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A fracture framework for Euler Bernoulli beams based on a full discontinuous Galerkin formulation/extrinsic cohesive law combination Becker, Gauthier ; Noels, Ludovic 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 ▲] Detailed reference viewed: 174 (76 ULg)On the numerical integration of an advanced Gurson model Ben Bettaieb, Mohamed ; ; Duchene, Laurent 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 ▲] Detailed reference viewed: 104 (37 ULg)A variational-inequality approach to stochastic boundary value problems with inequality constraints and its application to contact and elastoplasticity Arnst, Maarten ; 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 ▲] Detailed reference viewed: 37 (4 ULg)A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry Mercatoris, Benoît ; 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 ▲] Detailed reference viewed: 10 (2 ULg)High-Quality Surface Remeshing Using Harmonic Maps ; Geuzaine, Christophe ; et al in International Journal for Numerical Methods in Engineering (2010), 83(4), 403-425 Detailed reference viewed: 63 (3 ULg)Pure equilibrium tetrahedral finite elements for global error estimation by dual analysis ; Debongnie, Jean-François ; Beckers, Pierre 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 ▲] Detailed reference viewed: 78 (7 ULg)Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities Geuzaine, Christophe ; in International Journal for Numerical Methods in Engineering (2009), 79(11), 1309-1331 Detailed reference viewed: 212 (15 ULg)A discontinuous Galerkin formulation of non-linear Kirchhoff–Love shells Noels, Ludovic in International Journal for Numerical Methods in Engineering (2009), 78(3), 296-323 Discontinuous Galerkin (DG) methods provide a means of weakly enforcing the continuity of the unknown-field derivatives and have particular appeal in problems involving high-order derivatives. This ... [more ▼] Discontinuous Galerkin (DG) methods provide a means of weakly enforcing the continuity of the unknown-field derivatives and have particular appeal in problems involving high-order derivatives. This feature has previously been successfully exploited (Comput. Methods Appl. Mech. Eng. 2008; 197:2901-2929) to develop a formulation of linear Kirchhoff-Love shells considering only the membrane and bending responses. In this proposed one-field method - the displacements are the only unknowns, while the displacement field is continuous, the continuity in the displacement derivative between two elements is weakly enforced by recourse to a DG formulation. It is the purpose of the present paper to extend this formulation to finite deformations and non-linear elastic behaviors. While the initial linear formulation was relying on the direct linear computation of the effective membrane stress and effective bending couple-stress from the displacement field at the mid-surface of the shell, the non-linear formulation considered implies the evaluation of the general stress tensor across the shell thickness, leading to a reformulation of the internal forces of the shell. Nevertheless, since the interface terms resulting from the discontinuous Galerkin method involve only the resultant couple-stress at the edges of the shells, the extension to non-linear deformations is straightforward. [less ▲] Detailed reference viewed: 105 (25 ULg)A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method Béchet, Eric ; ; in International Journal for Numerical Methods in Engineering (2009), 78(8), 931-954 This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier ... [more ▼] This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier approaches. we do not work with an interior penalty formulation as, e.g. for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. Roughly speaking a stable and optimal discrete Lagrange multiplier space has to satisfy two criteria: a best approximation property and a uniform inf-sup condition. Owing to the fact that the interface does not match the edges of the mesh, the choice of a good discrete Lagrange Multiplier space is not trivial. Here we propose a new algorithm for the local construction of the Lagrange Multiplier space and show that a uniform inf-sup condition is satisfied. A counterexample is also presented, i.e. the inf-sup constant depends on the mesh-size and degenerates as it tends to zero. Numerical results in two-dimensional confirm the theoretical ones. Copyright (C) 2008 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 129 (7 ULg)Application of the X-FEM to the fracture of piezoelectric materials Béchet, Eric ; ; in International Journal for Numerical Methods in Engineering (2009), 77(11), 1535-1565 This paper presents an application of the extended finite element method (X-FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New ... [more ▼] This paper presents an application of the extended finite element method (X-FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the X-FEM has been applied mostly to model cracks in structural materials. The present paper focuses at first on the definition of new enrichment functions suitable for cracks in piezoelectric structures. At second, generalized domain integrals are used for the determination of crack tip parameters. The approach is based on specific asymptotic crack tip Solutions, derived for piezoelectric materials. We present convergence results in the energy norm and for the stress intensity factors, in various settings. Copyright (C) 2008 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 46 (10 ULg)Sensitivity analysis for dynamic mechanical systems with finite rotations Bruls, Olivier ; in International Journal for Numerical Methods in Engineering (2008), 74(13), 1897-1927 This paper presents a sensitivity analysis for dynamic systems with large rotations using a semi-analytical direct differentiation technique. The choice of a suitable time integration strategy for the ... [more ▼] This paper presents a sensitivity analysis for dynamic systems with large rotations using a semi-analytical direct differentiation technique. The choice of a suitable time integration strategy for the rotation group appears to be critical for the development of an efficient sensitivity analysis. Three versions of the generalized-alpha time integration scheme are considered: a residual form, a linear form, and a geometric form. Their consistency is discussed, and we show that the residual form, which is the most direct extension of the generalized-alpha algorithm defined in structural dynamics, should not be used for problems with large rotations. The sensitivity analysis is performed and close connections are highlighted between the structure of the sensitivity equations and of the linearized dynamic equations. Hence, algorithms developed for the original problem can be directly reused for the sensitivities. Finally, a numerical example is analysed in detail. [less ▲] Detailed reference viewed: 93 (15 ULg)A new finite element integration scheme. Application to a simple shear test of anisotropic material ; Habraken, Anne ; Duchene, Laurent in International Journal for Numerical Methods in Engineering (2008) Finite element simulations involving large strains and large displacements imply the setting up of a precise kinematics for the integration scheme. Moreover, anisotropic mechanical behaviours have to be ... [more ▼] Finite element simulations involving large strains and large displacements imply the setting up of a precise kinematics for the integration scheme. Moreover, anisotropic mechanical behaviours have to be expressed in an appropriate local reference frame. In the present paper, a computational procedure is derived from a particular velocity gradient definition. Its implementation in a finite element code is described. Application to a simple shear test is proposed. For anisotropic materials, a sinusoidal behaviour of the shear stress component is emphasized. This is due to the anisotropic yield locus and appears in the case of a saturated isotropic hardening law. [less ▲] Detailed reference viewed: 61 (23 ULg)An explicit discontinuous Galerkin method for non-linear solid dynamics. Formulation, parallel implementation and scalability properties. Noels, Ludovic ; in International Journal for Numerical Methods in Engineering (2008), 74 An explicit-dynamics spatially-discontinuous Galerkin (DG) formulation for non-linear solid dynamics is proposed and implemented for parallel computation. Discontinuous Galerkin methods have particular ... [more ▼] An explicit-dynamics spatially-discontinuous Galerkin (DG) formulation for non-linear solid dynamics is proposed and implemented for parallel computation. Discontinuous Galerkin methods have particular appeal in problems involving complex material response, e.g. non-local behavior and failure, as, even in the presence of discontinuities, they provide a rigorous means of ensuring both consistency and stability. In the proposed method, these are guaranteed: the former by the use of average numerical fluxes, and the latter by the introduction of appropriate quadratic terms in the weak formulation. The semi-discrete system of ordinary differential equations is integrated in time using a conventional second-order central-difference explicit scheme. A stability criterion for the time integration algorithm, accounting for the influence of the DG discretization stability, is derived for the equivalent linearized system. This approach naturally lends itself to efficient parallel implementation. The resulting DG computational framework is implemented in three dimensions via specialized interface elements. The versatility, robustness and scalability of the overall computational approach are all demonstrated in problems involving stress-wave propagation and large plastic deformations. [less ▲] Detailed reference viewed: 91 (10 ULg)Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method ; ; Béchet, Eric et al in International Journal for Numerical Methods in Engineering (2008), 76(5), 727-748 A numerical technique for non-planar three-dimensional linear elastic crack growth simulations is proposed. This technique couples the extended finite element method (X-FEM) and the fast marching method ... [more ▼] A numerical technique for non-planar three-dimensional linear elastic crack growth simulations is proposed. This technique couples the extended finite element method (X-FEM) and the fast marching method (FMM). In crack modeling using X-FEM, the framework of partition of unity is used to enrich the standard finite element approximation by a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields. The initial crack geometry is represented by two level set functions, and Subsequently signed distance functions are used to maintain the location of the crack and to compute the enrichment functions that appear in the displacement approximation. Crack modeling is performed without the need to mesh the crack, and crack propagation is simulated without remeshing. Crack growth is conducted using FMM; unlike a level set formulation for interface capturing, no iterations nor any time step restrictions are imposed in the FMM. Planar and non-planar quasi-static crack growth simulations are presented to demonstrate the robustness and versatility of the proposed technique. Copyright (C) 2008 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 64 (5 ULg)A natural neighbour method for linear elastic problems based on Fraeijs de Veubeke variational principle Cescotto, Serge ; in International Journal for Numerical Methods in Engineering (2007), 71(9), 1081-1101 The natural neighbour method can be considered as belonging to the meshless methods. Classically, the development of this method is based on the virtual work principle. In the present paper, we use the ... [more ▼] The natural neighbour method can be considered as belonging to the meshless methods. Classically, the development of this method is based on the virtual work principle. In the present paper, we use the natural neighbour method for 2D domains starting from the Fraeijs de Veubeke variational principle and we approximate separately the displacement field, the stress field and the strain field: the assumed strains and the assumed stresses are constant over each Voronoi cell, the assumed surface reactions are constant along the edge where the displacements are imposed, while the assumed displacements are interpolated by Laplace interpolants. In the absence of body forces, it is shown that the calculation of integrals on the area of the solid domain can be avoided: only integrals on the edges of the Voronoi cells are necessary. On the other hand, displacements can be imposed in the average sense on some boundaries of the domain. Patch tests and sot-tie applications in the elastic domain are given in the paper and show the effectiveness of the method. Copyright (C) 2007 John Wiley [less ▲] Detailed reference viewed: 31 (6 ULg)The global modal parameterization for non-linear model-order reduction in flexible multibody dynamics Bruls, Olivier ; Duysinx, Pierre ; Golinval, Jean-Claude in International Journal for Numerical Methods in Engineering (2007), 69(5), 948-977 In flexible multibody dynamics, advanced modelling methods lead to high-order non-linear differential-algebraic equations (DAEs). The development of model reduction techniques is motivated by control ... [more ▼] In flexible multibody dynamics, advanced modelling methods lead to high-order non-linear differential-algebraic equations (DAEs). The development of model reduction techniques is motivated by control design problems, for which compact ordinary differential equations (ODEs) in closed-form are desirable. In a linear framework, reduction techniques classically rely on a projection of the dynamics onto a linear subspace. In flexible multibody dynamics, we propose to project the dynamics onto a submanifold of the configuration space, which allows to eliminate the non-linear holonomic constraints and to preserve the Lagrangian structure. The construction of this submanifold follows from the definition of a global modal parameterization (GMP): the motion of the assembled mechanism is described in terms of rigid and flexible modes, which are configuration-dependent. The numerical reduction procedure is presented, and an approximation strategy is also implemented in order to build a closed-form expression of the reduced model in the configuration space. Numerical and experimental results illustrate the relevance of this approach. Copyright (c) 2006 John Wiley [less ▲] Detailed reference viewed: 119 (48 ULg)Efficient Visualization of High-Order Finite Elements ; ; et al in International Journal for Numerical Methods in Engineering (2007), 69(4), 750--771 Detailed reference viewed: 18 (1 ULg)A variational formulation of constitutive models and updates in non-linear finite viscoelasticity ; Ponthot, Jean-Philippe ; Stainier, Laurent in International Journal for Numerical Methods in Engineering (2006), 65(11), 1831-1864 The purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a ... [more ▼] The purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a minimum principle within each load increment. The set of internal variables is strain-based and employs, according to the specific model chosen, a multiplicative decomposition of strain into elastic and viscous components. The present approach shares the same technical procedures used for analogous models of plasticity or viscoplasticity, such as the Solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration. However. instead of using the classical decomposition of inelastic strains into amplitude and direction, we take advantage of a spectral decomposition that provides additional facilities to accommodate, into simple analytical expressions, a wide set of specific models. Moreover, appropriate choices of the constitutive potentials allow the reproduction of other formulations in the literature. The final part of the paper presents a set of numerical examples in order to explore the characteristics of the formulation as well as its applicability to usual large-scale FEM analyses. Copyright (c) 2005 John Wiley [less ▲] Detailed reference viewed: 23 (1 ULg)Monolithic modelling of electro-mechanical coupling in micro-structures Rochus, Véronique ; ; Golinval, Jean-Claude in International Journal for Numerical Methods in Engineering (2006), 65(4), 461-493 The purpose of the present work is to model and to simulate the Coupling between the electric and mechanical fields. A new finite element approach is proposed to model strong electro-mechanical coupling ... [more ▼] The purpose of the present work is to model and to simulate the Coupling between the electric and mechanical fields. A new finite element approach is proposed to model strong electro-mechanical coupling in micro-structures with capacitive effect. The proposed approach is based oil it monolithic formulation: the electric and the mechanical fields are solved simultaneously in the same formulation. This method provides a tangent stiffness matrix for the total coupled problem which allows to determine accurately the pull-in voltage and the natural frequency of electro-mechanical systems such as MEMs. To illustrate the methodology results are Shown For the analysis of a micro-bridge. Copyright (c) 2005 John Wiley [less ▲] Detailed reference viewed: 41 (8 ULg)A 2.5 D finite element model for bending and straightening in continuous casting of steel slabs Pascon, Frédéric ; Cescotto, Serge ; Habraken, Anne in International Journal for Numerical Methods in Engineering (2006), (68), 125-149 This paper presents a bi-dimensional slice model of the continuous casting process developed to focus on the risk of transverse cracking during bending and straightening of steel slabs. The model is based ... [more ▼] This paper presents a bi-dimensional slice model of the continuous casting process developed to focus on the risk of transverse cracking during bending and straightening of steel slabs. The model is based on the finite element method and it integrates both thermal and mechanical aspects: temperature evolution, solidification, stress and strain developments. Generalized plain strain conditions are applied in the casting direction, allowing taking account of the extraction force applied to the slab as well as strains in this direction. The model also includes an original solution to counteract the generally wrong modelling of slab bulging with such slice models. The model has been applied to an industrial case of slab casting. Some numerical results illustrate the accuracy of the model compared to results of other models, measurements and observations on the caster. Transverse cracks are predicted to be the most likely to occur at the edge on the upper face, at the end of straightening of the slab. This is due to the combination of low ductility of the material with tensile stress and elongation in the casting direction in the straightening zone. This conclusion has been confirmed by the examination of slabs that present transverse cracks. [less ▲] Detailed reference viewed: 133 (5 ULg) |
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