Comparison of Field Transfer Methods between two meshes

In many cases, the numerical computation of mechanical problem with Finite Element Method has to transfer some information between two different meshes. For example, if a remeshing is needed or if several meshes are used (e.g. one for a thermal problem and another one for a mechanical problem). In spite of the research on the Transfer Methods, none of them has been so far clearly established as the best. Each method has advantages and disadvantages. Many problems can happen during the field transfer, like the minimization of the numerical diffusion, the value of the field on the boundaries, etc. This paper compares on the one hand the performances of the Field Transfer Method by classical interpolation with on the other hand one using Mortar Elements. The comparison of the two methods is based on two indicators: the numerical diffusion and the evaluation of the field on the boundaries. In this paper, only the continuous fields are considered

A variational framework for nonlinear viscoelastic models in finite deformation regime

International audienceThis work presents a general framework for constitutive viscoelastic models in the finite deformation regime. The approach is qualified as variational since the constitutive updates consist of a minimization problem within each load increment. The set of internal variables is strain-based and uses a multiplicative decomposition of strain in elastic and viscous components. Spectral decomposition is explored in order to accommodate, into analytically tractable expressions, a wide set of specific models. Moreover, it is shown that, through appropriate choices of the constitutive potentials, the proposed formulation is able to reproduce results obtained elsewhere in the literature. Finally, numerical examples are included to illustrate the characteristics of the present formulation. MSC: 74C20; 74D10; 74S05; 35J5

Automatic time stepping algorithms for implicit numerical simulations of blade/casing interactions

peer reviewedAn automatic time stepping algorithm for non-linear problems, solved by implicit schemes, is presented. The time step computation is based on the estimation of an integration error calculated from the acceleration difference. It is normalised according to the size of the problem and the integration parameters. This time step control algorithm modifies the time step size only if the problem has a long time physical change. Additionally, the Hessian matrix can be kept constant for several iterations, even though the problem is non-linear. A criterion selecting if the Hessian matrix must be calculated or not is developed. Finally, a criterion of iterations divergence is also proposed. It avoids the determination, by the user, of a maximal iteration number. This minimises the total number of iterations, and thus the computation cost. Industrial numerical examples are presented that demonstrate the performances (precision and computational cost) of the algorithms

Détermination automatique de la taille du pas de temps pour les schémas implicites en dynamique non-linéaire

Pour les problèmes caractérisés par de fortes non-linéarités, ainsi que des phénomènes d'impacts et de contacts, une stratégie d'intégration à pas de temps variables est particulièrement intéressante. Ces phénomènes sont par exemple rencontrés lors de l'étude dynamique d'une interaction aube-carter d'un moteur d'avion, le cas le plus critique étant la perte de l'aube. Une stratégie d'intégration implicite à pas de temps constant donne rarement satisfaction du fait qu'il est pratiquement impossible de déterminer une durée de pas qui ne conduise pas à la divergence ou à un coût de calcul prohibitif. Une gestion automatique du pas de temps, qui tient compte de l'histoire récente des accélérations dans le corps considéré, est proposée. En fait, l'algorithme est basé sur la mesure de l'erreur d'intégration des équations d'équilibre. Cela permet d'intégrer correctement les phénomènes transitoires avec un pas de temps très long (en régime) ou très petit (lors de la perte d'aube), en garantissant une bonne précision en un temps de calcul raisonnable. De plus, un algorithme qui décide automatiquement de recalculer ou non, la matrice hessienne est proposé. Cet algorithme permet d'éviter un nombre important de remises à jour de cette matrice, ce qui permet de réduire le coût de calcul tout en assurant la convergence. Enfin, un critère de divergence des itérations est proposé. Afin d'illustrer l'efficacité des algorithmes développés, des simulations numériques sont présentées. Il s'agit aussi bien de problèmes académiques que de problèmes industriels (contacts aubes carter)

Particle Finite Element Method for simulations of Selective Laser Melting with vaporization

editorial reviewedThe purpose of this work is the simulation of selective laser melting processes. Such processes involve multiple physical phenomena that need to be taken into account altogether such as thermo-mechanical coupling, solid-liquid-solid phase change, surface tension and vaporization. The variety of different physical phenomena, as well as the presence of a highly deformed fluid free surface, implies multiple constraints on the required numerical procedure. Notably, the need to compute the free surface position and curvature leads to complex interface tracking algorithms in the widely-used Eulerian-based models. The Particle Finite Element Method (PFEM), a Lagrangian method with fast triangulation and boundary identification algorithms, has been chosen to overcome some of the difficulties mentioned previously. A new version of the 2D/3D PFEM code presented in (S. Février, “Development of a 3D Compressible Flow Solver for PFEM Fluid Simulations”, ULiège Master Thesis, 2020) has been developed to take into account the aforementioned physical phenomena, notably Marangoni forces and recoil pressure, and the interactions with a laser. Alongside the presentation of the mathematical formulation and the description of its numerical implementation, some simulations involving a moving laser melting a block of material are presented and discusse

Particle Finite Element Method for simulations of Selective Laser Melting with vaporization

editorial reviewedThe purpose of this work is the simulation of selective laser melting processes. Such pro- cesses involve multiple physical phenomena that need to be taken into account altogether such as thermo-mechanical coupling, solid-liquid-solid phase change, surface tension and vaporization [Cook et al., 2020]. The variety of different physical phenomena, as well as the presence of a highly deformed fluid free surface, implies multiple constraints on the required numerical procedure. Notably, the need to compute the free surface position and curvature leads to complex interface tracking algorithms in the widely-used Eulerian-based models [Chen, 2018]. The Particle Finite Element Method (PFEM), a Lagrangian method with fast triangulation and boundary identification algorithms, has been chosen to overcome some of the diffi- culties mentioned previously [Février, 2020]. A new version of the 2D/3D PFEM code presented in [Février, 2020 ; Cerquaglia 2019] has been developed to take into account the aforementioned physical phenomena, notably Marangoni forces and recoil pressure, and the interactions with a laser. Alongside the presentation of the mathematical formulation and the description of its numerical im- plementation, some simulations involving a moving laser melting a block of material are presented and discussed