References of "International Journal for Numerical Methods in Engineering"
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See detailA Frontal Delaunay Quad Mesh Generator Using the L ∞  Norm
Remacle, J.-F.; Henrotte, F.; Carrier-Baudouin, T. et al

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

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See detailElectromechanical FEM models and electrostatic forces near sharp corners
Hannot, Stephan; Rixen, Daniel; Andreykiv, Andriy et al

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

Accounting for multiphysical coupling in models of Micro Electro Mechanical Systems (MEMS) is essential for accurate simulations. One essential multiphysical effect in MEMS is the electromechanical ... [more ▼]

Accounting for multiphysical coupling in models of Micro Electro Mechanical Systems (MEMS) is essential for accurate simulations. One essential multiphysical effect in MEMS is the electromechanical coupling since electrostatic forces are often used for actuation or sensing in those devices. Often MEMS are designed such that their shape exhibits many corners. In this paper two different numerical approaches are used to model this coupling using the Finite Element Method: the electrostatic forces are either derived from the variational approach or a local approach based on the Maxwell stress tensor such as implemented in commercial Finite Element codes. The evaluation of electrostatic forces near corners is investigated in detail and in this paper the two approaches are compared around corners. Although the issue of numerical models around singularities is not new, the question addressed here is related to the computation of electric forces in the vicinity of corners. Since those forces are quadratic functions of the electric field, namely the gradient of the electric potential, here the primal unknown, computing those forces accurately is a challenge in itself. Elements which use special shape functions are used to discretize the field near this corner singularity as well. In the work presented here, it is shown that a significant discrepancy appears in the electrostatic force computed around a corner depending on the discretization approach considered, and we conclude that the variational approach or equivalently the full Maxwell tensor should be used to properly evaluate electrostatic forces around corners. [less ▲]

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See detailOptimizing Perfectly Matched Layers in Discrete Contexts
Modave, Axel ULg; Delhez, Eric ULg; Geuzaine, Christophe ULg

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

Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic ... [more ▼]

Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic cases, their performance critically depends on the so-called absorption function. This paper deals with the choice of this function when classical numerical methods are used (based on finite differences, finite volumes, continuous finite elements and discontinuous finite elements). After reviewing the properties of the PMLs at the continuous level, we analyse how they are altered by the different spatial discretizations. In the light of these results, different shapes of absorption function are optimized and compared by means of both one- and two-dimensional representative time-dependent cases. This study highlights the advantages of the so-called shifted hyperbolic function, which is efficient in all cases and does not require the tuning of a free parameter, by contrast with the widely used polynomial functions. [less ▲]

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See detailReduced chaos expansions with random coefficients in reduced-dimensional stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2014), 97

We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed ... [more ▼]

We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed method entails a partitioned iterative solution algorithm that relies on a reduced-dimensional representation of information exchanged between subproblems to allow each subproblem to be solved within its own stochastic dimension while interacting with a reduced projection of the other subproblems. The proposed method extends previous work by the authors by introducing a reduced chaos expansion with random coefficients. The representation of the exchanged information by using this reduced chaos expansion with random coefficients enables an expeditious construction of doubly stochastic polynomial chaos expansions that separate the effect of uncertainty local to a subproblem from the effect of statistically independent uncertainty coming from other subproblems through the coupling. After laying out the theoretical framework, we apply the proposed method to a multiphysics problem from nuclear engineering. [less ▲]

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See detailTransient Fokker-Planck-Kolmogorov equation solved with smoothed particle hydrodynamics method
Canor, Thomas ULg; Denoël, Vincent ULg

in International Journal for Numerical Methods in Engineering (2013), 94(6), 535553

Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function (pdf). The time ... [more ▼]

Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function (pdf). The time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient Fokker-Planck-Kolmogorov equation (FPK). The FPK equation is a conservation equation of a hypothetical or abstract fluid, which models the transport of probability. This paper presents a generalized formalism for the resolution of the transient FPK equation using the well-known mesh-free Lagrangian method, Smoothed Particle Hydrodynamics (SPH). Numerical implementation shows notable advantages of this method in an unbounded state space: (i) the conservation of total probability in the state space is explicitly written, (ii) no artifact is required to manage far- eld boundary conditions , (iii) the positivity of the pdf is ensured and (iv) the extension to higher dimensions is straightforward. Furthermore, thanks to the moving particles, this method is adapted for a large kind of initial conditions, even slightly dispersed distributions. The FPK equation is solved without any a priori knowledge of the stationary distribution; just a precise representation of the initial distribution is required. [less ▲]

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See detailA full-discontinuous Galerkin formulation of non-linear Kirchhoff-Love shells: elasto-plastic finite deformations, parallel computation & fracture applications
Becker, Gauthier ULg; Noels, Ludovic ULg

in International Journal for Numerical Methods in Engineering (2013), 93(1), 80-117

Due to its ability to take into account discontinuities, the discontinuous Galerkin (DG) method presents some advantages for modeling crack initiations and propagations. This concept has been recently ... [more ▼]

Due to its ability to take into account discontinuities, the discontinuous Galerkin (DG) method presents some advantages for modeling crack initiations and propagations. This concept has been recently applied to 3D simulations and to elastic thin bodies. In this last case, the assumption of small elastic deformations before crack initiations or propagations reduces drastically the applicability of the framework to a reduced number of materials. To remove this limitation, a full-DG formulation of non-linear Kirchhoff-Love shells is presented and is used in combination with an elasto-plastic finite deformations model. The results obtained by this new formulation are in agreement with other continuum elasto-plastic shell formulations. Then this full-DG formulation of Kirchhoff-Love shells is coupled with the cohesive zone model to perform thin body fracture simulations. As this method allows considering elasto-plastic constitutive laws in combination with the cohesive model, accurate results compared to the experiments are found. In particular, the crack path and propagation rate of a blasted cylinder are shown to match experimental results. One of the main advantages of this framework is its ability to run in parallel with a high speed-up factor, allowing the simulation of ultra fine meshes. [less ▲]

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See detailEfficient ALE mesh management for 3D quasi-Eulerian problems
Boman, Romain ULg; Ponthot, Jean-Philippe ULg

in International Journal for Numerical Methods in Engineering (2012), 92(10), 857-890

In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is ... [more ▼]

In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is said to be quasi-Eulerian because the nodes remain almost fixed—or almost Eulerian—in the main process direction, although they are required to move in the orthogonal plane in order to follow the lateral displacements of the solid. This paper extensively presents a complete node relocation procedure dedicated to such ALE models. The discussion focusses on quadrangular and hexahedral meshes with local refinements. The main concern of this work is the preservation of the geometrical features and the shape of the free boundaries of the mesh. With this aim in view, each type of nodes (corner, edge, surface and volume) is treated sequentially with dedicated algorithms. A special care is given to highly curved 3D surfaces for which a CPU-efficient smoothing technique is proposed. This new method relies on a spline surface reconstruction, on a very fast weighted Laplacian smoother with original weights and on a robust reprojection algorithm. The overall consistency of this mesh management procedure is finally demonstrated in two numerical applications. The first one is a 2D ALE simulation of a drawbead, which provides similar results to an equivalent Lagrangian model yet is much faster. The second application is a 3D industrial ALE model of a 16-stand roll forming line. In this case, all attempts to perform the same simulation by using the Lagrangian formalism have been unsuccessful. [less ▲]

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See detailMeasure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2012), 92

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼]

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower-dimensional space than the sources themselves. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲]

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See detailDimension reduction in stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2012), 92

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼]

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced-dimensional representation and in particular by an adaptation of the Karhunen-Loève decomposition. The effectiveness of the proposed dimension–reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲]

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See detailA bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate
Gao, Tong ULg; ZHANG, Weihong; Duysinx, Pierre ULg

in International Journal for Numerical Methods in Engineering (2012), 91(1), 98-114

The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding ... [more ▼]

The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme is proposed to this aim. The idea of the BCP scheme is to “code” each material phase using integer values of +1 and -1. Each available material phase has one unique “code” consisting of +1 and/or -1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. This is very beneficial when the number of candidate materials becomes important. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the proposed scheme in solving this kind of problem. It proves that the BCP is an interesting and potential scheme to achieve the optimal orientations for large-scale design problems. [less ▲]

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See detailA mixed solid-shell element for the analysis of laminated composites
Rah, Kamran; Paepegem, Wim; Habraken, Anne ULg et al

in International Journal for numerical methods in engineering (2012), 89(7), 805-828

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See detailBlossom-Quad: a non-uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm
Remacle, J.-F.; Lambrechts, J.; Seny, B. et al

in International Journal for Numerical Methods in Engineering (2012), 89

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See detailHigh Quality Surface Remeshing Using Harmonic Maps. Part II: Surfaces with High Genus and of Large Aspect Ratio
Marchandise, E.; Carton de Wiart, C.; Vos, W. et al

in International Journal for Numerical Methods in Engineering (2011), 86(11), 1303-1321

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See detailElectrostatic Simulation using XFEM for Conductor and Dielectric Interfaces
Rochus, Véronique ULg; Rixen, Daniel; Van Miegroet, Laurent ULg et al

in International Journal for Numerical Methods in Engineering (2011), 85(10), 12071226

ManyMicro-Electro-Mechanical Systems (e.g. RF-switches, micro-resonators and micro-rotors) involve mechanical structures moving in an electrostatic field. For this type of problems, it is required to ... [more ▼]

ManyMicro-Electro-Mechanical Systems (e.g. RF-switches, micro-resonators and micro-rotors) involve mechanical structures moving in an electrostatic field. For this type of problems, it is required to evaluate accurately the electrostatic forces acting on the devices. Extended Finite Element (X-FEM) approaches can easily handle moving boundaries and interfaces in the electrostatic domain and seem therefore very suitable to model Micro-Electro-Mechanical Systems. In this study we investigate different X-FEM techniques to solve the electrostatic problem when the electrostatic domain is bounded by a conducting material. Preliminary studies in one-dimension have shown that one can obtain good results in the computation of electrostatic potential using X-FEM. In this paper the extension of these preliminary studies to 2D problem is presented. In particular a new type of enrichment functions is proposed in order to treat accurately Dirichlet boundary conditions on the interface. [less ▲]

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See detailA fracture framework for Euler Bernoulli beams based on a full discontinuous Galerkin formulation/extrinsic cohesive law combination
Becker, Gauthier ULg; Noels, Ludovic ULg

in International Journal for Numerical Methods in Engineering (2011), 85(10), 12271251

A new full Discontinuous Galerkin discretization of Euler Bernoulli beam is presented. The main interest of this framework is its ability to simulate fracture problems by inserting a cohesive zone model ... [more ▼]

A new full Discontinuous Galerkin discretization of Euler Bernoulli beam is presented. The main interest of this framework is its ability to simulate fracture problems by inserting a cohesive zone model in the formulation. With a classical Continuous Galerkin method the use of the cohesive zone model is di cult because as insert a cohesive element between bulk elements is not straightforward. On one hand if the cohesive element is inserted at the beginning of the simulation there is a modification of the structure stiffness and on the other hand inserting the cohesive element during the simulation requires modification of the mesh during computation. These drawbacks are avoided with the presented formulation as the structure is discretized in a stable and consistent way with full discontinuous elements and inserting cohesive elements during the simulation becomes straightforward. A new cohesive law based on the resultant stresses (bending moment and membrane) of the thin structure discretization is also presented. This model allows propagating fracture while avoiding through-the-thickness integration of the cohesive law. Tests are performed to show that the proposed model releases, during the fracture process, an energy quantity equal to the fracture energy for any combination of tension-bending loadings. [less ▲]

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See detailOn the numerical integration of an advanced Gurson model
Ben Bettaieb, Mohamed ULg; Lemoine, Xavier; Duchene, Laurent ULg et al

in International Journal for Numerical Methods in Engineering (2011), 85(8), 1049-1072

This article is focused on a new extended version of Gurson's model (J. Eng. Mater. Technol. 1977; 99:2–15), its numerical integration scheme and its consistent tangent matrix being within an FE code ... [more ▼]

This article is focused on a new extended version of Gurson's model (J. Eng. Mater. Technol. 1977; 99:2–15), its numerical integration scheme and its consistent tangent matrix being within an FE code. First, this new advanced Gurson model is proposed, which is an extension of the original to take into account plastic anisotropy and mixed (isotropic+kinematic) hardening. In this paper, only the growth phase of cavities is considered (the nucleation of new voids is ignored). Second, a new numerical algorithm for the integration of this new Gurson model is presented. The algorithm is implicit in all variables and is unconditionally stable. This algorithm is generic and could be used for other anisotropic yield functions and other hardening laws. Third, the consistent tangent matrix is computed in an explicit way by exact linearization of the constitutive equations. To check its efficiency and robustness, the proposed integration algorithm is compared, under some simplified assumptions and choices, with the algorithms of Aravas (Int. J. Numer. Meth. Engng 1987; 24:1395–1416) and Kojic (Int. J. Numer. Meth. Engng 2002; 53(12):2701–2720). The performance of the developed consistent modulus, compared to other techniques for the computation of the tangent matrix is assessed. The paper ends with numerical simulations of tensile tests on homogeneous and notched specimens. [less ▲]

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See detailA variational-inequality approach to stochastic boundary value problems with inequality constraints and its application to contact and elastoplasticity
Arnst, Maarten ULg; Ghanem, Roger

in International Journal for Numerical Methods in Engineering (2011)

This paper is concerned with stochastic boundary value problems (SBVPs) whose formulation involves inequality constraints. A class of stochastic variational inequalities (SVIs) is defined, which is well ... [more ▼]

This paper is concerned with stochastic boundary value problems (SBVPs) whose formulation involves inequality constraints. A class of stochastic variational inequalities (SVIs) is defined, which is well adapted to characterize the solution of specified inequality-constrained SBVPs. A methodology for solving such SVIs is proposed, which involves their discretization by projection onto polynomial chaos and collocation of the inequality constraints, followed by the solution of a finite-dimensional constrained optimization problem. Simulation studies in contact and elastoplasticity are provided to demonstrate the proposed framework. [less ▲]

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See detailA coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry
Mercatoris, Benoît ULg; Massart, T. J.

in International Journal for Numerical Methods in Engineering (2011), 85(9), 1177-1206

This paper presents a multi-scale framework for the failure of periodic quasi-brittle thin planar shells. The failure behavior of textured or periodic heterogeneous materials is strongly influenced by ... [more ▼]

This paper presents a multi-scale framework for the failure of periodic quasi-brittle thin planar shells. The failure behavior of textured or periodic heterogeneous materials is strongly influenced by their mesostructure. Their periodicity and the quasi-brittle nature of their constituents result in complex behaviors such as damage-induced anisotropy properties with localization of damage, which are difficult to model by means of macroscopic closed-form constitutive laws. A computational homogenization procedure is used for the in-plane and out-of-plane behavior of such planar shells, and is combined with an acoustic tensor-based failure detection adapted to shell kinematics to detect the structural-scale failure. Based on an assumption of single period failure, the localization of damage at the structural scale is represented by means of mesostructurally informed embedded strong discontinuities incorporated in the macroscopic shell description. A new enhanced scale transition is outlined for shell failure, based on an approximate energy consistency argument to objectively upscale the energy dissipation. The corresponding multi-scale framework results are compared with direct fine-scale modeling results used as a reference for the case of masonry, showing good agreement in terms of the load-bearing capacity, of failure mechanisms and of associated energy dissipation. © 2010 John Wiley & Sons, Ltd. [less ▲]

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See detailHigh-Quality Surface Remeshing Using Harmonic Maps
Remacle, J.-F.; Geuzaine, Christophe ULg; Compère, G. et al

in International Journal for Numerical Methods in Engineering (2010), 83(4), 403-425

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See detailPure equilibrium tetrahedral finite elements for global error estimation by dual analysis
Kempeneers, Martin; Debongnie, Jean-François ULg; Beckers, Pierre ULg

in International Journal for Numerical Methods in Engineering (2010)

This study presents a general porocedure of creating pure equilibrium tetrahedral finite elements. These elements are of the Fraeijs de Veubeke type. The spurious kinematical modes which inevitably appear ... [more ▼]

This study presents a general porocedure of creating pure equilibrium tetrahedral finite elements. These elements are of the Fraeijs de Veubeke type. The spurious kinematical modes which inevitably appear in this approach are eliminated by converting each tetrahedron in a super-element consisting of four tetrahedral primitive elements. A mathematical discussion on the number of spurious kinematical modes is presented. The development of first and second degree elements is presented in detail, and their efficiency in the frame of global errror estimation by dual analysis is emphasized by two numerical applications. The main attribute of the error estimation by dual analysis is that it provides an upper bound of the discretization error. [less ▲]

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