A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications

in International Journal for Numerical Methods in Engineering (2006), 68(1), 6497

A discontinuous Galerkin formulation of the boundary value problem of finite-deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large ... [more ▼]

A discontinuous Galerkin formulation of the boundary value problem of finite-deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the DG concept can show its superiority compared to the continuous formulation. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. It is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation. The consistency and linearized stability of the method in the non-linear range as well as its convergence rate are proven. An implementation in three dimensions is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Copyright (c) 2006 John Wiley [less ▲]

Lagrangian simulations of penetration environments via mesh healing and adaptative optimisation

(2006)

In this work, we demonstrate the feasibility of fully-Lagrangian finite element simulations of the mechanics of three-dimensional penetration environments. The key enabling component is a robust library ... [more ▼]

In this work, we demonstrate the feasibility of fully-Lagrangian finite element simulations of the mechanics of three-dimensional penetration environments. The key enabling component is a robust library informed with state-of-the-art algorithms for mesh healing and optimization, which is repeatedly used during the simulations to eliminate deformation-induced mesh distortion and to maintain the quality of the numerical solution. The computational strategy effectively avoids the need to resort to artifacts such as element deletion or conversion to meshless particles which have been proposed to eliminate the issue of mesh distortion. The effectiveness of the computational strategy is demonstrated in a simulation of deep oblique penetration of a spherical-nosed steel rod on an aluminum target. [less ▲]

Simulation of crashworthiness problems with improved contact algorithms for implicit time integration

in International Journal of Impact Engineering (2006), 32(5), 799-825

When studying crashworthiness problems, contact simulation can be the source of a number of problems. A first one is the discontinuities in the normal evolution for a boundary discretized by finite ... [more ▼]

When studying crashworthiness problems, contact simulation can be the source of a number of problems. A first one is the discontinuities in the normal evolution for a boundary discretized by finite elements. Another problem is the treatment of the contact forces that can introduce numerical energy in the system. In this paper, we propose to combine a method of discontinuity smoothing with the energy-momentum consistent scheme that recently appeared in the literature. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲]

Energy conserving balance of explicit time steps to combine implicit and explicit algorithms in structural dynamics

in Computer Methods in Applied Mechanics & Engineering (2006), 195(19-22), 21692192

Recent developments have proved the advantage of combining both time implicit and time explicit integration algorithms in structural dynamics. A major problem is to define the initial conditions for the ... [more ▼]

Recent developments have proved the advantage of combining both time implicit and time explicit integration algorithms in structural dynamics. A major problem is to define the initial conditions for the implicit simulation on the basis of a solution obtained from an unbalanced explicit resolution. The unbalanced nature of the explicit algorithm leads to oscillations in the fields of interest. Therefore, the values obtained after an explicit computation cannot be used directly as initial conditions for an implicit simulation. In this paper, we develop such initial values that lead to a stable (no numerical creation of energy) and energy-conserving transition. (c) 2005 Elsevier B.V. All rights reserved. [less ▲]

Simulation of complex impact problems with implicit time algorithms: Application to a turbo-engine blade loss problem

in International Journal of Impact Engineering (2005), 32(1-4), 358386

Recent developments, in non-linear structural dynamics, have led to a new kind of implicit algorithms: the energy-momentum conserving algorithm (EMCA) and the energy-dissipative, momentum-conserving ... [more ▼]

Recent developments, in non-linear structural dynamics, have led to a new kind of implicit algorithms: the energy-momentum conserving algorithm (EMCA) and the energy-dissipative, momentum-conserving algorithm. Contrarily to commonly used algorithms, such as the explicit central difference or the alpha-generalized method, the stability of those algorithms is always ensured in the non-linear range. Thanks to this unconditional stability the only requirement on the time step size is that it must be small enough to capture the physics. This requirement is less restrictive than a conditional stability. In previous works, we have developed a new formulation of the internal forces for a hypoelastic model, that leads to an EMCA. In this paper, we will extend this formulation to an energy-dissipative, momentum-conserving algorithm. We will prove with an academic example, that our algorithm is more accurate than the alpha-generalized method in the non-linear range. Then we will simulate a blade loss problem to demonstrate the efficiency of our developments on complex dynamics simulations. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲]

Combined implicit/explicit time-integration algorithms for the numerical simulation of sheet metal forming

in Journal of Computational & Applied Mathematics (2004), 168(1-2, Sp. Iss. SI), 331-339

In order to simulate stamping processes, an explicit method, which is conditionally stable, is generally thought to be the most adapted. Such an algorithm presents the advantage of being noniterative ... [more ▼]

In order to simulate stamping processes, an explicit method, which is conditionally stable, is generally thought to be the most adapted. Such an algorithm presents the advantage of being noniterative while, the contact configuration evolves rapidly, and the conditional stability is not a disadvantage since time steps must be small enough anyway for an accurate computation. But during the springback simulation, an implicit method, which is iterative, presents the advantage of unconditional stability. The optimal solution is then to have both implicit and explicit methods readily available in the same code and to be able to switch automatically from one to the other. Criteria that decide to switch from a method to another, depending on the current dynamic, have been developed. Implicit restarting conditions are also proposed that annihilate numerical oscillations resulting from an explicit calculation. (C) 2003 Elsevier B.V. All rights reserved. [less ▲]

An energy-momentum conserving algorithm for non-linear hypoelastic constitutive models

in International Journal for Numerical Methods in Engineering (2004), 59(1), 83-114

This paper presents an extension of the energy momentum conserving algorithm, usually developed for hyperelastic constitutive models, to the hypoelastic constitutive models. For such a material no ... [more ▼]

This paper presents an extension of the energy momentum conserving algorithm, usually developed for hyperelastic constitutive models, to the hypoelastic constitutive models. For such a material no potential can be defined, and thus the conservation of the energy is ensured only if the elastic work of the deformation can be restored by the scheme. We propose a new expression of internal forces at the element level which is shown to verify this property. We also demonstrate that the work of plastic deformation is positive and consistent with the material model. Finally several numerical applications are presented. Copyright (C) 2003 John Wiley Sons, Ltd. [less ▲]

Contributions aux algorithmes d'intégration temporelle conservant l'énergie en dynamique non-linéaire des structures

Doctoral thesis (2004)

Les points fondamentaux de mes recherches consistent en une étude mathématique des algorithmes d'intégration temporelle d'une discrétisation de type éléments-finis. Les algorithmes traditionnels d ... [more ▼]

Les points fondamentaux de mes recherches consistent en une étude mathématique des algorithmes d'intégration temporelle d'une discrétisation de type éléments-finis. Les algorithmes traditionnels d'intégration temporelle (Newmark, famille alpha-généralisée, ...) peuvent introduire numériquement de l'énergie dans les systèmes non-linéaires. De nouveaux algorithmes sont dès lors apparus pour permettre d'éviter cette perte de stabilité. Lors de mes études, ces algorithmes ont été étendus, de manière originale, au traitement de la plasticité à l'aide d'un modèle de type hypo-élastique. Ils ont également été étendus au traitement généralisé, dans le cadre tridimensionnel, de l'interaction de contact. Ensuite la mise en oeuvre d'une méthode permettant de combiner, au cours du temps un algorithme implicite stable, avec un algorithme explicite traditionnel a été envisagée. La stabilité du passage d'une méthode explicite vers une méthode implicite a été démontrée par nos soins. Une définition originale de critères automatiques de choix de basculement entre les méthodes a été proposée. Des exemples numériques complexes ont mis en évidences les bonnes performances des algorithmes développés, tant du point de vue de la précision des résultats - confrontés aux résultats expérimentaux si ces derniers existent -, que du point de vue de la réduction des coûts de calcul lorsque la méthode combinée est utilisée. [less ▲]

Simulation of complex impact problems with implicit time algorithms. Application to crashworthiness problems

in Matériaux et Techniques (2004)

Recently, robust implicit energy and momentum conserving algorithms have been developed in the non-linear range. The authors extended these algorithms to hypoelasticity-based constitutive models and ... [more ▼]

Recently, robust implicit energy and momentum conserving algorithms have been developed in the non-linear range. The authors extended these algorithms to hypoelasticity-based constitutive models and introduced numerical dissipation, opening the way to more complex simulations such as blade-loss in a turbofan. [less ▲]

Combined implicit/explicit time integration algorithms for crashworthiness analysis and metal forming simulation

in Proceedings of IMPLAST'2003, 8th International Symposium on Plasticity and Impact Mechanics (2003, March)