On some aspects of the CNEM implementation in 3D in order to simulate high speed machining or shearing

his paper deals with the implementation in 3D of the constrained natural element method (CNEM) in order to simulate material forming involving large strains. The CNEM is a member of the large family of mesh-free methods, but is at the same time very close to the finite element method. The CNEM’s shape function is built using the constrained Voronoï diagram (the dual of the constrained Delaunay tessella- tion) associated with a domain defined by a set of nodes and a description of its border. The use of the CNEM involves three main steps. First, the constrained Voronoï diagram is built. Thus, for each node, a Voronoï cell is geometrically defined, with respect of the boundary of the domain. Then, the Sibson-type CNEM shape functions are computed. Finally, the discretization of a generic variational for- mulation is defined by invoking an ‘‘stabilized conforming nodal integration’’. In this work, we focus especially on the two last points. In order to compute the Sibson shape function, five algorithms are pre- sented, analyzed and compared, two of them are developed. For the integration task, a discretization strategy is proposed to handle domains with strong non-convexities. These approaches are validated on some 3D benchmarks in elasticity under the hypothesis of small transformations. The obtained results are compared with analytical solutions and with finite elements results. Finally, the 3D CNEM is applied for addressing two forming processes: high speed shearing and machining

On some aspects of the CNEM implementation in 3D in order to simulate high speed machining or shearing

his paper deals with the implementation in 3D of the constrained natural element method (CNEM) in order to simulate material forming involving large strains. The CNEM is a member of the large family of mesh-free methods, but is at the same time very close to the finite element method. The CNEM’s shape function is built using the constrained Voronoï diagram (the dual of the constrained Delaunay tessella- tion) associated with a domain defined by a set of nodes and a description of its border. The use of the CNEM involves three main steps. First, the constrained Voronoï diagram is built. Thus, for each node, a Voronoï cell is geometrically defined, with respect of the boundary of the domain. Then, the Sibson-type CNEM shape functions are computed. Finally, the discretization of a generic variational for- mulation is defined by invoking an ‘‘stabilized conforming nodal integration’’. In this work, we focus especially on the two last points. In order to compute the Sibson shape function, five algorithms are pre- sented, analyzed and compared, two of them are developed. For the integration task, a discretization strategy is proposed to handle domains with strong non-convexities. These approaches are validated on some 3D benchmarks in elasticity under the hypothesis of small transformations. The obtained results are compared with analytical solutions and with finite elements results. Finally, the 3D CNEM is applied for addressing two forming processes: high speed shearing and machining

A general method to accurately simulate material removal in virtual machining of flexible workpieces

Multi-axis milling and other computer numerical control machining processes allow us to create very complex geometries and thin parts. In this context, virtual machining is a powerful tool, but the simultaneous vibrations of the tool and workpiece are not easy to define and take into account. This paper presents a general method with which to simulate material removal when both the workpiece and tool are assumed to be non-rigid. We consider that they both vibrate when we define the Boolean chip. This is not usually considered with the aim of predicting the machined surface vibrations and the resulting geometric defects including roughness. By extending the material frame associated with the non-rigid workpiece, our method precisely defines the material removal for any tool or workpiece. It then allows us to establish a method of deriving efficient numerical approximations with which to simulate a succession of machining operations from roughening to finishing. Two kinds of finite element approximations are linked. One is a classical elastic finite element model including damping. The second, which is kinematically linked to the first, accurately describes the relative motion of each part of the tool with respect to the workpiece, and ensures the description of material removal and related forces. Two industrial examples show the potential of the method

Simulation of the laser drilling process with the Constraint Natural Element Method

These works present a numerical alternative to the simulation of the laser drilling process. The use of the finite element method to modeling the hole creation during a laser pulse shows difficulties in front of a moving boundary problem. This moving boundary is induced by a fast phase transformation and also by high thermal gradient. The C-NEM (Constraint Natural Element Method) was tested in order to solve these numerical difficulties and to use the high potential of this original method. The physical interaction of the laser drilling will be reminded and the chosen mathematical model will be specified. A simulation was made with the data for pure iron in order to validate the numerical choice

Gymnodinium chlorophorum causante de proliferaciones de altas biomasas en aguas recreativas de las Islas Baleares (veranos 2004-2006)

[ESP] Diversas playas del archipiélago Balear sufren discoloraciones asociadas a las proliferaciones del dinoflagelado Alexandrium taylori. El fenómeno es recurrente y conocido por la población y administración locales. Los resultados del presente trabajo muestran por primera vez la presencia, en la cuenca Calatano-Balear, de Gymnodinium chlorophorum, un dinoflagelado gymnodial productor de proliferaciones de altas biomasas y discoloraciones desde el año 82 en las costa francesas del Atlántico. La concentración máxima (12·106 células L-1) fue registrada en Eivissa, el verano de su primera detección (2004). Durante los veranos 2005 y 2006, el fenómeno parece recurrente, ampliándose a varias playas. La especie puede provocar proliferaciones monoespecíficas y mantenerse durante un mes con concentraciones superiores a 105 células L-1.Al Convenio para la evaluación y monitorización de la calidad de aguas costeras de las Islas Baleares (2004-2006) por la concesión de una beca predoctoral a Hassina Illoul. Agradecimiento a J-M Fortuño (microscopia electrónica CMIMA, Barcelona)

Effects of a bent structure on the linear viscoelastic response of diluted carbon nanotube suspensions

Commonly isolated carbon nanotubes in suspension have been modelled as a perfectly straight structure. Nevertheless, single-wall carbon nanotubes (SWNTs) contain naturally side-wall defects and, in consequence, natural bent configurations. Hence, a semi-flexile filament model with a natural bent configuration was proposed to represent physically the SWNT structure. This continuous model was discretized as a non-freely jointed multi-bead-rod system with a natural bent configuration. Using a Brownian dynamics algorithm the dynamical mechanical contribution to the linear viscoelastic response of naturally bent SWNTs in dilute suspension was simulated. The dynamics of such system shows the apparition of new relaxation processes at intermediate frequencies characterized mainly by the activation of a mild elasticity. Storage modulus evolution at those intermediate frequencies strongly depends on the flexibility of the system, given by the rigidity constant of the bending potential and the number of constitutive rods

Modeling laser drilling in percussion regime using constraint natural element method

The laser drilling process is the main process used in machining procedures on aeronautic engines, especially in the cooling parts. The industrial problematic is to reduce geometrical deviations of the holes and defects during manufacturing. The interaction between a laser beam and an absorbent metallic matter in the laser drilling regime involves thermal and hydrodynamical phenomenon. Their role on the drilling is not yet completely understood and a realistic simulation of the process could contribute to a better understanding of these phenomenon. The simulation of such process induces strong numerical difficulties. This work presents a physical model combined with the use of the original Constraint Natural Element Method to simulate the laser drilling. The physical model includes solid/liquid and liquid/vapor phase transformations, the liquid ejection and the convective and conductive thermal exchanges. It is the first time that all these phenomena are included in a modelling and numerically solved in a 2D axisymmmetric problem. Simulations results predict most of measurements (hole geometry, velocity of the liquid ejection and laser drilling velocity) without adjusting any parameter

Simulation numérique du perçage laser par la méthode C-NEM

Ces travaux présentent une alternative numérique au problème de simulation du procédé de perçage par laser. L’utilisation des éléments finis pour modéliser la propagation du trou au cours du temps montre des limites face à un problème de frontières mobiles induit par un changement de phase rapide et des forts gradients thermiques. L’utilisation d’un code C-NEM a donc été testé avec comme objectif de résoudre ces difficultés numériques et d’utiliser le fort potentiel de cette méthode originale. Le principe physique du perçage laser sera rappelé et le modèle mathématique choisi pour le modéliser sera précisé. Un cas test de simulation a été réalisé avec les grandeurs physiques du fer pur afin de valider le choix du code C-NEM

Implementation of surface tension force in fluid flow during reactive rotational molding

During Reactive Rotational Molding (RRM), it is very important to predict the fluid flow in order to obtain the piece with homogeneous shape and high quality. This prediction may be possible by simulation the fluid flow during rotational molding. In this study we have used a mixture of isocyanate and polyol as reactive system. The kinetic rheological behaviors of thermoset polyurethane are investigated in anisothermal conditions. Thanks to these, rheokinetik model of polyurethane was identified. Then, to simulate the RRM, we have applied Smoothed Particles Hydrodynamics (SPH) method which is suited method to simulate the fluid flow with free surface such as occurs at RRM. Modelling and simulating reactive system flow depend on different parameters; one of them is the surface tension of reactive fluid. To implement force tension surface, the interface between polymer and air is dynamically tracked by finding the particles on this border. First, the boundary particles are detected by free-surface detection algorithm developed by Barecasco, Terissa and NAA [1, 2] in two and three dimension. Then, analytical and geometrical algorithms have been used for interface reconstructions. The aim of this work is the implementation of surface tension force in the SPH solver applied to RRM. To illustrate that, we used novel and simple geometric algorithm fitting circle and fitting sphere, in two and three dimensional configurations, respectively. The model has been validated using a well-known dam break test case which covered the experimental data

Simulation numérique du perçage laser par la méthode C-NEM

Ces travaux présentent une alternative numérique au problème de simulation du procédé de perçage par laser. L’utilisation des éléments finis pour modéliser la propagation du trou au cours du temps montre des limites face à un problème de frontières mobiles induit par un changement de phase rapide et des forts gradients thermiques. L’utilisation d’un code C-NEM a donc été testé avec comme objectif de résoudre ces difficultés numériques et d’utiliser le fort potentiel de cette méthode originale. Le principe physique du perçage laser sera rappelé et le modèle mathématique choisi pour le modéliser sera précisé. Un cas test de simulation a été réalisé avec les grandeurs physiques du fer pur afin de valider le choix du code C-NEM