtained from a homogenization procedure. The methodology holds for 2-phase composites with moderate fiber volume ratios, and for which, at the RVE size, the matrix can be considered as homogeneous isotropic and the ellipsoidal fibers can be considered as homogeneous transversely isotropic. Under these assumptions, the method is successfully applied to simulate the damage process occurring in unidirectional carbon-fiber reinforced epoxy composites submitted to different loading conditions. [less ▲] Detailed reference viewed: 141 (50 ULg)Multiscale Simulations of Composites with Non-Local Damage-Enhanced Mean-Field Homogenization Wu, Ling ; Noels, Ludovic ; 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 ▲] Detailed reference viewed: 54 (5 ULg) |
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