References of "Noels, Ludovic"
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See detailA coupled electro-thermal Discontinuous Galerkin method
Homsi, Lina ULg; Geuzaine, Christophe ULg; Noels, Ludovic ULg

in Journal of Computational Physics (in press)

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental ... [more ▼]

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H1-norm and in the L2-norm are shown to be optimal in the mesh size with the polynomial approximation degree. [less ▲]

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See detailAn incremental-secant mean-field homogenization method with second statistical moments for elasto-visco-plastic composite materials
Wu, Ling ULg; Adam, Laurent; Doghri, Issam et al

in Mechanics of Materials (in press)

This paper presents an extension of the recently developed incremental-secant mean-field homogenization (MFH) procedure in the context of elasto-plasticity to elasto-visco-plastic composite materials ... [more ▼]

This paper presents an extension of the recently developed incremental-secant mean-field homogenization (MFH) procedure in the context of elasto-plasticity to elasto-visco-plastic composite materials while accounting for second statistical moments. In the incrementalsecant formulation, a virtual elastic unloading is performed at the composite level in order to evaluate the residual stress and strain states in the different phases, from which a secant MFH formulation is applied. When applying the secant MFH process, the Linear-Comparison-Composite is built from the piece-wise heterogeneous residual strain-stress state using naturally isotropic secant tensors defined using either first or second statistical moment values. As a result non-proportional and non-radial loading conditions can be considered because of the incremental-secant formulation, and accurate predictions can be obtained as no isotropization step is required. The limitation of the incremental-secant formulation previously developed was the requirement in case of hard inclusions to cancel the residual stress in the matrix phase, resulting from the composite material unloading, to avoid over-stiff predictions. It is shown in this paper that in the case of hard inclusions by defining a proper second statistical moment estimate of the von Mises stress, the residual stress can be kept in the different composite phases. Moreover it is shown that the method can be extended to visco-plastic behaviors without modifying the homogenization process as the incremental-secant formulation only requires the definition of the secant operator of the different phase material models. Finally, it is shown that although it is also possible to define a proper second statistical moment estimate of the von Mises stress in the case of soft inclusions, this does not improve the accuracy as compared to the increment-secant method with first order statistical moment estimates. [less ▲]

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See detailA damage to crack transition model accounting for stress triaxiality formulated in a hybrid non-local implicit discontinuous Galerkin - cohesive band model framework
Leclerc, Julien ULg; Wu, Ling ULg; Nguyen, Van Dung ULg et al

in International Journal for Numerical Methods in Engineering (in press)

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent ... [more ▼]

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect. In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a non-local elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality-dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D-state, mandatory to incorporate the in-plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction-separation law is then built from the underlying damage model. [less ▲]

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See detailPropagation of material and surface profile uncertainties on MEMS micro-resonators using a stochastic second-order computational multi-scale approach
Lucas, Vincent ULg; Golinval, Jean-Claude ULg; Voicu, Rodica et al

in International Journal for Numerical Methods in Engineering (2017), 111(1), 26-68

This paper aims at accounting for the uncertainties due to material structure and surface topology of microbeams in a stochastic multiscale model. For micro-resonators made of anisotropic polycrystalline ... [more ▼]

This paper aims at accounting for the uncertainties due to material structure and surface topology of microbeams in a stochastic multiscale model. For micro-resonators made of anisotropic polycrystalline materials, micro-scale uncertainties are due to the grain size, grain orientation, and to the surface profile. First, microscale realizations of stochastic volume elements (SVEs) are obtained based on experimental measurements. To account for the surface roughness, the SVEs are defined as a volume element having the same thickness as the MEMS, with a view to the use of a plate model at the structural scale. The uncertainties are then propagated up to an intermediate scale, the meso-scale, through a second-order homogenization procedure.From the meso-scale plate resultant material property realizations, a spatially correlated random field of the in plane, out of plane, and cross resultant material tensors can be characterized. Owing to this characterized random field, realizations of MEMS-scale problems can be defined on a plate finite element model. Samples of the macro-scale quantity of interest can then be computed by relying on a Monte-Carlo simulation procedure. As a case study, the resonance frequency of MEMS micro-beams is investigated for different uncertainty cases, such as grain preferred orientations and surface roughness effects. [less ▲]

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See detailCohesive Band Model: a triaxiality-dependent cohesive model inside an implicit non-local damage to crack transition framework
Leclerc, Julien ULg; Wu, Ling ULg; Nguyen, Van Dung ULg et al

Conference (2017, June 14)

Accurate numerical prediction of the whole ductile failure process is still a challenge. The adequate numerical scheme has to concord with the physical reality composed of an initial diffuse damage step ... [more ▼]

Accurate numerical prediction of the whole ductile failure process is still a challenge. The adequate numerical scheme has to concord with the physical reality composed of an initial diffuse damage step followed by ultimate localised crack initiation and propagation. Currently, two main modelling philosophies exist. On the one hand, continuous approaches, described by damage models, are suited for diffuse damage, but are unable to represent physical discontinuities. On the other hand, discontinuous approaches are suitable to describe crack propagation behaviour and other localised processes, but fail in diffuse damage prediction of ductile materials. Moreover, they do not usually capture triaxiality effects or in other words, in-plane stretch effects, which are mandatory for accurate ductile failure simulations. To describe the ductile failure process, the numerical scheme proposed here combines both approaches and by this way, their respective advantages: an implicit non-local damage model combined with an extrinsic cohesive law in a discontinuous Galerkin finite element framework [1]. An application example of this scheme is shown on the attached figure with a comparison of the experimental force-displacement curve [2]. An implicit non-local model [3] is involved to model the initial diffuse damage stage. Upon damage to crack transition, a cohesive band [4] is used as cohesive law in order to introduce in-plane stretch effects during the crack propagation. This model is based on the assumption that all the damaging process occurs inside a band of small but finite thickness ahead of the crack surface. The strains inside this band is obtained from the neighbouring strains and from the cohesive jump. Then, the stress-state inside the band and the cohesive traction forces on the crack lips are deduced from the underlying continuum damage model. The band thickness is not a new material parameter but it is computed to ensure the energetic consistency of the numerical scheme [5]. [1] Wu L, Becker G, Noels L. Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Comput. Methods Appl. Mech. Eng. 279 (2014): 379–409 [2] Geers M., de Borst R., Brekelmans W., Peerlings R. Validation and internal length scale determination for a gradient damage model: application to short glass-fibre-reinforced polypropylene. Int. J. of Sol. and Struct. 36 (1999): 2557‑2583. [3] Peerlings R., de Borst R., Brekelmans W., Ayyapureddi S. Gradient-enhanced damage for quasi-brittle materials, Int. J. for Num. Methods in Eng. 39 (1996): 3391-3403 [4] Remmers J. J. C., de Borst R., Verhoosel C. V., Needleman A. The cohesive band model: a cohesive surface formulation with stress triaxiality. Int. J. Fract. 181 (2013): 177–18 [5] Leclerc J., Wu L., Nguyen V.D., Noels L. Cohesive band model: a cohesive model with triaxiality for crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Int. J. for Num. Methods in Eng. (2017): In preparation. [less ▲]

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See detailStochastic multiscale method applied to thermo-elasticity of polycrystalline micro-structures
Wu, Ling ULg; Lucas, Vincent; Golinval, Jean-Claude ULg et al

Conference (2017, June 05)

A stochastic 3-scale approach is developed in order to predict the probabilistic behavior of micro-resonators made of polycrystalline materials. In this method, stochastic volume elements (SVEs) [1] are ... [more ▼]

A stochastic 3-scale approach is developed in order to predict the probabilistic behavior of micro-resonators made of polycrystalline materials. In this method, stochastic volume elements (SVEs) [1] are defined from Voronoï tessellations using experimental measurements of the grain size, orientation, and surface roughness [2]. For each SVE realization, the mesoscopic apparent thermo-elastic properties such as elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor are extracted using a coupled homogenization theory [3, 4]. A stochastic model is then built from the homogenized properties extracted from Voronoï tessellations using a moving window technique in order to generate spatially correlated meso-scale random fields. These random fields are then used as input for stochastic finite element simulations. As a result, the probabilistic distribution of micro-resonator properties can be extracted. The applications are two-fold: either a stochastic thermo-elastic homogenization is coupled to thermo-elastic 3D models of the micro-resonator in order to extract the probabilistic distribution of the Quality factor of the micro-resonators [5], or a stochastic second-order mechanical homogenization is coupled to a plate model of the micro-resonator in order to extract the effect of the uncertainties related to the surface roughness of the polycrystalline structures [1]. References [1] Lucas, V., Golinval, J.-C., Voicu, R., Danila, M., Gravila, R., Muller, R., Dinescu, A., Noels, L., & Wu, L. (in press). Propagation of material and surface profile uncertainties on MEMS micro-resonators using a stochastic second-order computational multi-scale approach. International Journal for Numerical Methods in Engineering. [2] Ostoja-Starzewski, M., Wang, X. (1999) Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering, 168, 35-49, 1999 [3] Temizer, I., Wriggers, P. (2011) Homogenization in finite thermoelasticity, Journal of the Mechanics and Physics of Solids 59 (2), 344-372 [4] Nguyen, V. D., Wu, L., Noels, L. (in press). Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method. Computational Mechanics. [5] Wu, L., Lucas, V., Nguyen, V. D., Golinval, J.-C., Paquay, S., & Noels, L. (2016) A Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators. Computer Methods in Applied Mechanics & Engineering, 310, 802-839. [less ▲]

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See detailA computational stochastic multiscale methodology for MEMS structures involving adhesive contact
Hoang Truong, Vinh ULg; Wu, Ling ULg; Paquay, Stéphane et al

in Tribology International (2017), 110

This work aims at developing a computational stochastic multiscale methodology to quantify the uncertainties of the adhesive contact problems due to capillary effects and van der Waals forces in MEMS ... [more ▼]

This work aims at developing a computational stochastic multiscale methodology to quantify the uncertainties of the adhesive contact problems due to capillary effects and van der Waals forces in MEMS. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the involved structural behaviors suffer from a scatter. To numerically predict the probabilistic behaviors of structures involving adhesion, the proposed method introduces stochastic meso-scale random apparent contact forces which can be integrated into a stochastic finite element model. Because the evaluation of their realizations is expensive, a generator for the random apparent contact force using the polynomial chaos expansion is constructed in an efficient way. [less ▲]

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See detailUnified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method
Nguyen, Van Dung ULg; Wu, Ling ULg; Noels, Ludovic ULg

in Computational Mechanics (2017), 59(3), 483-505

This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems ... [more ▼]

This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time. [less ▲]

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See detailA Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
Hoang Truong, Vinh ULg; Wu, Ling ULg; Paquay, Stéphane et al

in Starman, La Vern; Hay, Jennifer; Karanjgaokar, Nikhil (Eds.) Micro and Nanomechanics, Volume 5: Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics (2017)

Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on ... [more ▼]

Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the adhesive forces cannot be determined in a deterministic way. To quantify the uncertainties on the structural stiction behavior of a MEMS, this work proposes a “stochastic multi-scale methodology”. The key ingredient of the method is the evaluation of the random meso-scale apparent contact forces, which homogenize the effect of the nano-scale roughness and are integrated into a numerical model of the studied structure as a random contact law. To obtain the probabilistic behavior at the structural MEMS scale, a direct method needs to evaluate explicitly the meso-scale apparent contact forces in a concurrent way with the stochastic multi-scale approach. To reduce the computational cost, a stochastic model is constructed to generate the random meso-scale apparent contact forces. To this end, the apparent contact forces are parameterized by a vector of parameters before applying a polynomial chaos expansion in order to construct a mathematical model representing the probability of the random parameters vector. The problem of micro-beam stiction is then studied in a probabilistic way. [less ▲]

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See detailChapter 6: Effective Properties
Noels, Ludovic ULg; Wu, Ling ULg; Adam, Laurent et al

in Ulrich, Prahl; Schmitz, Georg J. (Eds.) Handbook of Software Solutions for ICME (2016)

As one of the results of an ambitious project, this handbook provides a well-structured directory of globally available software tools in the area of Integrated Computational Materials Engineering (ICME ... [more ▼]

As one of the results of an ambitious project, this handbook provides a well-structured directory of globally available software tools in the area of Integrated Computational Materials Engineering (ICME). The compilation covers models, software tools, and numerical methods allowing describing electronic, atomistic, and mesoscopic phenomena, which in their combination determine the microstructure and the properties of materials. It reaches out to simulations of component manufacture comprising primary shaping, forming, joining, coating, heat treatment, and machining processes. Models and tools addressing the in-service behavior like fatigue, corrosion, and eventually recycling complete the compilation. An introductory overview is provided for each of these different modelling areas highlighting the relevant phenomena and also discussing the current state for the different simulation approaches. A must-have for researchers, application engineers, and simulation software providers seeking a holistic overview about the current state of the art in a huge variety of modelling topics. This handbook equally serves as a reference manual for academic and commercial software developers and providers, for industrial users of simulation software, and for decision makers seeking to optimize their production by simulations. In view of its sound introductions into the different fields of materials physics, materials chemistry, materials engineering and materials processing it also serves as a tutorial for students in the emerging discipline of ICME, which requires a broad view on things and at least a basic education in adjacent fields. [less ▲]

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See detailA Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators
Wu, Ling ULg; Lucas, Vincent ULg; Nguyen, Van Dung ULg et al

in Computer Methods in Applied Mechanics & Engineering (2016), 310

The aim of this work is to study the thermo-elastic quality factor (Q) of micro-resonators with a stochastic multi-scale approach. In the design of high-Q micro-resonators, thermo-elastic damping is one ... [more ▼]

The aim of this work is to study the thermo-elastic quality factor (Q) of micro-resonators with a stochastic multi-scale approach. In the design of high-Q micro-resonators, thermo-elastic damping is one of the major dissipation mechanisms, which may have detrimental effects on the quality factor, and has to be predicted accurately. Since material uncertainties are inherent to and unavoidable in micro-electromechanical systems (MEMS), the effects of those variations have to be considered in the modeling in order to ensure the required MEMS performance. To this end, a coupled thermo-mechanical stochastic multi-scale approach is developed in this paper. Thermo-mechanical micro-models of polycrystalline materials are used to represent micro-structure realizations. A computational homogenization procedure is then applied on these statistical volume elements to obtain the stochastic characterizations of the elasticity tensor, thermal expansion, and conductivity tensors at the meso-scale. Spatially correlated meso-scale random fields can thus be generated to represent the stochastic behavior of the homogenized material properties. Finally, the distribution of the thermo-elastic quality factor of MEMS resonators is studied through a stochastic finite element method using as input the generated stochastic random field. [less ▲]

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See detailA large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers
Nguyen, Van Dung ULg; Lani, Frédéric; Pardoen, Thomas et al

in International Journal of Solids and Structures (2016), 96

A large strain hyperelastic phenomenological constitutive model is proposed to model the highly nonlinear, rate-dependent mechanical behavior of amorphous glassy polymers under isothermal conditions. A ... [more ▼]

A large strain hyperelastic phenomenological constitutive model is proposed to model the highly nonlinear, rate-dependent mechanical behavior of amorphous glassy polymers under isothermal conditions. A corotational formulation is used through the total Lagrange formalism. At small strains, the viscoelastic behavior is captured using the generalized Maxwell model. At large strains beyond a viscoelastic limit characterized by a pressure-sensitive yield function, which is extended from the Drucker-Prager one, a viscoplastic region follows. The viscoplastic flow is governed by a non-associated Perzyna-type flow rule incorporating this pressure-sensitive yield function and a quadratic flow potential in order to capture the volumetric deformation during the plastic process. The stress reduction phenomena arising from the post-peak plateau and during the failure stage are considered in the context of a continuum damage mechanics approach. The post-peak softening is modeled by an internal scalar, so-called softening variable, whose evolution is governed by a saturation law. When the softening variable is saturated, the rehardening stage is naturally obtained since the isotropic and kinematic hardening phenomena are still developing. Beyond the onset of failure characterized by a pressure-sensitive failure criterion, the damage process leading to the total failure is controlled by a second internal scalar, so-called failure variable. The final failure occurs when the failure variable reaches its critical value. To avoid the loss of solution uniqueness when dealing with the continuum damage mechanics formalism, a non-local implicit gradient formulation is used for both the softening and failure variables, leading to a multi-mechanism non-local damage continuum. The pressure sensitivity considered in both the yield and failure conditions allows for the distinction under compression and tension loading conditions. It is shown through experimental comparisons that the proposed constitutive model has the ability to capture the complex behavior of amorphous glassy polymers, including their failure. [less ▲]

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See detailUnified treatment of microscopic boundary conditions in computational homogenization method for multiphysics problems
Nguyen, Van Dung ULg; Wu, Ling ULg; Homsi, Lina ULg et al

Conference (2016, September 08)

Computational homogenization (so-called FE2) method is an effective tool to model complex behavior of heterogeneous media allowing direct coupling between the structure response and the evolving ... [more ▼]

Computational homogenization (so-called FE2) method is an effective tool to model complex behavior of heterogeneous media allowing direct coupling between the structure response and the evolving microstructure not only in purely mechanical problems but also in multiphysics problems [1]. The basic idea of this method is to obtain the macroscopic constitutive relationships from the resolution of the microscopic boundary value problem (BVP) defined on a representative volume element. This method does not requires any constitutive assumption at the macroscopic level, but an appropriate microscopic boundary condition has to be defined. Our work focuses on the unified treatment of the microscopic boundary condition in a multiphysics microscopic BVP. In particular, an efficient way to compute the tangent operator is developed for an arbitrary kind of boundary conditions. When considering the FE2method, the homogenized stresses and homogenized tangents at every macroscopic integration points are required. From the energy consistency condition between macroscopic and microscopic problems, the homogenized stresses can be easily computed by the volumetric averaging integrals of the microscopic counterparts. The required homogenized tangents often follows a stiffness condensation from the microscopic stiffness matrix at the equilibrium state [2]. When using the stiffness condensation, the microscopic stiffness matrix needs to be partitioned, and dense matrices based on Schur complements (under a matrix form 𝐊̃ 𝑏𝑏=𝐊𝑏𝑏−𝐊𝑏𝑖𝐊𝑖𝑖−1𝐊𝑖𝑏) have to be estimated. The matrix operations based on Schur complements require a large time consuming and a lot of memory when increasing the number of degrees of freedom of the microscopic BVPs. This work proposes an efficient method allowing to compute the homogenized tangents without significant effort. The microscopic stiffness matrix does not need to be partitioned. The homogenized tangents are computed by solving a linear system, which is based on the linearized system at the converge solution of the microscopic BVP, with multiple right hand sides. With proposed numerical improvements, the FE2 method is used in a fully thermo-mechanically-coupled simulation. The temperature-dependent elastoplastic behavior, thermal conduction as well as the heat conversion from the mechanical deformation are considered in the hyperelastic large strain framework. [1]. Geers, M. G. D., Kouznetsova, V. G., Brekelmans, W. A. M., 2010. J. Comput. Appl. Math. 234 (7), 2175-2182. [2]. Kouznetsova, V., Brekelmans, W. A. M., Baaijens, F. P. T., 2001. Comput. Mech. 27 (1), 37-48. [less ▲]

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See detailProbabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach
Wu, Ling ULg; Lucas, Vincent ULg; Golinval, Jean-Claude ULg et al

Conference (2016, September 07)

As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical ... [more ▼]

As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical systems (MEMS) made of poly-crystalline materials exhibit a scatter, due to the existing randomness in the grain size, grain orientation, surface roughness... In order to predict the probabilistic behavior of micro-resonators, the authors extend herein a previously developed stochastic 3-scale approach [1] to the case of thermoelastic damping [2]. In this method, stochastic volume elements (SVEs) [3] are defined by considering random grain orientations in a tessellation. For each SVE realization, the mesoscopic apparent elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor can be obtained using thermo-mechanical computational homogenization theory [4]. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated meso-scale random field, which is in turn used as input for stochastic finite element simulations. As a result, the probabilistic distribution of the quality factor of micro-resonator can be extracted by considering Monte-Carlo simulations of coarse-meshed micro-resonators, accounting implicitly for the random micro-structure of the poly-silicon material. [1] V. Lucas, J.-C. Golinval, S. Paquay, V.-D. Nguyen, L. Noels, L. Wu, A stochastic computational multiscale approach; Application to MEMS resonators. Computer Methods in Applied Mechanics and Engineering, 294, 141-167, 2015. [2] L. Wu, V. Lucas, V.-D. Nguyen, J.-C. Golinval, S. Paquay, L. Noels, A Stochastic Multiscale Approach for the Modeling of Thermoelastic Damping in Micro-Resonators. Submitted. [3] M. Ostoja-Starzewski, X.Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering, 168, 35--49, 1999. [4] I. Özdemir, W. A. M. Brekelmans, M. G. D. Geers, Computational homogenization for heat conduction in heterogeneous solids, International Journal for Numerical Methods in Engineering 73, 185-204, 2008. [less ▲]

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See detailA coupled electro-thermo-mechanical discontinuous Galerkin method applied on composite materials
Homsi, Lina ULg; Noels, Ludovic ULg

Conference (2016, September 07)

Carbon fiber reinforced polymer composites have become increasingly important due to their unique properties which are appreciated in many practical applications such as low weight, low cost, low density ... [more ▼]

Carbon fiber reinforced polymer composites have become increasingly important due to their unique properties which are appreciated in many practical applications such as low weight, low cost, low density, high mechanical characteristics. Moreover the range of their electrical conductivity can be controlled by the amount of carbon fibers. Carbon fiber reinforced polymer composites consist of at least two components, a polymer matrix (generally dielectric) and electrically conductive fillers. This combination results in multifunctional composites, both structural and conductive. The existence of the polymer matrix will avoid catastrophic failure due to fiber breaking, and the existence of the carbon fibers will enhance strength and stiffness on one hand, and will allow to a significant temperature gradient when electric current is applied on the other hand. The objective of this paper is to study the response of the carbon fiber reinforced polymer composites when an electric power is applied and to determine the effective properties. To this end governing equations describing electro-thermo-mechanical coupling in composite materials are developed and discretized using the Discontinuous Galerkin (DG) finite element method. DG methods have many advantages such as optimal convergence and local approximation properties in addition to their flexibility for mesh adaption and their straightforward use of high order polynomial approximations. A micromechanical model of unidirectional carbon fibers dispersed in a polymer matrix is formulated considering the interaction of electrical, thermal and mechanical fields It is then solved using the DG method to determine the time dependent response of the electro-thermo-mechanical coupling and quantify the variation of the fields. [less ▲]

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See detailSimulations of composite laminates inter and intra-laminar failure using on a non-local mean-field damage-enhanced multi-scale method
Wu, Ling ULg; Adam, Laurent; Bidaine, Benoît et al

Conference (2016, September 07)

The failure of carbon fiber reinforced composite laminates is studied using a multiscale method. A non-local mean-field homogenization (MFH) method accounting for the damage evolution of the matrix phase ... [more ▼]

The failure of carbon fiber reinforced composite laminates is studied using a multiscale method. A non-local mean-field homogenization (MFH) method accounting for the damage evolution of the matrix phase of the composite material [1] is considered in each ply in order to capture the intra-laminar failure. In that formulation, an incremental-secant MFH approach is used to account for the elastic unloading of the fibers during the strain softening of the matrix. In order to avoid the strain/damage localization caused by the matrix material softening, the damage enhanced MFH was formulated in an implicit non-local way [2]. Accurate predictions of the composite softening behavior and of the different phases response is then achieved. The delamination process is modeled by recourse to a hybrid discontinuous Galerkin (DG)/ extrinsic cohesive law approach. An open-hole composite laminate with a quasi-isotropic sequence ([90/45/-45/90/0]S) is then studied experimentally and using the multiscale method [3]. The numerical model is found to predict the damage bands along the fiber directions in agreement with the experimental samples inspected by X-ray computed tomography (XCT). Moreover, the predicted delamination pattern is found to match the experimental observations. Finally, with a view to stochastic analysis, the effect of the volume fraction and orientation variations on the failure is studied by defining them as random variables. REFERENCES [1] L. Wu, L. Noels, L. Adam, I. Doghri, An implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage, International Journal of Solids and Structures, 50, 3843-3860, 2013. [2] R. Peerlings, R. de Borst, W. Brekelmans, S. Ayyapureddi, Gradient-enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering, 39, 3391-3403, 1996. [3] L. Wu, F. Sket, J.M. Molina-Aldareguia, A. Makradi, L. Adam, I. Doghri, L. Noels, A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model, Composite Structures, 126, 246–264, 2015. [less ▲]

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See detailMean-Field-Homogenization-based stochastic multiscale methods for composite materials
Wu, Ling ULg; Lucas, Vincent ULg; Adam, Laurent et al

Conference (2016, July 12)

When considering a homogenization-based multiscale approach, at each integration-point of the macro-structure, the material properties are obtained from the resolution of a micro-scale boundary value ... [more ▼]

When considering a homogenization-based multiscale approach, at each integration-point of the macro-structure, the material properties are obtained from the resolution of a micro-scale boundary value problem. At the micro-level, the macro-point is viewed as the center of a Representative Volume Element (RVE). However, to be representative, the micro-volume-element should have a size much bigger than the micro-structure size. For composite materials which suffer from a large property and geometrical dispersion, either this requires RVE of sizes which cannot usually be obtained numerically, or simply the structural properties exhibit a scatter at the macro-scale. In both cases, the representativity of the micro-scale volume element is lost and Statistical Volume Elements (SVE) [1] should be considered in order to account for the micro-structural uncertainties, which should in turn be propagated to the macro-scale in order to predict the structural properties in a probabilistic way. In this work we propose a non-deterministic multi-scale approach for composite materials following the methodology set in [2]. Uncertainties on the meso-scale properties and their (spatial) correlations are first evaluated through the homogenization of SVEs. This homogenization combines both mean-field method in order to gain efficiency and computational homogenization to evaluate the spatial correlation. A generator of the meso-scale material tensor is then implemented using the spectral method [3]. As a result, a meso-scale random field can be generated, paving the way to the use of stochastic finite elements to study the probabilistic behavior of macro-scale structures. [1] M. Ostoja-Starzewski, X.Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering, 168, 35–49, 1999. [2] V. Lucas, J.-C. Golinval, S. Paquay, V.-D. Nguyen, L. Noels, L. Wu, A stochastic computational multiscale approach; Application to MEMS resonators. Computer Methods in Applied Mechanics and Engineering, 294, 141–167, 2015. [3] Shinozuka, M., Deodatis, G. Simulation of stochastic processes by spectral representation. Appl. Mech. Rev., 1991: 44(4): 191-204, 1991. [less ▲]

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See detailFailure multiscale simulations of composite laminates based on a non-local mean-field damage-enhanced homogenization
Wu, Ling ULg; Adam, Laurent; Doghri, Issam et al

Conference (2016, July 12)

A multiscale method is developed to study the failure of carbon fiber reinforced composites. In order to capture the intra-laminar failure, a non-local mean-field homogenization (MFH) method accounting ... [more ▼]

A multiscale method is developed to study the failure of carbon fiber reinforced composites. In order to capture the intra-laminar failure, a non-local mean-field homogenization (MFH) method accounting for the damage evolution of the matrix phase of the composite material [1] is considered. In that formulation, an incremental-secant MFH approach is used to account for the elastic unloading of the fibers during the strain softening of the matrix. In order to avoid the strain/damage localization caused by the matrix material softening, an implicit non-local method [2] was reformulated to account for the composite material anisotropy. As a result, accurate predictions of the composite softening behavior and of the different phases response is possible, even for volume ratios of inclusions around 60%. In particular it is shown that the damage propagation direction in each ply follows the fiber orientation in agreement with experimental data. The delamination process is modeled by recourse to a hybrid discontinuous Galerkin (DG)/ extrinsic cohesive law approach. As for the extrinsic cohesive law (ECL), which represents the fracturing response only, and for which cohesive elements are inserted at failure onset, the method does not suffer from a mesh-dependent effect. However, because of the underlying discontinuous Galerkin method, interface elements are present since the very beginning of the simulation avoiding the need to propagate topological changes in the mesh with the propagation of the delamination. Moreover, the pre-failure response is accurately captured by the material law though the DG implementation, by contrast to usual intrinsic cohesive laws. As a demonstration of the efficiency and accuracy of the method, a composite laminate with a quasi-isotropic sequence ([90/45/-45/90/0]S) and an open-hole geometry is studied using the multiscale method [3] and the results are compared to experimental data. The numerical model is found to predict the damage bands along the fiber directions as observed in the experimental samples inspected by X-ray computed tomography (XCT). Moreover, the predicted delamination pattern is found to match the experimental observations. REFERENCES [1] L. Wu, L. Noels, L. Adam, I. Doghri, An implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage, International Journal of Solids and Structures, 50, 3843-3860, 2013. [2] R. Peerlings, R. de Borst, W. Brekelmans, S. Ayyapureddi, Gradient-enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering, 39, 3391-3403, 1996. [3] L. Wu, F. Sket, J.M. Molina-Aldareguia, A. Makradi, L. Adam, I. Doghri, L. Noels, A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model, Composite Structures, 126, 246–264, 2015. [less ▲]

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