ORBi Collection: Mechanical engineering
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Embedded solids of any dimension in the X-FEM defined on higher-order approximations
http://hdl.handle.net/2268/201087
Title: Embedded solids of any dimension in the X-FEM defined on higher-order approximations
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<br/>Author, co-author: Duboeuf, Frédéric; Béchet, Eric
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<br/>Abstract: Embedded interface methods bring a significant simplification of the modelling process before analysis. Complex geometries and moving boundaries may be described with great flexibility, reducing the meshing step to that of a simple bounding box. Following this idea – to dissociate the field approximation from the geometric description – manifolds of different dimensions may be embedded in the same bulk mesh. However, special attention should be given to the difference of dimensions between that of problem domain and that of bulk mesh (the codimension).
Whereas the direct use of the shape functions of the bulk mesh is possible for a problem domain of codimension zero, this approach is no longer possible in other configurations, for instance a beam in a 3D mesh. Unlike approaches introducing independent overlapping meshes for each subdomain, function spaces may be built from the traces of higher dimensional spaces built upon the bulk mesh. For closed curves in 2D and closed surfaces in 3D, the resulting discrete method based on P1 FE have already been studied in the literature. To avoid badly conditioned linear systems, specific treatments are required, e.g. preconditioning approaches or stabilization techniques. Here, we propose to deplete wisely the trace space.
We investigate higher-order function spaces to solve the diffusion equation in embedded solids of any codimension. A new space-reducer algorithm is introduced to design the dedicated spaces that avoids ill-conditionning while treating boundary conditions. We present the results of several numerical experiments with convergence analyses. To conclude, applications of this technique to embedded beams or shells is discussed.X-FEM : Aux frontières du réel
http://hdl.handle.net/2268/201086
Title: X-FEM : Aux frontières du réel
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<br/>Author, co-author: Duboeuf, Frédéric
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<br/>Commentary: Le concours « Ma thèse en 180 secondes » vise à informer le grand public de la richesse et de l’intérêt des recherches scientifiques, tout en développant les compétences communicationnelles des doctorants avec le grand public. Le but ? Chaque participant (doctorant ou docteur diplômé de l’année académique précédente) présente, en trois minutes, un exposé de vulgarisation en français, clair, concis et convaincant sur sa thèse. Le tout avec l’appui d’une seule diapositive !
-> [fr] Vidéo disponible en suivant l'URL mentionné ci-dessus.
-> [en] Watch the presentation accessible at the URL given above.Evaluation of the contact force between two rigid bodies using kinematic data only
http://hdl.handle.net/2268/200931
Title: Evaluation of the contact force between two rigid bodies using kinematic data only
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<br/>Author, co-author: Van Hulle, Romain; Schwartz, Cédric; Denoël, Vincent; Croisier, Jean-Louis; Forthomme, Bénédicte; Bruls, OlivierOn the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications
http://hdl.handle.net/2268/200928
Title: On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications
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<br/>Author, co-author: ben bettaieb, Amine; Velosa de Sena, J.I.; Alves de Sousa, Ricardo; Valente, Robertt; Habraken, Anne; Duchene, Laurent
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<br/>Abstract: In the present paper, a detailed description of the formulation of the new SSH3D solid-shell element is presented. This formulation is compared with the previously proposed RESS solid-shell element [1, 2]. Both elements were recently implemented within the LAGAMINE in-house research finite element code. These solid-shell elements possess eight nodes with only displacement nodal degrees of freedom (DOF). In order to overcome various locking pathologies, the SSH3D formulation employs the well known Enhanced Assumed Strain (EAS) concept originally introduced by Simo and Rifai [3] and based on the Hu-Veubeke-Washizu variational principle combined with the Assumed Natural Strain (ANS) technique based on the work of Dvorkin and Bathe [4]. For the RESS solid-shell element, on the other hand, only the EAS technique is used with a Reduced Integration (RI) Scheme. A particular characteristic of these elements is their special integration schemes, with an arbitrary number of integration points along the thickness direction, dedicated to analyze problems involving non-linear through-thickness distribution (i.e. metal forming applications) without requiring many element layers. The formulation of the SSH3D element is also particular, with regard to the solid-shell elements proposed in the literature, in the sense that it is characterized by an in-plane full integration and a large variety in terms of (i) enhancing parameters, (ii) the ANS version choice and (iii) the number of integration points through the thickness direction. The choice for these three parameters should be adapted to each problem so as to obtain accurate results and to keep the calculation time low.
Numerous numerical examples are performed to investigate the performance of these elements. These examples illustrate the reliability and the efficiency of the proposed formulations in various cases including linear and non-linear problems. SSH3D element is more robust thanks to the various options proposed and its full in-plane integration scheme, while RESS element in more efficient from a computational point of view.A multiscale computational scheme based on a hybrid discontinuous Galerkin/cohesive zone model for damage and failure of microstructured materials
http://hdl.handle.net/2268/200913
Title: A multiscale computational scheme based on a hybrid discontinuous Galerkin/cohesive zone model for damage and failure of microstructured materials
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<br/>Author, co-author: Nguyen, Van Dung; Wu, Ling; Leclerc, Julien; Noels, LudovicStructural design considering damage within an XFEM-level set framework
http://hdl.handle.net/2268/200812
Title: Structural design considering damage within an XFEM-level set framework
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<br/>Author, co-author: Noël, Lise; Duysinx, Pierre; Maute, KurtStructural design under damage constraints with XFEM and level sets
http://hdl.handle.net/2268/200811
Title: Structural design under damage constraints with XFEM and level sets
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<br/>Author, co-author: Noël, Lise; Duysinx, Pierre; Maute, KurtSolving the inverse dynamics of a flexible 3D robot for a trajectory tracking task
http://hdl.handle.net/2268/200795
Title: Solving the inverse dynamics of a flexible 3D robot for a trajectory tracking task
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<br/>Author, co-author: Lismonde, Arthur; Sonneville, Valentin; Bruls, Olivier
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<br/>Abstract: The end-effector trajectory tracking of robotic manipulators
with flexible links requires advanced control concepts.
In order to compute the feedforward component of the control
scheme, the inverse dynamics of such flexible 3D multibody
system is solved using an optimal control method. The robot is
modeled using nonlinear finite elements formulated on the SE(3)
group. Hence singularity and parameterization issues that can
arise from 3D rotations are avoided. A numerical example of a
3D flexible arm is analyzed to demonstrate the capabilities of the
method.A stochastic 3-Scale approach to study the thermomechanical damping of MEMS
http://hdl.handle.net/2268/200758
Title: A stochastic 3-Scale approach to study the thermomechanical damping of MEMS
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<br/>Author, co-author: Wu, Ling; Lucas, Vincent; Nguyen, Van Dung; Paquay, Stéphane; Golinval, Jean-Claude; Noels, Ludovic; Voicu, Rodica; Baracu, Angela; Muller, Raluca
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<br/>Abstract: 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.Eulerian Formulation of Elastic Rods
http://hdl.handle.net/2268/200701
Title: Eulerian Formulation of Elastic Rods
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<br/>Author, co-author: Huynen, Alexandre; Detournay, Emmanuel; Denoël, Vincent
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<br/>Abstract: In numerous biological, medical and engineering applications, elastic rods are constrained to deform inside or around tube-like surfaces. To solve efficiently this class of problems, the equations governing the deflection of elastic rods are reformulated within the Eulerian framework of this generic tubular constraint defined as a perfectly stiff canal surface. This reformulation hinges on describing the rod deformed configuration by means of its relative position with respect to a reference curve, defined as the axis or spine curve of the constraint, and on restating the rod local equilibrium in terms of the curvilinear coordinate parameterizing this curve. Associated with a segmentation strategy, which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact (except for their extremities), this approach not only trivializes the detection of new contacts but also suppresses the isoperimetric constraints resulting from the self-feeding feature of these elementary problems and the imposition of the rod position at the extremities of each rod segments.DEM modeling of ball mills with experimental validation: influence of contact parameters on charge motion and power draw
http://hdl.handle.net/2268/200623
Title: DEM modeling of ball mills with experimental validation: influence of contact parameters on charge motion and power draw
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<br/>Author, co-author: Boemer, Dominik; Ponthot, Jean-Philippe
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<br/>Abstract: Discrete element method simulations of a 1:5-scale laboratory ball mill are presented in this paper to study the influence of the contact parameters on the charge motion and the power draw. The position density limit is introduced as an efficient mathematical tool to describe and to compare the macroscopic charge motion in different scenarios, i.a. with different values of the contact parameters. While the charge motion and the power draw are relatively insensitive to the stiffness and the damping coefficient of the linear spring-slider-damper contact law, the coefficient of friction has a strong influence since it controls the sliding propensity of the charge. Based on the experimental calibration and validation by charge motion photographs and power draw measurements, the descriptive and predictive capabilities of the position density limit and the discrete element method are demonstrated, i.e. the real position of the charge is precisely delimited by the respective position density limit and the power draw can be predicted with an accuracy of about 5 %.Topology optimization for minimum weight with compliance and simpli ed nominal stress constraints for fatigue resistance
http://hdl.handle.net/2268/200576
Title: Topology optimization for minimum weight with compliance and simpli ed nominal stress constraints for fatigue resistance
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<br/>Author, co-author: Collet, Maxime; Bruggi, Matteo; Duysinx, Pierre
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<br/>Abstract: This work investigates a simpli ed approach to cope with the optimization of preliminary design of structures under local fatigue constraints along with a global enforcement on the overall compliance. The problem aims at the minimization of the weight of linear elastic structures
under given loads and boundary conditions. The expected sti ness of the optimal structure is provided by the global constraint, whereas a set of local stress-based constraints ask for a structure to be fatigue resistant. A modi ed Goodman fatigue strength comparison is implemented through the same formalism to address pressure-dépendent failure in materials as in Drucker-Prager strength criterion. As a simplification, the Sines approach is used to de ne the equivalent mean and alternating stresses to address the fatigue resistance for an infinite life time. Sines computation is based on the equivalent mean and alternate stress depending on the invariants of the stress tensor and itsdeviatoric part, respectively. The so-called singularity phenomenon is overcome by the implementation of a suitable qp-relaxation of the equivalent stress measures. Numerical examples are presented to illustrate the features of the achieved optimal layouts and of the proposed algorithm.A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
http://hdl.handle.net/2268/200451
Title: A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
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<br/>Author, co-author: Hoang Truong, Vinh; Wu, Ling; Paquay, Stéphane; Golinval, Jean-Claude; Arnst, Maarten; Noels, Ludovic
<br/>
<br/>Abstract: 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.Mean-Field-Homogenization-based stochastic multiscale methods for composite materials
http://hdl.handle.net/2268/200450
Title: Mean-Field-Homogenization-based stochastic multiscale methods for composite materials
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<br/>Author, co-author: Wu, Ling; Lucas, Vincent; Adam, Laurent; Noels, Ludovic
<br/>
<br/>Abstract: 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.Failure multiscale simulations of composite laminates based on a non-local mean-field damage-enhanced homogenization
http://hdl.handle.net/2268/200449
Title: Failure multiscale simulations of composite laminates based on a non-local mean-field damage-enhanced homogenization
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<br/>Author, co-author: Wu, Ling; Adam, Laurent; Doghri, Issam; Noels, Ludovic
<br/>
<br/>Abstract: 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.A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
http://hdl.handle.net/2268/200354
Title: A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
<br/>
<br/>Author, co-author: Hoang Truong, Vinh; Paquay, Stéphane; Golinval, Jean-Claude; Wu, Ling; Arnst, Maarten; Noels, Ludovic
<br/>
<br/>Abstract: 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.Numerical Properties of a Discontinuous Galerkin formulation for electro-thermal coupled problems
http://hdl.handle.net/2268/200352
Title: Numerical Properties of a Discontinuous Galerkin formulation for electro-thermal coupled problems
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<br/>Author, co-author: Homsi, Lina; Geuzaine, Christophe; Noels, Ludovic
<br/>
<br/>Abstract: 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.Nonlinear analysis of compliant mechanisms: application to tape springs
http://hdl.handle.net/2268/200302
Title: Nonlinear analysis of compliant mechanisms: application to tape springs
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<br/>Author, co-author: Dewalque, Florence; Bruls, Olivier
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<br/>Abstract: Brief summary of the mechanical behaviour of tape springs. Main results obtained by the means of finite element models. Description of the experimental set-up and results. See the extended abstract for more details.Inverse dynamics of a flexible 3D robotic arm for a trajectory tracking task
http://hdl.handle.net/2268/200182
Title: Inverse dynamics of a flexible 3D robotic arm for a trajectory tracking task
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<br/>Author, co-author: Lismonde, Arthur; Sonneville, Valentin; Bruls, OlivierModelling of multibody systems in the local frame
http://hdl.handle.net/2268/200140
Title: Modelling of multibody systems in the local frame
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<br/>Author, co-author: Bruls, Olivier; Sonneville, Valentin
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<br/>Abstract: A local frame finite element approach is proposed to describe the kinematics of a flexible multibody system, derive the equations of motion and solve them numerically. It is argued that this approach leads to reduced geometric nonlinearities and improved computational efficiency.