References of "Noels, Ludovic"
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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 (in press)

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

in Micro and Nanomechanics (in press)

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, 6.1.1 Review of Homogenization Methods for Heterogeneous Materials
Noels, Ludovic ULg; Wu, Ling ULg; Adam, Laurent et al

in Integrated Computational Materials Engineering (ICME) (in press)

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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 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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See detailA stochastic 3-Scale approach to study the thermomechanical damping of MEMS
Wu, Ling ULg; Lucas, Vincent ULg; Nguyen, Van Dung ULg et al

Scientific conference (2016, June 20)

A stochastic 3-scale approach is developed to study the thermo-elastic quality factor (Q) of micro-electromechanical systems (MEMS) resonators. Thermo-elastic damping is one of the major dissipation ... [more ▼]

A stochastic 3-scale approach is developed to study the thermo-elastic quality factor (Q) of micro-electromechanical systems (MEMS) resonators. Thermo-elastic damping is one of the major dissipation mechanisms in high-Q micro-resonators, which may have detrimental effects on the quality factor, and has to be predicted accurately. Since material uncertainties are inherent to and unavoidable in MEMS, the effects of those variations have to be considered in the numerical models. To this end, a coupled thermo-mechanical stochastic 3-scale approach is considered. Thermo-mechanical micro-models of poly-silicon materials are used to represent micro-structure realizations. A computational stochastic homogenization procedure is then applied on these statistical volume elements to obtain the probabilistic distribution of the elasticity tensor, thermal expansion and conductivity tensors at the meso-scale. Spatially correlated meso-scale random fields are then generated in order to represent the probabilistic behavior of the homogenized material properties, feeding macro-scale stochastic finite element simulations. [less ▲]

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See detailMulti-scale stochastic study of the grain orientation and roughness effects on polycrystalline thin structures
Lucas, Vincent ULg; Wu, Ling ULg; Golinval, Jean-Claude ULg et al

Conference (2016, June 09)

When studying micro-electro-mechanical systems (MEMS) made of poly-crystalline materials, as the size of the device is only one or two orders of magnitude higher than the size of the the grains, the ... [more ▼]

When studying micro-electro-mechanical systems (MEMS) made of poly-crystalline materials, as the size of the device is only one or two orders of magnitude higher than the size of the the grains, the structural properties exhibit a scatter at the macro-scale due to the existing randomness in the grain size, grain orientation, surface roughness... In order to predict the probabilistic behavior at the structural scale, the authors have recently developed a stochastic 3-scale approach [1]. In this method, stochastic volume elements (SVEs) [2] are defined by considering random grain orientations in a tessellation. For each SVE realization, a meso-scopic apparent material tensor can be obtained using the computational homogenization theory. The extracted meso-scopic apparent material tensors can then be used to defined a spatially correlated meso-scale random field, which is in turn used as input for stochastic finite element simulations. In this work we intend to study the effect of different material-related uncertainty sources on the structural behavior of vibrating micro-devices manufactured using low pressure chemical vapor deposition. First, the effect of preferred grain orientation on vibrating micro-structures is assessed. To this end, SVEs are generated so that their grain orientation distributions follow XRD measurements. Second, the effect of the roughness of the vibrating micro-structures is studied. Toward this end, SVEs, whose rough surface statistical properties follow AFM measurements, are generated. A second-order computational homogenization [3] applied on the different SVE realizations allows defining a meso-scale random field of the in-plane and out-of-plane meso-scale shell properties. Stochastic shell finite elements can then be applied to predict the MEMS probabilistic behavior. [1] V. Lucas, et al., Comp. Meth. in Appl. Mech. and Eng., 294, 141-167, 2015 [2] M. Ostoja-Starzewski, X.Wang, Comp. Meth. in Appl. Mech. and Eng., 168, 35–49, 1999 [3] E.W.C. Coenen, V. Kouznetsova, M.G.D. Geers. Int. J. for Numer. Meth. in Eng., 83, 1180–1205, 2010. [less ▲]

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See detailPrediction of intra- and inter-laminar failure of laminates using non-local damage-enhanced mean-field homogenization simulations
Wu, Ling ULg; Sket, Federico; Adam, Laurent et al

Conference (2016, June 08)

The failure of carbon fiber reinforced composites with a quasi-isotropic sequence ([90/45/-45/90/0]S) and open-hole geometry is studied using a multiscale method [1]. On the one hand, the intra-laminar ... [more ▼]

The failure of carbon fiber reinforced composites with a quasi-isotropic sequence ([90/45/-45/90/0]S) and open-hole geometry is studied using a multiscale method [1]. On the one hand, the intra-laminar failure is captured using a damage-enhanced mean-field homogenization scheme. To this end, each ply is modeled as a homogenized material whose anisotropic damage behavior is captured from the homogenization method [2]. In order to avoid the problem of loss of solution uniqueness the mean-field homogenization process is formulated in the context of the non-local continuum damage theory [3]. On the other hand, an hybrid discontinuous Galerkin/extrinsic cohesive law method is used to model the delamination process at the ply interfaces. This hybrid method avoids the need to propagate topological changes in the mesh with the propagation of the delamination while it preserves the consistency and stability in the un-cracked interfaces. As a result, the multiscale framework allows predicting damage propagation directions in each ply along the fiber directions accordingly to the experimental results as it is demonstrated by considering an openhole [90/45/-45/90/0]S-laminate studied both numerically and experimentally. [1] L. Wu, et al., Composite Struct., 126, 246–264, 2015. [2] L. Wu, L. Noels, L. Adam, I. Doghri, Int. J. of Solids and Struct., 50, 3843-3860, 2013. [3] R. Peerlings, et al., Int. J. for Numer. Meth. in Eng., 39, 3391-3403, 1996 [less ▲]

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See detailCohesive band model: a triaxiality-dependent cohesive model for damage to crack transition in a non-local implicit discontinuous Galerkin framework
Leclerc, Julien ULg; Wu, Ling ULg; Noels, Ludovic ULg et al

Conference (2016, June 07)

Numerical modelling of the complete ductile failure process is still a challenge. On the one hand, continuous approaches, described by damage models, succeed in the initial diffuse damage stage but are ... [more ▼]

Numerical modelling of the complete ductile failure process is still a challenge. On the one hand, continuous approaches, described by damage models, succeed in the initial diffuse damage stage but are still unable to represent physical discontinuities. On the other hand, discontinuous approaches, such as the cohesive zone models, are able to represent the crack propagation behaviour. They are suited for local damaging processes as crack initiation and propagation, and so, fail in diffuse damage prediction of ductile materials. Moreover, they do not usually capture triaxiality effects, mandatory for accurate ductile failure simulations. To describe the ductile failure process, the numerical scheme proposed here combines both approaches [1] in order to beneficiate from their respective advantages: a non-local damage model combined with an extrinsic cohesive law in a discontinuous Galerkin finite element framework. An application example of this scheme is shown on the attached figure. The initial diffuse damage stage is modelled by an implicit nonlocal damage model as suggested by [2]. Upon damage to crack transition, a cohesive band [3] is used to introduce in-plane stretch effects inside the cohesive law or in other words, a triaxiality-dependent behaviour. Indeed, these in-plane strains play an important role during the ductile failure process and have to be considered. Concretely, when crack appears in the last failure stage, all the damaging process is assumed to occur inside a thin band ahead of the crack surface. Thanks to the small but finite numerical band thickness, the strains inside this band can be obtained from the in-plane 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 is computed to ensure the energetic consistency during the transition. [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] 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 [3] 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): 177–188 [less ▲]

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

in Proceedings of the SEM XIII International Congress and Exposition on Experimental and Applied Mechanics. (SEMXIII 2016) (2016, June 06)

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 miro-beam stiction is then studied in a probabilistic way. [less ▲]

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See detailNumerical Properties of a Discontinuous Galerkin formulation for electro-thermal coupled problems
Homsi, Lina; Geuzaine, Christophe ULg; Noels, Ludovic ULg

in Papadrakakis, M.; Papadopoulos, V.; Stefanou, G. (Eds.) et al Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 5–10 June 2016 (2016, June 05)

Discontinuous Galerkin (DG) methods are attractive tools to integrate several PDEs in engineering sciences, due to their high order accuracy and their high scalability in parallel simulations. The main ... [more ▼]

Discontinuous Galerkin (DG) methods are attractive tools to integrate several PDEs in engineering sciences, due to their high order accuracy and their high scalability in parallel simulations. The main interest of this work is to derive a constant and stable Discontinuous Galerkin method for two-way electro-thermal coupling analyses. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations which are discretized using the Discontinuous Galerkin method. Toward this end, the weak form is written in terms of energetically conjugated fields gradients and fluxes. In order to validate the effectiveness of the formulation and illustrate the algorithmic properties, a numerical test for composite materials is performed. [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; Nguyen, Van Dung ULg et al

Scientific conference (2016, May 23)

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 to the case of thermoelastic damping. In this method, stochastic volume elements (SVEs) 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. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated mesoscale 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 microstructure of the poly-silicon material. [less ▲]

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See detailA Study Of Dry Stiction Phenomenon In MEMS Using A Computational Stochastic Multi-scale Methodology
Hoang Truong, Vinh ULg; Wu, Ling ULg; Paquay, Stéphane et al

in EuroSimE 2016 in Montpellier (2016, April 19)

This work studies the uncertainties of the adhesive contact problems for reduced size structures, e.g. the stiction failure of microelectromechanical systems (MEMS). In MEMS, because of the large surface ... [more ▼]

This work studies the uncertainties of the adhesive contact problems for reduced size structures, e.g. the stiction failure of microelectromechanical systems (MEMS). In MEMS, because of the large surface to volume ratio, the surfaces forces, such as van der Waals forces and capillary forces, are dominant in comparison with the body forces. As these force magnitudes strongly depend on the contact distance, when the two contacting surfaces are rough, the contact distances vary, and the physical contact areas are limited at the highest asperities of the contacting surfaces. Therefore, the adhesive contact forces between two rough surfaces can suffer from a scatter, and the involved structural behaviors can be indeterministic. To numerically predict the probability behaviors of structures involving adhesion in dry environments, in this paper, a computational stochastic model-based multi-scale method developed by the authors is applied. The effects of van der Waals is studied and compared with experimental data as well as with the effects of capillary forces. [less ▲]

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See detailExperimental and computational micro–mechanical investigations of compressive properties of polypropylene/multi–walled carbon nanotubes nanocomposite foams
Wan, Fangyi; Tran, Minh Phuong; Leblanc, Christophe ULg et al

in Mechanics of Materials (2015), 91(Part 1), 95-118

The compressive behavior of nanocomposite foams is studied by both experimental and computational micro-mechanics approaches with the aim of providing an efficient computational model for this kind of ... [more ▼]

The compressive behavior of nanocomposite foams is studied by both experimental and computational micro-mechanics approaches with the aim of providing an efficient computational model for this kind of material. The nanocomposites based on polypropylene (PP) and different contents of multi-walled carbon nanotubes (CNTs) are prepared by melt mixing method. The nanocomposite samples are foamed using super-critical carbon dioxide (ScCO2) as blowing agent at different soaking temperatures. The influence of this foaming parameter on the morphological characteristics of the foam micro-structure is discussed. Differential Scanning Calorimetry (DSC) measurements are used to quantify the crystallinity degree of both nanocomposites and foams showing that the crystallinity degree is reduced after the foaming process. This modification leads to mechanical properties of the foam cell walls that are different from the raw nanocomposite PP/CNTs material. Three--point bending tests are performed on the latter to measure the flexural modulus in terms of the crystallinity degree. Uniaxial compression tests are then performed on the foamed samples under quasi-static conditions in order to extract the macro-scale compressive response. Next, a two-level multi-scale approach is developed to model the behavior of the foamed nanocomposite material. On the one hand, the micro-mechanical properties of nanocomposite PP/CNTs cell walls are evaluated from a theoretical homogenization model accounting for the micro-structure of the semi-crystalline PP, for the degree of crystallinity, and for the CNT volume fraction. The applicability of this theoretical model is demonstrated via the comparison with experimental data from the described experimental measurements and from literature. On the other hand, the macroscopic behavior of the foamed material is evaluated using a computational micro-mechanics model using tetrakaidecahedron unit cells and periodic boundary conditions to estimate the homogenized properties. The unit cell is combined with several geometrical imperfections in order to capture the elastic collapse of the foamed material. The numerical results are compared to the experimental measurements and it is shown that the proposed unit cell computational micro-mechanics model can be used to estimate the homogenized behavior, including the linear and plateau regimes, of nanocomposite foams. [less ▲]

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