A Virtual Element Method for Contact Modeling and Dynamics

Decreasing resources and limited energy results in a greater demand for virtual development processes and efficient product development. This trend points out the importance of digitalization and the subsequent need for efficient and accurate numerical prediction methods for product development. Due to their flexibility, numerical methods are gradually and steadily replacing physical tests in industrial product developments. The finite element method is perhaps the most well-known and widely used numerical method in industry and science. Increasing computer capabilities and further developments of these methods in recent years have increased the amount of application fields, including civil, automotive, naval, space and geo-technical engineering. However, along with complex geometries the spatial discretization of the domain emerges as a very time consuming step. Due to the fact that the classical finite element method is restricted to basic regular shaped element topologies, a more general choice of element shapes would give more flexibility. Within mesh-based methods, polygonal methods are a helpful alternative and showed great performance in engineering and science. However, most of these methods seem to need more computational effort and beside the aforementioned advantage of flexible element shapes, disadvantages appear as well. A relatively new method, the virtual element method, promises great numerical properties and can be seen as a generalization of the classical finite element method. All new methods need to be investigated for different applications in engineering and science before they can be applied commercially. This work deals with the application of the virtual element method to dynamic and elastoplastic material behavior. To deal with elastic and plastic incompressibility, a mixed virtual element formulation is presented as well. As a further development, the virtual element method is used to model three dimensional contact with different contact discretizations. A new projection algorithm is developed to manipulate the mesh at the contact interface, such that a very simple and efficient node-to-node contact formulation can be used. Various numerical examples for all aforementioned applications are performed, including benchmark problems such as the classical patch test. For comparison purposes, different finite element formulations are also adopted. As a final example, all models, including plasticity, dynamics and contact, are coupled to model mechanical impact.Eine Verringerung von Ressourcen und die damit einhergehende Energieknappheit f ¨uhren zu einem erh¨ohten Bedarf an virtuellen Entwicklungsprozessen und effizienter Produktentwicklung. Dieser Trend verdeutlicht die Bedeutung der Digitalisierung und den daraus resultierenden Bedarf an effizienten und hoch genauen numerischen Vorhersagemethoden f ¨ur die Produktentwicklung. Aufgrund ihrer Flexibilit¨at und mit steigenden Rechnerkapazit¨aten ersetzen numerische Methoden allm¨ahlich und stetig physikalische Tests in der industriellen Produktentwicklung. Die Finite Elemente Methode ist vielleicht die bekannteste und am weitesten verbreitete numerische Methode in Industrie und Wissenschaft. Durch die zunehmenden Rechnerkapazit ¨aten und die Weiterentwicklung dieser Methoden in den letzten Jahren hat sich die Zahl der Anwendungsbereiche vergr¨oßert. Numerische Methoden werden unter anderem im Bauwesen, im Automobilbau, in der Schifffahrt, in der Luft- und Raumfahrt und in der Geotechnik eingesetzt. Bei komplexen Geometrien erweist sich jedoch die r¨aumliche Diskretisierung des Gebiets als ein sehr zeitaufw¨andiger Prozess. Da die klassische Finite Elemente Methode auf einfache, regelm¨aßig geformte Elementgeometrien beschr¨ankt ist, w¨urde eine allgemeinere Auswahl von Elementgeometrien mehr Flexibilit¨at bieten. Innerhalb der netzbasierten Methoden sind polygonale Methoden eine hilfreiche Alternative und haben sich bereits in Industrie und Wissenschaft bew¨ahrt. Allerdings scheinen die meisten dieser Methoden einen h¨oheren Rechenaufwand zu erfordern, und neben dem bereits erw¨ahnten Vorteil der flexiblen Elementgeometrien treten auch gewisse Nachteile auf. Eine relativ neue Methode, die Virtuelle Elemente Methode, verspricht gute numerische Eigenschaften und kann als eine Verallgemeinerung der klassischen Finite Elemente Methode angesehen werden. Wie bei allen neuen Methoden m¨ussen auch hier verschiedene Anwendungen in der Industrie und Wissenschaft untersucht werden, bevor die Methode kommerziell eingesetzt werden kann. Diese Arbeit befasst sich mit der Anwendung der Methode der virtuellen Elemente auf dynamisches und elasto-plastisches Materialverhalten. Um elastische und plastische Inkompressibilit¨at zu behandeln, wird auch eine gemischte virtuelle Elementformulierung vorgestellt. In einem weiteren Schritt wird die Virtuelle Elemente Methode zur Modellierung dreidimensionaler Kontaktprobleme mit verschiedenen Kontaktdiskretisierungen verwendet. Es wird ein neuer Projektionsalgorithmus vorgestellt, welcher das Netz an der Kontaktschnittstelle so manipuliert, dass eine sehr einfache und effiziente Knoten-zu-Knoten Kontaktformulierung verwendet werden kann. Es werden verschiedene numerische Beispiele f ¨ur alle oben genannten Anwendungen behandelt, darunter auch Benchmark-Probleme wie der klassische Patch-Test. Um einen geeigneten Vergleich durchzuf¨uhren, werden die entwickelten Formulierungen mit verschiedene Finite Elemente Formulierungen verglichen. Als letztes Beispiel werden alle Modelle, einschließlich Plastizit¨at, Dynamik und Kontakt, gekoppelt, um einen mechanischen Stoß zu modellieren

Pressure development due to viscous fluid flow through a converging gap

The behaviour of fluid flow in industrial processes is essential for numerous applications and there have been vast amount of work on the hydrodynamic pressure generated due to the flow of viscous fluid. One major manifestation of hydrodynamic pressure application is the wire coating/drawing process, where the wire is pulled through a unit either conical or cylindrical bore filled with a polymer melt that gives rise to the hydrodynamic pressure inside the unit. The hydrodynamic pressure distribution may change during the process due to various factors such as the pulling speed, process temperature, fluid viscosity, and geometrical shape of the unit (die). This work presents the process of designing a new plasto-hydrodynamic pressure die based on a tapered-stepped-parallel bore shape; the device consists of a fixed hollow outer cylinder and an inner rotating shaft, where the hollow cylinder represents a pressure chamber and the rotating shaft represents the moving surface of the wire. The geometrical shape of the bore is provided by different shaped inserts to set various gap ratios, ancl the complex geometry of the gap between the shaft and the pressure chamber is filled with viscous fluid materials. The device allows the possibility of determining changes in the hydrodynamic pressure as the shaft speed is altered while different fluid viscosity during the process is considered. A number of experimental procedures and methods have been carried out to determine the effects of various shaft speeds by using Glycerine at 1 to 18 °C and two different types of silicone oil fluids at 1 to 25 °C on the hydrodynamic pressure and shear rate. Viscosities of the viscous fluids were obtained at atmospheric pressure by using a Cone-plate Brookfield viscometer at low shear rate ranges. Moreover, Computational fluid dynamics (CFD) was used to develop and analyze computational simulation models that demonstrate the pressure units, which studies the drawing process involving viscous fluids in a rotating system. A finite volume technique was used to observe the change in fluid viscosity during the process based on non-Newtonian characteristics at high shear rate ranges. The maximum shaft speed used in these models was 1.5m.sec'1. Results from experimental and Computational models were presented graphically and discussed

Elastic, thermal expansion, plastic and rheological processes - theory and experiment

Rocks are important examples for solid materials where, in various engineering situations, elastic, thermal expansion, rheological/viscoelastic and plastic phenomena each may play a remarkable role. Nonequilibrium continuum thermodynamics provides a consistent way to describe all these aspects in a unified framework. This we present here in a formulation where the kinematic quantities allow arbitrary nonzero initial (e.g., in situ) stresses and such initial configurations which - as a consequence of thermal or remanent stresses - do not satisfy the kinematic compatibility condition. The various characteristic effects accounted by the obtained theory are illustrated via experimental results where loaded solid samples undergo elastic, thermal expansion and plastic deformation and exhibit rheological behaviour. From the experimental data, the rheological coefficients are determined, and the measured temperature changes are also explained by the theory.Comment: 15 pages, to appear in Period. Polytech. Civil En

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Structure-preserving space-time discretization in a mixed framework for multi-field problems in large strain elasticity

The present work deals with the design of structure-preserving numerical methods in the field of nonlinear elastodynamics with an extension to multi-field problems. A new approach to the design of energy-momentum (EM) consistent time-stepping schemes for nonlinear elastodynamics is proposed. Moreover, we extend the formalism to multi-field problems

Virtual product development and testing for aerospace tube hydroforming industry : improved non-linear solid-shell element

Dans les recherches réalisées pour ce projet de thèse, il est démontré qu’une traverse existante de train d’atterrissage d’hélicoptère à patins fabriquée par pliage et érosion chimique, pourrait être remplacée par une autre traverse, dont la forme innovante est fabricable par le procédé d’hydroformage de tubes. Ce procédé présente par exemple l’avantage d’être plus respectueux de l’environnement que le procédé de fabrication actuel, car il ne nécessite pas l’utilisation de produits chimiques polluant. De plus, la méthodologie développée dans le cadre des recherches réalisées permet de prendre en compte l’histoire du matériau de la traverse dans toutes les étapes de son processus de fabrication. Les performances d’un train d’atterrissage équipé de la nouvelle traverse ont été évaluées numériquement. Des travaux, développés avec le logiciel de calculs par éléments finis ABAQUS, ont permis de mettre en évidence l’intérêt d’utiliser des éléments finis de coque solides fiables et précis. Ces éléments sont en effet capables de prendre en compte le comportement dans l’épaisseur de structures minces avec une seule couche d’éléments. Une nouvelle technique de lissage appelé «Smoothed finite element method» ou «SFEM» a retenu l’attention pour sa simplicité de mise en œuvre et son insensibilité à la distorsion de maillage parfois rencontrée dans les simulations de formage de formes complexes. Un élément de coque solide résultant linéaire développé en utilisant cette méthode SFEM pour traiter de la cinématique en membrane et en flexion a été testé avec succès au travers d’exemples classiques identifiés dans la littérature. Ce nouvel élément a montré un niveau de précision souvent supérieur à celui d’autres éléments déjà existants. En outre, un élément de coque solide à intégration réduite, capable de fonctionner avec la plupart des lois de comportement en trois dimensions et cela même en présence de structures minces a été développé. Cet élément, libre de tout blocage a montré un bon niveau de précision par rapport aux éléments existants dans le cas de problèmes implicites géométriquement linéaires et non-linéaires. L’élément a été étendu en formulation explicite puis couplé avec une loi de comportement hyper élastoplastique en trois dimensions. Il a enfin été testé dans une simulation d’hydroformage de tubes en présence de pressions élevées, de frottement et de grandes déformations.In the current work, it is shown that an existing helicopter skid landing gear cross tube, made by tube bending and chemical milling, could be replaced by another cross tube, whose innovative shape is producible by tube hydroforming. This method has for example the advantage of being more environmentally friendly than the current manufacturing process, because it does not require the use of hazardous chemicals. In addition, the methodology developed in this project takes into account the cross tube material’s history throughout the manufacturing process. Moreover, the performance of a skid landing gear equipped with this new cross tube has been evaluated numerically. This thesis simulation work has been developed with the finite element analysis software ABAQUS. It highlights the potential gains of using a reliable and accurate solid-shell finite element which is capable to take into account the through-thickness behavior of thin structures with a single layer of elements. A new smoothing technique called «Smoothed finite element method» or «SFEM» has been considered for its simplicity and insensitivity to mesh distortion, sometimes encountered while simulating complex shapes forming. A new resultant linear solid-shell element using this SFEM to deal with membrane and bending kinematics has been developed and successfully tested through classical benchmark problems found in the literature. This new element has often shown much greater level of accuracy than other existing elements. In addition, a novel reduced integration solid-shell element, able to work with most three dimensions constitutive laws even in the presence of thin structures is also discussed. This element, free of locking, shows a good accuracy level with respect to existing elements in implicit geometrically linear and non-linear benchmark problems. Its extension to explicit formulation is coupled with a three dimensions hyper elastoplastic constitutive law and tested in a tube hydroforming simulation involving high pressures, friction and large deformations

The Combined Finite/Discrete Element Method in Transient Dynamics of Reinforced Concrete Structures under Blast Loading

PhDThe research here presented has employed the newly evolved finite-discrete element method in the development of novel numerical solutions for the analysis of failure and collapse of reinforced concrete structures under hazardous blast loads. The first step to achieving this was to study the structural response, failure and collapse of individual structural elements. Thus the research in this area is taken further by using numerical solutions to study the behaviour of reinforced concrete beams to the point of failure. The results are implemented into the combined finite-discrete element method through a novel computationally efficient two noded beam element. Numerical integration across the cross section of the beam element is applied to facilitate the application of nonlinear constitutive laws for both steel and concrete for the case of multi-axial bending coupled with axial force. The accuracy of this new element is tested and validated under both static and dynamic loading situations using analytical solutions together with experiments undertaken at the University of Alberta and The Swiss Federal Institute of Technology. The proposed element has the advantage of reducing the size of the problem by fifty percent through the elimination of the rotational degrees of freedom using static condensationT. he new element,w hen coupledw ith NBS contactd etection, enables the same finite element mesh to be used for the discretised contact solutions, thus further reducing the CPU time required. When implemented into the finite-discrete element method, the proposed numerical solution also takes into account contact-impact and inertia effects. It is therefore both an accurate and CPU efficient solution to the combined finite-discrete element analysis of structural response, failure and collapse of real life structuresw hen subjectedt o hazardouslo ads as demonstratedin the thesis. T Bangas