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See detailA One-Field Discontinuous Galerkin Formulation of Non-Linear Kirchhoff-Love Shells
Noels, Ludovic ULg

Conference (2009)

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior. This is particularly appealing ... [more ▼]

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior. This is particularly appealing for problems involving high-order derivatives, since discontinuous Galerkin (DG) methods can also be seen as a means of enforcing higher-order continuity requirements. Recently, DG formulations of linear and non-linear Kirchhoff-Love shell theories have been proposed. This new one-field formulations take advantage of the weak enforcement in such a way that the displacements are the only discrete unknowns, while the C1 continuity is enforced weakly. The resulting one field formulation is a simple and efficient method to model thin structures and can be applied to various computational methods. [less ▲]

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See detailInfluence of Adhesive Rough Surface Contact on Micro-Switches
Wu, Ling ULg; Rochus, Véronique ULg; Noels, Ludovic ULg et al

Scientific conference (2009)

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See detailA discontinuous Galerkin formulation of non-linear Kirchhoff–Love shells
Noels, Ludovic ULg

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 ▲]

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See detailComputational biology — Modeling of primary blast effects on the central nervous system
Moore, David; Jérusalem, Antoine; Nyen, Michelle et al

in NeuroImage (2009), 47(Sup. 2), 10-20

Objectives Recent military conflicts in Iraq and Afghanistan have highlighted the wartime effect of traumatic brain injury. The reason for the prominence of TBI in these particular conflicts as opposed to ... [more ▼]

Objectives Recent military conflicts in Iraq and Afghanistan have highlighted the wartime effect of traumatic brain injury. The reason for the prominence of TBI in these particular conflicts as opposed to others is unclear but may result from the increased survivability of blast due to improvements in body armor. In the military context blunt, ballistic and blast effects may all contribute to CNS injury, however blast in particular, has been suggested as a primary cause of military TBI. While blast effects on some biological tissues, such as the lung, are documented in term of injury thresholds, this is not the case for the CNS. We hypothesized that using bio-fidelic models, allowing for fluid-solid interaction and basic material properties available in the literature, that a blast wave would interact with CNS tissue and cause a possible concussive effect. Methods The blast shockwave on CNS tissue was modeled using a coupled computational fluid-solid dynamic simulation. The model included a complex finite element mesh of the head and intra-cranial contents. The effects of threshold and 50% lethal blast lung injury were compared with concussive impact injury using the full head model allowing know upper and lower bounds of tissue injury to be applied using pulmonary injury as the reference tissue. Results The effects of a 50% lethal dose blast lung injury (LD50) were comparable with concussive impact injury using the DVBIC – MIT full head model. Interpretation CNS blast concussive effects were found to be similar between impact mild TBI and the blast field associated with LD50 lung blast injury sustained without personal protective equipment. With the ubiquitous use of personal protective equipment this suggests that blast concussive effects may more readily occur in personnel due to enhanced survivability in the current conflicts. [less ▲]

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See detailA Discontinuous Galerkin Formulation of Kirchhoff-Love Shells: From Linear Elasticity to Finite Deformations
Noels, Ludovic ULg; Radovitzky, Raul

Conference (2008, June)

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior [1]. When considering problems ... [more ▼]

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior [1]. When considering problems involving high-order derivatives, discontinuous Galerkin methods can also be seen as a means of enforcing higher-order continuity requirements in a weak manner [2,3]. Recently, the authors [4] have proposed a DG formulation for Kirchhoff-Love shell theory for which both the membrane and the bending response of the shell are considered. The proposed one-field formulation takes advantage of the weak enforcement in such a way that the displacements are the only discrete unknowns, while the C1 continuity is enforced weakly. The consistency, stability and rate of convergence of the numerical method are demonstrated for the case of a linear elastic material. In this work, this method is extended to shell problems involving finite displacements and finite deformations. [less ▲]

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See detailA first-order energy-dissipative momentum-conserving scheme for elasto-plasticity using the variational updates formulation
Noels, Ludovic ULg; Stainier, Laurent ULg; Ponthot, Jean-Philippe ULg

in Computer Methods in Applied Mechanics & Engineering (2008), 197(6-8), 706726

In a previous paper [L. Noels, L. Stainier, J.-P. Ponthot, An energy momentum conserving algorithm using the variational formulation of visco-plastic updates, Int. J. Numer. Methods Engrg. 65 (2006) 904 ... [more ▼]

In a previous paper [L. Noels, L. Stainier, J.-P. Ponthot, An energy momentum conserving algorithm using the variational formulation of visco-plastic updates, Int. J. Numer. Methods Engrg. 65 (2006) 904-942] the authors demonstrated the efficiency of the variational formulation of elasto-plastic updates to develop energy-momentum conserving time integration algorithms. Indeed, within such a framework, the stress tensor always derives from an incremental potential, even when plastic behavior is considered. Therefore the verification of the conservation of energy in the non-linear range can easily be demonstrated: the sum of the reversible stored energy and irreversible dissipated energy exactly corresponds to the work of the external forces applied to the structure. Although this formulation was shown to be accurate and robust, the introduction of numerical dissipation for high-frequency numerical modes can be necessary to simulate complex phenomena. In this work, we propose a modification of the variational updates framework to introduce this numerical property, leading to a new energy-dissipative momentum-conserving time-integration algorithm for elasto-plasticity. (c) 2007 Elsevier B.V. All rights reserved. [less ▲]

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See detailComparative study of numerical explicit schemes for impact problems
Nsiampa, Nestor; Ponthot, Jean-Philippe ULg; Noels, Ludovic ULg

in International Journal of Impact Engineering (2008), 35(12), 1688-1694

Explicit numerical schemes are used to integrate in time finite element discretization methods. Unfortunately, these numerical approaches can induce high-frequency numerical oscillations into the solution ... [more ▼]

Explicit numerical schemes are used to integrate in time finite element discretization methods. Unfortunately, these numerical approaches can induce high-frequency numerical oscillations into the solution. To eliminate or to reduce these oscillations, numerical dissipation can be introduced. The paper deals with the comparison of three different explicit schemes: the central difference scheme which is a nondissipative method, the Hulbert Chung dissipative explicit scheme and the Tchamwa-Wielgosz dissipative scheme. Particular attention is paid to the study of these algorithms’ behavior in problems involving high-velocity impacts like Taylor anvil impact and bullet-target interactions. It has been shown that Tchamwa-Wielgosz scheme is efficient in filtering the high-frequency oscillations and is more dissipative than Hulbert Chung explicit scheme. Although its convergence rate is only first order, the loss of accuracy remains limited to acceptable values. [less ▲]

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See detailAn explicit discontinuous Galerkin method for non-linear solid dynamics. Formulation, parallel implementation and scalability properties.
Noels, Ludovic ULg; Radovitzky, Raúl

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 ▲]

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See detailA new discontinuous Galerkin method for Kirchhoff-Love shells
Noels, Ludovic ULg; Radovitzky, Raúl

in Computer Methods in Applied Mechanics & Engineering (2008), 197

Discontinuous Galerkin methods (DG) have particular appeal in problems involving high-order derivatives since they provide a means of weakly enforcing the continuity of the unknown-field derivatives. This ... [more ▼]

Discontinuous Galerkin methods (DG) have particular appeal in problems involving high-order derivatives since they provide a means of weakly enforcing the continuity of the unknown-field derivatives. This paper proposes a new discontinuous Galerkin method for Kirchhoff–Love shells considering only the membrane and bending response. The proposed one-field method utilizes the weak enforcement in such a way that the displacements are the only unknowns, while the rotation continuity is weakly enforced. This work presents the formulation of the new discontinuous Galerkin method for linear elastic shells, demonstrates the consistency and stability of the proposed framework, and establishes the method’s convergence rate. After a description of the formulation implementation into a finite-element code, these properties are demonstrated on numerical applications. [less ▲]

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See detailIdentificación de parámetros de viscoelasticidad finita aplicada a la simulación del comportamiento mecánico de masa encefálica
Fancello, Eduardo; Vigneron, Lara; Noels, Ludovic ULg et al

in Congreso Iberoamericano de Ingenieria Mecanica (2007, October)

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See detailDevelopment of discontinuous Galerkin method for linear strain gradient elasticity
Chandran, Ram B; Noels, Ludovic ULg; Radovitzky, Raul

Conference (2007)

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See detailA New Discontinuous Galerkin Formulation for Kirchhoff-Love Shells
Noels, Ludovic ULg; Radovitzky, Raul

Conference (2007)

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See detailNumerical simulation of the fluid-structure interaction between air blast waves and free-standing plates
Kambouchev, Nayden; Noels, Ludovic ULg; Radovitzky, Raúl

in Computers & Structures (2007), 85(nov-14 Sp. Iss. SI), 923931

A numerical method is used to compute the flow field corresponding to blast waves of different incident profiles propagating in air and impinging on free-standing plates. The method is suitable for the ... [more ▼]

A numerical method is used to compute the flow field corresponding to blast waves of different incident profiles propagating in air and impinging on free-standing plates. The method is suitable for the consideration of compressibility effects in the fluid and their influence on the plate dynamics. The history of the pressure experienced by the plate is extracted from numerical simulations for arbitrary blast strengths and plate masses and used to infer the impulse per unit area transmitted to the plate. The numerical results complement some recent analytical solutions in the intermediate range of plate masses and arbitrary blast intensities where exact solutions are not available. The resulting beneficial effect of the fluid-structure interaction (FSI) in reducing transmitted impulse in the presence of compressibility effects is discussed. In particular, it is shown that in order to take advantage of the impulse reduction provided by the FSI effect, large plate displacements are required which, in effect, may limit the practical applicability of exploiting FSI effects in the design of blast-mitigating systems. (C) 2006 Elsevier Ltd. All rights reserved. [less ▲]

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See detailFluid-structure interaction effects in the dynamic response of free-standing plates to uniform shock loading
Kambouchev, Nayden; Radovitzky, Raúl; Noels, Ludovic ULg

in Journal of Applied Mechanics (2007), 74

The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and ... [more ▼]

The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and interpretation of fluid–structure interaction (FSI) experiments in shock tubes. In contrast to previous work corresponding to the case of incident blast profiles of exponential distribution, all asymptotic limits obtained here are exact. The contributions include the extension of Taylor’s FSI analysis for acoustic waves, the exact analysis of the asymptotic limits of very heavy and very light plates for arbitrary shock intensity, and a general formula for the transmitted impulse in the intermediate plate mass range. One of the implications is that the impulse transmitted to the plate can be expressed univocally in terms of a single nondimensional compressible FSI parameter. [less ▲]

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See detailIntroduction of Numerical Dissipation in the Variational Updates Framework for Elasto-Plastic Constitutive Models
Noels, Ludovic ULg; Stainier, Laurent ULg; Ponthot, Jean-Philippe ULg

(2007)

The most widely used time integration algorithms for finite-element, based on the Newmark family, are numerically stable only for linear models. Using a variational formulation of elasto-plastic updates ... [more ▼]

The most widely used time integration algorithms for finite-element, based on the Newmark family, are numerically stable only for linear models. Using a variational formulation of elasto-plastic updates for which the stress tensor always derives from an incremental potential, even when plastic behavior is considered, a new Energy-Dissipative Momentum Conserving time integration algorithms can easily be developed. Indeed, the incremental potential guarantees the verification of the numerical dissipation of energy for non-linear elasto-plastic dynamics. [less ▲]

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See detailA New Energy-Dissipative Momentum-Conserving Time Integration Scheme Using the Variational Updates Framework.
Noels, Ludovic ULg; Stainier, Laurent ULg; Ponthot, Jean-Philippe ULg

(2007)

Although they are the most widely used time integration algorithms for finite-element discretizations, algorithms based on the Newmark family are numerically stable only for linear models. To overcome ... [more ▼]

Although they are the most widely used time integration algorithms for finite-element discretizations, algorithms based on the Newmark family are numerically stable only for linear models. To overcome that drawback, researches have recently focused on time integration algorithms stable in the non-linear range, leading to the development of Energy Momentum Conserving Algorithms or EMCA. A new Energy Momentum Conserving Algorithm was recently presented by the authors for elasto-plastic material models. This algorithm is based on a variational formulation of elasto-plastic updates for which the stress tensor always derives from an incremental potential, even when plastic behavior is considered. In this work this formalism is used to develop Energy-Dissipative Momentum-Conserving time integration algorithms, which have property of being stable in non-linear range, but also dissipate high-frequency numerical modes to improve the convergence properties. Using the potential existence of the variational updates framework, the verification of the numerical dissipation of energy in the non-linear range can easily be demonstrated. [less ▲]

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See detailAlternative approaches for the derivation of discontinuous Galerkin methods for nonlinear mechanics
Noels, Ludovic ULg; Radovitzky, Raúl

in Journal of Applied Mechanics (2007), 74

Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element ... [more ▼]

Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element interfaces of the discretization. In order to ensure consistency and stability of the formulation, this approach requires the definition of a numerical flux and a stabilization term. Discontinuous Galerkin methods may also be formulated from a linear combination of the governing and compatibility equations weighted by suitable operators. A third approach based on a variational statement of a generalized energy functional has been proposed recently for finite elasticity. This alternative approach naturally leads to an expression of the numerical flux and the stabilization terms in the context of large deformation mechanics problems. This paper compares these three approaches and establishes the conditions under which identical formulations are obtained. [less ▲]

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