This work describes the implementation of the eXtended Finite Element Method (XFEM) in the Abaqus software package. A user-defined element was developed containing the analytical functions relating to homogeneous and interface fracture mechanics. The long-term goal of such work is to increase the ability to analyze fractures and other imperfections in multimaterial systems containing large elastic mismatches, such as flexible electronics. A review of XFEM-related literature is presented, as well as an overview of fracture mechanics for both homogeneous and interface systems. The theoretical basis of the XFEM is then covered, including the concepts of Partition of Unity and stress intensity factor evaluation. Finally, numerical results of the implementation are compared to several benchmark cases, along with conclusions and suggestions for future work.

<p>Då godsvagnar skall vägas med trådtöjningsgivare monterade i järnvägsräls finns ett antal faktorer som inverkar på mätresultatet. Denna rapport utreder genom datorbaserade simuleringar hur underlag och hastighet inverkar på töjningen i rälsen och även i viss mån hur deformationen i rälsen påverkas. Vidare utreds hur störningar i form av temperaturförändring samt förändring av kontaktkraften mellan vagnshjul och räls inverkar på töjningen. Förändringen av kontaktkraften kan exempelvis bero på hjulplatta, vibrationer från godsvagn eller ojämnheter i rälsen.</p> / <p>When goods wagons are weighed out with a strain gage assembled to a rail there are certain factors that affect the results of the measurement. This report investigates by computer based simulations how the foundation and the speed of a wagon affect the strain and the deformation of a rail. Furthermore, in the report investigations are made how disturbances in the form of changes in temperature and changes of the contact force between the wheel of a wagon and the rail affect strain. The changes can occur due to non-round wheels, vibrations of a wagon or irregular rail.</p>

<p>This dissertation addresses interface problems simulated with the finite element method (FEM) with mesh adaptivity. More specifically, we concentrate on the strategies that adaptively modify the mesh and the associated data transfer issues. </p><p>In finite element simulations there often arises the need to change the mesh and continue the simulation on a new mesh. Analysts encounter such an issue when they adaptively refine the mesh to reduce the computational cost, smooth distorted elements to improve system conditioning, or introduce new surfaces and change the domain in simulations of fracture problems. In such circumstances, the transfer of data from the old mesh to the new one is of crucial importance, especially for nonlinear problems. We are concerned in this work with contact problems with adaptive re-meshing and fracture problems modeled with the eXtended finite element method (X-FEM). For the former ones, the transfer of surface data is built upon the technique of parallel transport, and the error of such a transfer strategy is investigated through classic benchmark tests. A transfer scheme based on a least squares problem is also proposed to transfer the bulk data when nearly incompressible hyperelastic materials are employed. For the latter type of problems, we facilitate the transfer of internal variables by making partial elements utilize the same quadrature points from the uncut parent elements and meanwhile adjusting the quadrature weights via the solution of moment fitting equations. The proposed scheme helps avoid the complicated remapping procedure of internal variables between two different sets of quadrature points. A number of numerical examples are presented to demonstrate the robustness and accuracy of our proposed approaches.</p><p>Another renowned technique to simulate fracture problems is based upon the phase-field formulation, where a set of coupled mechanics and phase-field equations are solved via FEM without modeling crack geometries. However, losing the ability to model distinct surfaces in the phase-field formulation has drawbacks, such as difficulties simulating contact on crack surfaces and poorly-conditioned stiffness matrices. On the other hand, using the pure X-FEM in fracture simulations mandates the calculation of the direction and increment of crack surfaces at each step, introducing intricacies of tracing crack evolution. Thus, we propose combining phase-field and X-FEM approaches to utilize their individual benefits based on a novel medial-axis algorithm. Consequently, we can still capture complex crack geometries while having crack surfaces explicitly modeled by modifying the mesh with the X-FEM.</p> / Dissertation

I detta projekt analyseras utmattningsbrott orsakade av ytdefekter i höghållfast stål som utsätts för fler än tio miljoner cykliska belastningar. Vanligen orsakas utmattningsbrott i denna region av interna materialdefekter där brottytan ofta innehåller ett område med grövre morfologi - fine granular area (FGA). FGA är en ackumulerad skada som bildas under sprickinitieringsstadiet och utgör cirka 99 % av den totala utmattningslivslängden. Resterande 1 % utgörs av spricktillväxt. På grund av detta är mekanismen som initierar sprickor i detta skede essentiell. Om FGA kan observeras vid ytinitierade utmattningsbrott för material som utsätts för fler än tio miljoner cykliska belastningar, är ännu inte fastställt. . Det här projektet syftar till att undersöka om FGA kan observeras i ytinitierat utmattningsbrott gällande material med väldigt långa livslängder, samt till att utreda hur ytinitieringar påverkar utmattningslivslängden. För att söka svar på dessa frågor utförs utmattningsprovning med ultraljudsutrustning, följt av karaktärisering av brottytorna i svepelektronmikroskop för att studera de morfologiska förändringarna. Vidare utförs finita element analyser med mjukvaran ABAQUS för att jämföra den maximala huvudspänningen mellan prov med, respektive utan ytdefekter. Resultatet från ABAQUS visar att proven med hårdhetsintryck utsätts för en större maximal huvudspänning än proven utan hårdhetsintryck, därigenom kan skillnaden i livslängder förklaras. . Testresultaten från utmattningsprovningen presenteras i ett S-N diagram som visar spänningsamplituden i förhållande till materialets livslängd. De analyserade bilderna från svepelektronmikroskopet av ytinitierat utmattningsbrott visar en antydan till FGA i två av 20 prov. Däremot tycks sprickorna, i samtliga fall, initiera på grund av ackumulering av plastisk deformation i ytan. Interna materialdefekter orsakade inte utmattningsbrott i något av de 20 testade proverna med ytdefekter. Två prover utan ytdefekter genomgick samma process och för båda dessa introducerades en spricka på grund av interna materialdefekter, båda innehöll ett tydligt FGA. Sammanfattningsvis indikerar resultaten från denna studie att FGA inte är lika uppenbara och eventuellt lika vanligt förekommande vid ytinitierat utmattningsbrott av höghållfasta stål med mycket långa livslängder. Även att ytdefekter introducerar en högre maximal huvudspänning i provets centrum, vilket resulterar i en kortare utmattningslivslängd.

This study aims to comprehend the bistable and multi-stable behaviour of flexible straws with the intention of utilising it for future engineering applications. This behaviour is achieved by the multiple inversions of conical frustum shells within the corrugation of a flexible straw. This study examined the effects of various material models, geometry variables and loading methods on the inversion of close-top and open-top conical frustum shells via experiments and FEM simulations. This thesis consists of three main parts, and the second and the third parts are complementary to each other: First, we investigated the effects of applying a uniform vertical load to the upper rim of open-top frustum shells via FEM simulations. A reference model was simulated based on the measurements of an ordinary polypropylene flexible straw specimen, using two material models - linear elastic and elastically perfectly plastic. The effects of the interactions between frusta of the corrugated segment of a flexible straw were also studied by evaluating the difference in responses between an individual frustum and conjugated models of two or three frusta. It was found that by constraining the rotation of its bottom rim, an individual frustum can fairly reproduce the complex bistable behaviour of the shorter frustum within the corrugated part of a flexible straw. Furthermore, detailed parametric studies that focused on the effects of various geometric parameters were conducted and generalised formulas that predicted the critical force were derived. A comparison between the simulated results and the analytical model in predicting progressive inversion was made to distinguish the geometric boundaries that separate the one-off snap-through to the progressive inversion of frustum shells. Next, the behaviour of close-top frustum shells in response to vertical point loading at various locations on the top surface was evaluated. A hyperelastic material was used to fabricate the physical specimens. During the experiments, the corresponding deformed shapes were recorded by 3D scanning in addition to measurements of the displacement and reaction force. We observed a close resemblance between the experimental and FEM simulated results, which validated the FEM models. Two local peaks were observed before the structure was fully inverted into its secondary stable state and the overall critical force of the structure was defined by the higher one of the two. The relationship between their magnitudes and the loading locations was analysed and an optimal loading location which gave the minimum critical force was proposed and verified by additional simulations. Furthermore, generalised formulas in predicting critical force were also acquired based on parametric studies. The optimal loading location was found to be constant in spite of variations in height and thickness. The third part of this thesis discussed the effects of lateral point loading on both close-top and open-top frustum shells at various locations on the side surface and supplemented the second part. It is found that the removal of the top surface could cause the critical force to decrease if a point load was applied laterally. Moreover, we were able to fully invert the structure with a lower critical force through lateral loading in comparison to vertical loading.

Lorsqu’un liquide est soumis à de fortes dépressions, des bulles de gaz etde vapeur peuvent apparaître en son sein. Ce phénomène est appelé cavitation Ces bulles sont susceptibles d’imploser dans les zones de surpression etd’endommager les parois solides environnantes à travers la création d’écoulements violents. Dans les applications industrielles, ce phénomène d’érosionpar cavitation peut réduire la durée de vie des machines hydrauliques. Dans ledomaine biomédical, le phénomène d’érosion par onde de choc est utilisé pourl’ablation de tissus mous ou la destruction de calculs rénaux.Dans ce travail, à caractère numérique, nous nous intéressons à une bulled’air isolée implosant au voisinage d’une paroi déformable sous l’effet d’unesurpression générée par une onde de choc incidente. Le travail de thèse aconsisté à mettre en place un couplage fluide structure pour simuler le phénomène d’implosion de la bulle dans la partie fluide et la déformation plastiqueengendrée dans la partie solide. Pour cela, une stratégie en deux étapes a étémise en oeuvre. La première étape a consisté à construire un code fluide avecmaillage mobile pour gérer le déplacement de l’interface fluide/solide. Le codedéveloppé est dérivé du modèle numérique développé par Eric Johnsen et al.à University of Michigan dans lequel nous avons implémenté une méthodeALE (Arbitrary Lagrangian Eulerian) permettant de passer d’une descriptioneulérienne sur maillage fixe à une description eulérienne sur maillage mobile.La seconde étape a consisté à modéliser la déformation élasto-plastique de lapartie solide au cours de l’implosion de la bulle grâce à un couplage fort ducode fluide avec le logiciel CAST3M. La communication entre les deux codesutilise la bibliothèque MPI.A l’issue du couplage, nous avons été en mesure de simuler l’implosiond’une bulle d’air à proximité d’une paroi déformable. Nous avons pu calculerle niveau de déformation de la paroi solide ainsi que l’amortissement de la sur-pression en paroi pour plusieurs matériaux. L’outil numérique ainsi développépermettra à terme d’étudier le comportement de revêtements amortissants capables de protéger des structures industrielles de l’érosion de cavitation oud’optimiser les effets bénéfiques des traitements par onde de choc dans lesapplications biomédicales. / His numerical work focuses on the collapse of a single air bubble close to adeformable wall generated by the impact of an incident high-pressure wave. A CFD code was fully coupled to a FEM solid code in order to compute the bubble collapse and the subsequent plastic deformation in the material. The CFD code was developed from the numerical model of Johnsen et al. (University of Michigan). A mobile mesh capability was added in order to account for the displacement of the fluid-structure interface. An ALE (Arbitrary LagrangianEulerian) method was implemented to switch from an Eulerian description in a fixed mesh to an Eulerian description in a moving mesh. The solid response to bubble collapse was computed with the FEM software CAST3M (developed by CEA) assuming an elastic-plastic constitutive law for the material. The communication between the two codes is achieved through the MPI library.For the CFD code, bubble collapse dynamics was validated by comparison with two others codes: research software CaviFlow and commercial software Ansys Fluent. The coupling between the CFD and the FEM code was validated on the case of the impact of a wave on an elastic medium.The paper will present a detailed analysis in 2D of both the dynamics of bubble collapse and solid behaviour for various conditions. They were obtained by changing the amplitude of the incident shock wave, the standoff distance and the material properties. Special attention will be given to the shock wave that forms when the microjet hits the bubble interface and to the impact of this shock wave on the material surface. In particular, the damping of the impactpressure with respect to a perfectly rigid wall was computed as well as the plastic deformation of the material surface. These final data gave us crucial information about the requirement of taking account of fluid-structure interaction in numerical modeling of cavitation erosion.

With the development of the vehicle industry and the innovation of technology, driving experience is improving in all aspects. Volvo is more and more focusing on improving the comfort of driving. Part of this is to minimize squeaks and rattle (S&amp;R) from vehicle seats. A physical measurement method was studied from component level in this thesis. The communication with the supplier has helped to better understand the definition and measurement method of play. Based on the previous work from Volvo and the supplier, a new improved algorithm has been developed to suit current production demands in this thesis work. A Graphical User Interface (GUI) has been finished for general engineers. The Study and exploration of a FEM simulation method make it possible to measure play in an economical way in the future.

Betongslipers är ett element i den moderna järnvägens uppbyggnad. Det har ersatt det traditionella virkesmaterialet som har ett antal nackdelar gentemot betong. Vid tillverkning av betongslipers förspänns armeringslinor med en kraft på 500 kN innan cementet gjuts in i produktionslinans formar. Undersökningen kommer in i bilden då en svetsad draglåda, där armeringslinorna är låsta, belastas av förspänningskraften. Uppdraget blir att analysera spänningsflödet i draglådan för att se var de största spänningarna förekommer. Detta görs genom en FEM-analys av hela konstruktionen samt hållfasthetsberäkningar av enbart gängorna. Slutsatsen som fastställdes var att analysen av konstruktionen resulterade att förspänningskraften inte påverkade gängorna eller svetsarna så pass kritisk att en allvarlig deformation skulle ske.

We study heat transfer in one dimension with and without convection, also called advection-diffusion. This is done using the Finite Element Method (FEM) to discretise the mathematical model, i.e. the heat equation. The results are compared to analytic Fourier series solutions. Our main result is that the FEM could be used to better model the heat transfer which allow for more accurate models than today's use of steady state models.

Datoriserade program för att göra konstruktionsberäkningar har utvecklats snabbt under de senaste 30 åren. Programmen har gått från att vara enkla och endast kunna utföra specifika beräkningar till att bli mer avancerade vilket ger möjlighet till utförligare beräkningar. Trots tillgången till avancerade beräkningsprogram används idag i stor utsträckning fortfarande handberäkningar eller enkla beräkningsprogram för kontroll och dimensionering av grundkonstruktioner. Syftet med examensarbetet är att undersöka hur beräkningsresultaten av grundtryck och sättningar skiljer sig mellan två program. Programmen som används är WIN-Statik Foundation vilket är ett enklare program och FEM-Design vilket är ett mer avancerat program. I programmet FEM-Design genomförs beräkningarna med två olika metoder: den ena där jorden modelleras med en bestämd styvhet (bäddmodul) och den andra där jorden modelleras som en volym (3D-soil) där aktuell jordlagerföljd och egenskaper anges direkt i programmet. Användarvänligheten och resultattolkning av programmet utvärderas för att ta reda på varför många konstruktörer frångår FEM-Design vid beräkning av grundkonstruktioner. Målet är att genom framtagande av en användarguide öka användandet av FEM-Design genom hela dimensioneringsprocessen. Tre olika typkonstruktioner har använts för att utföra beräkningarna: ett enskilt pelarfundament, en grupp av 3 pelarfundament samt en platta på mark. Beräkningsresultaten jämfördes dels mellan programmen och dels mellan konstruktionerna. Jämförelserna har visat att FEM-Design med metoden 3D-soil är att föredra speciellt vid beräkningar av fundament som ligger nära varandra då fundamentens påverkan på varandra försummas i de andra beräkningsmetoderna. Den största sättningen som fundamenten i pelargruppen beräknades orsaka, mer än fördubblades jämfört med sättningen för det enskilda fundamentet när beräkningen gjordes med 3D-soil. De andra två metoderna gav precis samma sättning för både det enskilda pelarfundamentet och gruppen av pelarfundament. För plattan på mark gav beräkning med 3D-soil mer än det dubbla maximala grundtrycket än beräkning med bäddmodul. Fördelen med WIN-Statik är att det endast krävs ett fåtal ingångsvärden och att beräkningen går snabbt att genomföra. I de flesta fall leder dock programmets förenklingar till att fundamenten blir fel dimensionerade. / Computerized programs which perform calculations have developed rapidly over the past 30 years. The programs have progressed from performing basic calculations to more advanced ones which gives an opportunity to perform more accurate calculations. Even though advanced calculation programs exist, many calculations are still done by hand or in simple programs when designing foundations. The purpose of this thesis is to study the differences in results of ground pressure and settlements when using two different programs. The programs that have been used are WIN-Statik Foundation (which is an easier program) and FEM-Design (which is a more advanced program). Two methods are used to describe the soil in FEM-Design. The first involves springs with a predetermined stiffness (bedding modulus). The second method involves modelling the soil as a solid mass (3D-soil) along with the stratigraphy and its properties. The programs are evaluated from a usability point of view and how easy it is to understand the results, in order to understand why many construction engineers choose to use simpler programs than FEM-Design. The objective of the thesis is to produce a user manual for FEM-Design’s 3D-soil module to increase the usage of FEM-Design throughout the whole design process. Three different constructions have been modelled in order to perform the calculations: an individual footing, a group of three individual footings and a foundation slab. The results from the calculations were compared between the programs but also between the constructions. The comparison showed that FEM-Design with 3D-soil is recommended when preforming calculations of foundations placed close to each other. This is because the other methods do not take into consideration the impact the foundations have on each other. The biggest settlement of the foundation group more than doubled compared to the single foundation when the calculations were done with 3D-soil. The two other methods gave the same result of settlement for both constructions. When the foundation slab was calculated with 3D-soil the ground pressure became more than twice as big compared to the calculation with the bedding modulus. The advantage of WIN-Statik is that only a few input values are needed and the calculation is easy to perform. In most cases the simplification of the calculations in WIN-Statik creates bigger foundations than needed.