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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 (in press)

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 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 (in press)

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 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 (in press)

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 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 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 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 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 detailClassifying simulated wheat yield responses to changes in temperature and precipitation across a european transect
Fronzek, S.; Pirttioja, N.; Carter, T. R. et al

Conference (2016, March)

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