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Full text available on 2024-06-29 Det har vært en økning i bruk av ikke-lineær elementmetode for bruks- og ulykkelaster. For tiden har industrien få retningslinjer for modelleringsprosedyrer som involverer knutepunkter i ikke-lineær elementmetode. Denne studien er det første steget til å lage validerte numeriske modelleringsteknikker for knutepunkter anvendelige for storskala analyser. Data fra to tidligere utførte eksperimentelle serier og korresponderende validerte numeriske modeller blir brukt til sammenligning. T-knutepunkter bestående av rektangulære hulprofiler og boltede dobbeltsidige bjelkesøyle-forbindelser ble undersøkt. Forenklede skallmodeller ble laget for sveiste T-knutepunkter. Enkelte idealiseringer fra tidligere studier ble videreført. Modellene produserte resultater med en feilmargin på 2% for fire forskjellige konfigurasjoner av geometri og last. Forskjellige materialer og geometriske egenskaper ble undersøkt gjennom en parameterstudie. Resultatet fra parameterstudien antyder at forenklinger i materialmodell og hjørnekonfigurasjoner påvirker kapasitet innenfor en margin på 10%. En forenklet prosedyre for boltete dobbeltsidig bjelkesøyle-forbindelser ble utviklet. Alle komponentene, utenom boltene, ble diskretisert med skallelementer. En bolt-mekanisme bestående av bjelke-elementer og multi-point constraints, ble brukt til å etterlikne boltenes oppførsel. To geometriske konfigurasjoner ble utforsket. I det kvasi-statiske lastregimet ga modellene resultater med en feilmargin på 10%. For kollisjonslast klarte ikke den numeriske representasjonen av boltene å representere skjærdeformasjon og hullkanttrykk mellom boltene og bolt-hullene. Følgelig ble de energiabsorberende egenskaper til knutepunktet drastisk underestimert. There has been an increase in the use of Non-Liner Finite Element Analysis for the design of service and accidental loads. Currently, the industry has few guidelines for modelling procedures involving joints in Non-Linear Finite Element Analysis. This study is the first step in providing validated numerical modelling techniques for joints applicable in large-scale analysis. Data from two previously conducted experimental series and corresponding validated numerical models are used for comparison. T-joints consisting of rectangular hollow sections and bolted double-sided beam-to-column joints were subjects of investigation. Simplified shell models with coarse meshes were created for the welded T-joints. Some idealizations from previous studies were adopted. The models provided results within a 2% margin of error for four different combinations of geometry and loading. Different material and geometric properties were investigated through a parametric study. The results from the parametric study suggest that material simplifications and corner configurations consistently impact the capacity within a margin of 10%. A simplified modelling procedure of bolted beam-to-column joints was developed. All components, except the bolts, were discretized with shell elements. A bolt mechanism consisting of beam elements and multi-point constraints was used to replicate the bolt behaviour. Two geometric configurations were explored. In the quasi-static loading regime, the models provided results within a 10% margin of error. For impact loading, the numerical representation of the bolt mechanism was not able to account for shear deformations and bearing due to contact between the bolts and the bolt holes. Consequently, energy-absorbing properties were severely underestimated.

Denne masteroppgaven har som mål å etablere og forbedre en elementmetode (FE) modell som fanger opp oppførselen til en bilfelg utsatt for støtlast, ved bruk av “state-of-the-art” modelleringsteknikker. Utvikling er en del av et pågående prosjekt ved Centre of Advanced Structural Analysis (SFI CASA) i samarbeid med Audi AG. Både eksperimentelt og numerisk arbeid ble gjennomført for å validere og forbedre både en eksisterende og nye FE modeller. Det har tidligere blitt gjennomført omfattende materialtesting på det støpte materialet som felgene er lagd av, og en elastisk-viskoplastisk materialmodell med et Cockcroft-Latham (CL) bruddkriterium har blitt kalibrert. Videre, har en FE modell blitt laget i FE-programvaren Abaqus, en testrigg for støttesting av felger har blitt lagd, og en prosedyre for estimering av krefter ved støtlast har blitt utviklet. Testriggen og prosedyren for beregning av krefter har blitt validert, og fire dynamiske felgtester ble gjennomført. I dette arbeidet har forbedring av de tidligere FE modellene blitt undersøkt på to forskjellige måter. Først ved å undersøke ytelsen av en tetraedermodell skapt med automatisk generert netting som, om funnet tilfredsstillende, kan lede til betydelig kortere modelleringstid. Videre, ved å forbedre materialmodellen ved å bruke en spenningstilstandsavhengig og probabilistisk bruddmodell, bestående av et utvidet Cockcroft-Latham (ECL) bruddkriterium og en Weibull-distribuert bruddparameter. Ytelse ble evaluert ved sammenligning med fysiske felgtester og de andre FE modellene, under kvasi-statiske og dynamiske lasttilfeller. Omfattende eksperimentelt og numerisk arbeid ble utført. For å unngå bruken av en prosedyre for kraftestimering, og for å oppnå mer pålitelige eksperimentelle resultater, ble fire felger testet under kvasi-statisk last. Flere materialtester ble gjennomført, både eksperimentelt og numerisk ved forskjellige spenningstilstander for å kalibrere ECL bruddkriteriet. Tre forskjellige utgangspunkts modeller ble lagt i FE-programvaren LS-DYNA. Disse er først og fremst ulike i diskretisering av geometrien, hvorav det var to skall-kube (S-B) hybridmodeller, referert til som “S-B Simple Coupling” og “S-B Full Coupling”, og en modell med tetraeder elementer. Alle modellene ble formulert med CL bruddkriteriet. Forskjellen mellom S-B modellene ligger i grensesnittet mellom skall og kubeelementene i den forstand at kun “S-B Full Coupling” modellen er i stand til å overføre momenter mellom de forskjellige elementtypene. “S-B Full Coupling” og tetraedermodellen var i stand til å fange de generelle trendene sett eksperimentelt. Samtidig som “S-B Full Coupling” har et klart fortrinn når det kommer til beregningskostnad, har tetraedermodellen en tidsfordel når det kommer til nettgenerering. Når den probabilistiske bruddmodellen ble brukt var “S-B Full Coupling” den eneste nøyaktige modellen. Dette er antatt å være på grunn av størrelseseffekter, ettersom størrelsen på S-B modellen er nærmere volumet til materialprøvestykkene. Størrelseseffekten er også trodd å være grunnen til at spenningstilstands dataen som ble brukt til å kalibrere ECL bruddkriteriet ble vurdert til å være upålitelig. Spenningstilstands dataen var i motsigelse med trendene at bruddtøyning reduseres når triaksialiteten øker, noe som er sett i litteraturen. I hvilken grad dette skyldtes de stokastisk fordelte defektene i det støpte materialet blir videre diskutert. Til slutt presenteres noen konkluderende bemerkninger og anbefalinger for videre arbeid. The present thesis aims to establish and improve a finite element (FE) model to accurately capture the behaviour of a car rim subjected to impact loadings, using state-of-the-art modelling techniques. This development is part of an ongoing project at the Centre of Advanced Structural Analysis (SFI CASA) in cooperation Audi AG. Both experimental and numerical work was carried out to validate and improve both existing and novel FE models. Previously, extensive material testing of the die-cast aluminium rim material has been performed, and an elastic-viscoplastic material model with a Cockcroft-Latham (CL) fracture criterion has been calibrated. Furthermore, a FE model has been established in the FE-software, Abaqus, a test rig for impact testing of rims has been constructed, and a force estimation scheme to estimate rim crushing forces during impact has been developed. The test rig and force estimation scheme have been validated, and four dynamic rim tests were performed. In the present work, improvements of the previously established FE model were pursued in two separate ways. Firstly, by investigating the performance of an automatically meshed tetrahedral model, which if satisfactory, can significantly cut modelling time. Secondly, by an improvement of the material model, making use of a stress state dependent and probabilistic fracture model, composed by the Extended Cockcroft-Latham (ECL) fracture criterion and a Weibull-distributed fracture parameter. The performance was evaluated by comparison to physical rim tests and the other FE models, in quasi-static and dynamic loading conditions. Extensive experimental and numerical work was conducted. To avoid the use of a force estimation scheme and to obtain more reliable experimental results, four rims were tested under quasi-static loading. Furthermore, several material tests were conducted experimentally and numerically in different stress states to calibrate the ECL fracture criterion. Three different baseline rim models were established in the FE-software, LS-DYNA, differing mainly in their geometric discretization, two shell-brick (S-B) hybrid models, referred to as S-B Simple Coupling and S-B Full Coupling, and one Tetrahedral model. These models were all formulated with the CL fracture criterion. With the S-B models differing in the interface between the shell and brick elements in the sense that only the S-B Full Coupling model transfers the moment between the element types. The S-B Full Coupling and the Tetrahedral model were able to capture the general trends seen experimentally. While the S-B Full Coupling model had a clear advantage in computational cost, the Tetrahedral model had the time advantage in meshing. When probabilistic fracture model was included, the S-B Full Coupling was the only accurate model. This is believed to be due to size effects, as the element size of the S-B model was closer to the volume of the material specimens. The size effect is also believed to be the reason why the stress state data, used to calibrate the ECL fracture criterion, is deemed unreliable. The stress state data contradicted the trend that fracture strain decreases as triaxiality increases, as indicated in literature. To what extent the stochastically distributed defects in the die-cast material caused this is further discussed. Lastly, some concluding remarks and recommendations for further work are presented.

The trend towards lightweight design in the automotive industry has led to increasingly optimal and complex structures, where fundamentally different materials are combined. An effective way of combining these would be to use adhesives as they are compatible with a large range of materials unlike traditional joining methods such as spot-welds. Adhesives exhibit beneficial properties including increased stiffness and improved energy absorption at the structure level. Further, adhesives are beneficial with respect to noise and vibration in addition to acting as a corrosion barrier. Therefore, adhesives have been increasingly used in the automotive industry. This makes adhesives a relevant topic to study for this thesis as there is generally a lack of understanding with respect to both the behaviour and the modelling of adhesives. This thesis is split into two parts, one for each of the two selected adhesives for this study. The first part treats a semi-structural two-component polyurethane adhesive that has not been thoroughly studied before. In order to investigate the behaviour of the adhesive it was performed several material tests on bulk adhesive test specimens. For a selection of these tests, field data was obtained for both deformations and temperature. Scanning electron microscopy was also used to look at the failure surface of one of the specimens. Three configurations of single lap joints, using two types of fibre reinforce polymers as adherents, were tested to see the behaviour of the adhesive in a joint setting. To model the adhesive, the Bergström-Boyce model was chosen as it proved to be able to capture the key phenomena governing the response of the adhesive. In addition, a modification of the model was implemented as a user subroutine in Abaqus to better capture the viscous response of the adhesive. Both models were calibrated based on the material tests and validated against the notched tension tests. The second part of the thesis studies a structural toughened epoxy adhesive. Bulk adhesive material tests, bonded cross tests, hybrid single lap joint tests, hybrid peel tests and hybrid component tests were performed as a part of a related thesis. Additionally, bonded component tests were tested as a part of this thesis. Data from the material tests were used to calibrate a previously implemented meso-scale polymer model for the adhesive. This model was then validated against the bonded cross tests, hybrid benchmark tests and the bonded component tests. A partial virtual laboratory calibration procedure was developed in order to calibrate macro-scale material models for the adhesive. The method was based on simulating virtual benchmark tests using the meso-scale polymer model, then using the response of those simulations as target curves for reverse engineering of the macro-scale parameters. Three macro-scale models were calibrated using this approach including a baseline model MAT_240, a modified version of the baseline model and a Gurson-based cohesive zone model (GCZM). Additionally, the GCZM had to be implemented as a user subroutine in LS-DYNA. All three models were validated against the bonded component tests. There were made some adjustments to the calibration procedure, which led to new calibrations that were further validated against the hybrid benchmark tests and hybrid component tests. Finally, a study on the influence of the adherent properties on the calibrated material parameters of the macro-scale models were performed using the partial virtual calibration approach. In conclusion, there was found a fundamental difference in the behaviour between the two adhesives that were studied in this thesis, which would imply significantly different modelling. The partial virtual laboratory calibration procedure was seen to give comparable results to what is obtained when using traditional calibration methods with physical experiments. Finally, the bending stiffness of the adherents were seen to have a larger influence on the calibrated m acro-scale properties of the adhesive than the material of the adherents. However, both were seen to have a minor influence overall based on the cases studied in this thesis.

Formålet med denne avhandlingen er å gjennomføre eksperimentell testing av støpt aluminiumfelg utsatt for dynamisk krasjbelastning. Basert på dette vil en numerisk modell bli etablert og brukt for numerisk validering. En stor del av oppgaven er brukt på å validere det eksperimentelle testoppsettet som har blitt utviklet det foregående år med formål om å utføre dynamisk testing av aluminiumfelger. Håndtering og prosessering av sensor og måledata for å oppnå troverdige resultater er i fokus. Den numeriske modellens formål er å oppnå en tilstrekkelig nøyaktighet for å kunne anvendes for industrielle formål. The aim and primary objective of this thesis is to perform experimental testing of a cast aluminum rim subjected to dynamic crash loading. Based on this, a numerical model is to be established and used for numerical validation. A substantial part of the thesis is used to validate the experimental test setup which was developed the previous year for the purpose of performing dynamic testing of aluminum rims. Managing and processing sensor and measurement data in order to get trustworthy results are in focus. The numerical model aims to achieve sufficient accuracy to be used for industrial applications.

When Toyota develop new polymer components for their vehicles, experimental drop tests are conducted at -30 °C to evaluate the cold impact performance of the parts. The objective of this thesis is to replicate the behaviour found in a drop test conducted on a Toyota Yaris polypropylene (PP) door trim, using the finite element method. The material characterisation involved a series of uniaxial tensile tests in three different strain rate regimes. Specimens from two sources were tested to expose any difference in properties due to process effects associated with the component. Small-scale impact tests were conducted in a drop tower, in an attempt to validate the calibrated material model under controlled conditions. Experimental full-scale drop tests were performed and compared to numerical simulations employing the validated material model. Ductile behaviour was found in the uniaxial tensile test campaign in the quasi-static and meso-dynamic regimes. The mechanical properties of the two material sources were nearly identical, with the exception of strain at fracture. A Split-Hopkinson tension bar test rig enabled testing in the dynamic regime, where entirely brittle material response was obtained. In addition, a log-bilinear strain rate sensitivity was observed for the material. The first material characterisation produced accurate results in the numerical representation of the small-scale impact test. In contrast, the ductility was clearly overestimated for the brittle failure mode observed for the second characterisation. A recalibration was performed to accommodate these discrepancies, also involving an inverse modelling procedure of the fracture parameters according to the results from the drop tower. However, the numerical model still demonstrated overly ductile behaviour when the full-scale component drop test was simulated.

This PhD thesis consists of experimental and numerical studies of the behaviour and modelling of flow-drill screw connections. It is comprised of four parts, and each part has been published, or accepted for publication, in scientific peer-reviewed journals. As such, each paper may be read independently. The papers are preceded by a synopsis that brings each part into a broader perspective, states the motivation, objectives, scope and research methodology of the work, and provides a summary of the work. A brief case study is presented at the end of the synopsis. Paper 1 is a purely experimental investigation of the behaviour of a flow-drill screw connection between sheets of aluminium alloy AA 6016 T4. Different quasi-static loadings were studied using cross, single lap-joint and peeling tests. This provided knowledge about the global force-displacement behaviour of the connections, as well as different deformation and failure modes. The paper also contains axial crushing tests of single-hat sections, joined with flow-drill screws. These tests were dominated by material deformation outside of the connections, which made it difficult to evaluate the connection behaviour. Paper 2 addresses macroscopic modelling of flow-drill screw connections in large-scale finite element simulations. Five common models were studied, of which two were element-based and three were constraint-based. They were evaluated for two different connections. The two element-based models did not perform well, as they over-estimated the force in mixedmode loadings. The constraint-based models yielded better results. One stood out as marginally better, appearing to be the most suited, of the five models, to represent flowdrill screw connections. Paper 3 deals with a detailed numerical model of a flow-drill screw connection, where the geometry of the connection was discretised with a fine solid element mesh. Five different tests were simulated, and the results compared to equivalent experimental tests. A microstructure analysis and Vickers hardness tests indicated that there was a processaffected zone close to the screw. Despite that process effects were neglected in the numerical model, satisfactory results were achieved. The simulations provided a deeper understanding of the underlying deformation and failure mechanisms. Paper 4 presents a component suited for quasi-static and dynamic testing of flow-drill screw connections, of which the design is such that the dominating deformation is taking place in the connections, and at the same time has relevant and sufficiently complex loadings in the connections. Large-scale simulations were carried out, where the preferred model in Paper 2 was employed at the connections. An improvement of the connection modelling technique was presented. The component was well-suited for validation of large-scale finite element models. Digital full text not available

Current and future strategic challenges in the construction industry require safe and lightweight structures to achieve a good strength to weight ratio. Authentic material combinations together with numerical simulations are urgently needed to reduce development time and to remain competitive. Aluminium provides favourable strength to weight ratio, low density and high resistance to corrosion. In addition, it is recyclable and flexible as it can be processed in different ways, e.g. casting, extrusion and rolling. Properly applied, aluminium alloys are competitive to other structural materials such as steel. Aluminium extrusions supplied by Hydro Aluminium were used as an example to investigate failure behaviour. Fibrous- and recrystallised microstructure were investigated for an AA6005A-T6 alloy under combined bending and stretching loads and axial crushing simulations. The material model for the aluminium alloy were established using a damage regularisation scheme for shell elements. This model assesses the elements deformation mode based on the thinning strain rate of the through-thickness gradient. Input data for the finite element models and stretch bending and crash simulation were generated through quasi-static material tests. For an initial validation of the material models, the quasi-static tests were simulated with very good correlation of the results. From the quasi-static uni-axial tensile tests, the materials strain data was accumulated using a digital image correlation analysis with the software eCorr. This data was processed, and the material characteristics were described using Hooke s law, Hershey-Hosford yield criterion, an associated flow, extended Voce law and Cockroft-Latham failure criterion. From these procedures material cards for both the alloy with fibrous- and the recrystallised microstructure were implemented for use in Abaqus/Explicit. Experimental- and numerical results for the quasi-static stretch bending and axial crushing were separately discussed and compared. The validity of the numerical model and its ability to replicate the physical experiments were reviewed and how different features affected the results considered. Components yielded high reproducibility within each test setup and only minor deviations in the material behaviour and failure characteristics were observed. Consequently the constitutive model ability to replicate the test results were examined. The combined bending and stretching loads, and axial loads for both test setups were reproduced in the simulation models with high accuracy. The models ability to replicate a more complex deformations with complex stress states and severe bending were decisive to conclude that the constitutive numerical models were able to predict failure accurately. A parameter sensitivity study was performed on the numerical models, evaluating mesh dependency, boundary conditions and fillet contribution. The increased bearing capacity added by the fillets had small effect on the result, and only a minor variation were caused by use of symmetry planes. With a coarser mesh, the accuracy of the numerical model decreased. In this Thesis it was proven that aluminium extrusions could be sufficiently simulated by means of finite element methods under bending and stretching loads as well as in axial crushing situations utilising the damage regularisation scheme. However, some discrepancies were found between the numerical- and experimental result, particularly for the fibrous material model. Further work should include an introduction of an anisotropic yield criterion as the material exhibited anisotropic behaviour.

The aim of this master s project is to evaluate the capabilities of the SIMLab Metal models (cast aluminium model) to predict the response including failure of a given rim subjected to impact loading conditions. The modelling has to take into account any variation in the mechanical properties mainly driven by the manufacturing process (e.g. casting process and heat treatment). The main outcome should be a reliable crash model with sufficient accuracy for industrial applications. Physical rims will be provided by Audi for material characterization as well as crash test data of the chosen rim on a component level. Furthermore, Audi will provide CAD data of the rim as a basis for a finite element model.

This thesis is concerned with a strength model for float glass. Failure of glass is usually initiated from surface flaws and the glass is reckoned as failed with the first failing flaw. The model implements a flaw map over the glass surface of arbitrary orientations and flaw lengths of maximum 200 μm. Every flaw is checked for failure for an applied load until the critical load for the first failing flaw is found through a search method. The plate geometry is applied several flaw maps for a Monte Carlo analysis, resulting in a probability distribution for strength. This means that rather than assuming the probability distribution a priori which requires parameters obtained from experimental test series, as is done for the traditional probabilistic strength model Weibull distribution, it is generated from the analysis. Additionally, the model provides information about fracture origin in the glass plate. An analytical solution of the model was implemented in MATLAB, and verified with data from Abaqus FEA. Then the model was implemented in an Abaqus post-processing Python script and further verified by comparing with the analytical solution. The verification processes yielded satisfying results and the model is assumed to be working according to the mathematical foundation. Additionally the flaw map property of the model was applied to an Abaqus VUSDLFD subroutine, exploring visualization of failing flaws. The model was subjected to parameter studies examining the model response from different plate and flaw geometries, yielding reasonable results. The resulting distributions were compared with fitted Normal and Weibull distributions, and in most cases the Weibull distribution provided the best fit. The Weibull modulus from the fitted Weibull distributions varied for plates with different numbers of flaws, suggesting it is inaccurate to assume this parameter as a material constant. Further, case studies comparing the model behavior to experimental results from four point bending tests were performed. In addition the model behavior were examined under the influence of blast loads. The studies disclosed the notable potential of the model. Finally, suggestions for further work with the model and the software in this thesis were presented.

In this master thesis stiffened aluminium plates of the aluminium alloy AA6082 subjected to impact loading was studied. The main objective was to study the behaviour of welded and stiffened aluminium plates exposed to impact loading from a ship, and determine how to model this in a large scale analysis. This master thesis was initiated in a cooperation between CASA at NTNU, Hydro Aluminium and SAPA, as a part of the project Ferry-free coastal route E39 . This project is a continuation of the master thesis that Bente Larsen Kårstad and Birgitte Skajaa wrote in 2015. It was planned to conduct both material tests and quasi-static impact tests of the stiffened aluminium plates in the laboratory as part of this report. Due to problems in the production line, the components never arrived on time. After a discussion with our supervisors in mid-May, the laboratory tests were cancelled and it was decided to focus on the establishment and validation of numerical models to replicate the experiments that Hilde Giæver Hildrum carried through in her Dr.Ing- thesis, and to do a preliminary analysis of a different test setup with both T4- and T6-plates. A literature study on the behaviour and modelling of stiffened aluminium plates subjected to impact loading has also been conducted. As a part of this thesis a numerical model in the finite element software Abaqus has been established in order to replicate the static tests that Hildrum carried through. The numerical models give acceptable estimations and captures the failure modes for all of the different test setups in a satisfactorily way. However, there are some aberrations in predictions of failure and the stiffness of the plate. The material model was simplified by implementing the isotropic von Mises yield criterion, in which case the great degree of anisotropy in the AA6082-T6 alloy is neglected. It was also decided to model the plate without a weld. This could explain some of the varying accuracy in the numerical simulations. The numerical model in the preliminary analysis was conducted with two different heat treatments of the AA6082 alloy, namely T4 and T6. The difference between the behaviour of the plate with the two alloys is large, since different heat treatments yields different material properties and behaviour. For both the T4- and T6-plate, two different fracture criterions has been implemented, the Cockcroft-Latham (CL) fracture criterion and the Bressan-Williams-Hill (BWH) instability criterion. The numerical simulations show difference in both initiations of fracture and failure modes for the two criterions. Analyses run with BWH yields a better coherence between different mesh sizes than CL, and is also less computational expensive, which makes it more favourable in large scale analysis.

Extreme loading may cause failure or damage to structural building members. Redistribution of forces might propagate the local failure into a complete or partial progressive collapse of the building. The prevailing method for analyzing the potential for such collapse is the alternate path method. One structural member is notionally removed to see if the forces are able to find an alternate path. Explosions might cause damage to more than one structural member and produce a structural response not included in an alternate path analysis. A literature review have been conducted to study analysis methods using both the alternate path method and methods incorporating blast loading in the collapse analysis. It is possible to model building collapse resulting from an explosion with complex models that require large computational force. This thesis have tried to use implicit time integration instead of explicit in order to reduce computational cost, but this was not found beneficial. Beam elements are effective, computationally effective and are easy to model. Only a small number of studies have used blast loading on beam elements in some way. A steel frame building was analyzed using beam elements with an incident wave interaction in Abaqus to model the blast load. This was compared with a model using shell elements to model the steel sections with Conwep blast loading. The blast loading on the beam elements did not produce a satisfactory response.

This project is set as a part of the ongoing development of the constitutive model the SIMLab Polymer Model (SPM) developed at SIMLab, NTNU. The goal with this thesis is to explore the capabilities of this model using two validation cases set up in cooperation with Toyota Motor Europe (TME). The validation cases are designed with the purpose to reproducing similar loading conditions and deformations as observed in pedestrian protection tests on full cars. The experimental part of this thesis was performed with a standard drop tower. The test components are both made of a PP material provided by Toyota. The test specimen for the first validation case is a generic test box with a simple geometry. The test results show generally low test variability. However there are some problems with imperfections on the boxes. The test specimen for the second validation case is a lower absorber provided by TME. The tests results show significant test variability in the first series of tests as the fixtures were not properly handled, the second series of tests show very consistent results. The majority of the work done during this thesis is in the two numerical studies performed on the box and the lower absorber respectively. The overall results of the box study show that high accuracy is achieved prior to fracture occurring. The box study highlights some key properties of this type of problems. Firstly that it is very sensitive to geometry, and secondly that fracture is in its current state unreliable. Fracture is seen to be very mesh dependent and to require heavy models. The results of the lower absorber study show good accuracy using the SPM and a significant improvement compared to a standard material model. This improvement is due to how the SPM is able to better capture key physical properties of the ductile polymer like viscoelasticity and pressure sensitivity. The added complexity of the SPM comes at a significant cost in terms CPU. It is also observed that for complex geometries as the lower absorber a solid model may be needed to fully capture all the critical events.

A finite element method implementation of lower-order strain gradient plasticity is developed. Its validity is checked against known analytical solutions. The implementation gives expected trends when applied to particle strengthening and void growth. During implementation, stability issues are encountered. The instability is denoted the tower/canyon defect, and traced back to nodal averaging as a basis for strain gradient computation. A conservative stability criterion for stability is developed, and within the stability limit given by the criterion, no tested models are unstable. Instabilities are shown to appear under a combination of (a) large plastic strains, (b) small length scale and (c) fine element mesh. Nodal averaging underestimates the strain gradient at boundaries. An alternative to nodal averaging is developed, denoted nodal contributions. Nodal contributions has not been implemented for use in finite element simulations, but analytical verification indicates that nodal contributions is resilient to previously encountered stability issues. Nodal contributions is shown to represent strain gradients exactly for linear strain fields, even at boundaries. The exact, mathematical solution to the applied lower-order strain gradient plasticity theory is shown to be singular given a prescribed stress field. Iterative solutions based on load incrementation choose one of the possible resulting strain distributions. Nodal averaging is biased towards small strain gradients at boundaries.

The impact behavior of stiffened steel plates subjected to impact loading from concentrated loads was studied experimentally and numerically. Both dynamic and quasi-static tests of stiffened steel plates with geometry adopted from a typical external deck area on an offshore platform were conducted. The quasi-static tests were performed to study the relationship between dynamic impact behavior and the corresponding static ones. All tests were carried out in scale 1:4. To allow the execution of generic testing in the laboratory, a steel frame that defines the support conditions for the test components is designed and constructed. Prior to the execution of the experimental programme, numerical models were created and several preliminary simulations of the tests were performed. The results from the preliminary simulations were directly used in the design phase of the tests, i.e. design of the test components and the support frame, determination of appropriate contact area between load and component, and determination of the load magnitude. Tension tests were carried out to provide the necessary information on the strength and ductility of the steel material used in the stiffened plates. Based on the information obtained from the material tension tests, material models were created and implemented into the numerical models of the dynamic and quasi-static tests. Comparisons between the numerical and experimental results were performed, mainly by comparing force-displacement curves. In order to determine the capacity of the stiffened steel plates by numerical simulations, three main approaches that involve predicting tensile failure was implemented. The first approach is to use the Cockcroft-Latham fracture criterion which is based on calculation of accumulated damage during straining. With this approach it was possible to calculate the capacity with high precision. However, the way this fracture criterion was implemented it was inefficient with regard to computational time as it required a very dense mesh to obtain reliable results. In the second approach, the Bressan-Williams-Hill instability criterion which is based on predicting the onset of local necking in a sheet metal was implemented. This method can be used with success for large-scale shell structures, where the element length is considerable larger than the plate thickness. For the applicable structure in this report, the Bressan-Williams-Hill instability criterion predicted acceptable estimates of the capacity, although with a higher degree of conservatism than expected in advance. In the final approach a simplified check against tensile failure was performed according to a recommended practice from DNV-GL. The simplified approach provided conservative values of the plate capacity compared to the tests.

In this master thesis, impact loading against stiffened aluminium plates of the aluminium alloy AA6082-T6 was studied. The main objective was to study the behaviour of extruded aluminium profiles welded together when exposed to impact loading from a ship, and how to model it in a large scale analysis. The study was part of a cooperation between SIMLab at NTNU, Hydro Aluminium and Sapa, as a part of the project Coastal Highway Route E39 . Eight plates were tested in the laboratory experiment, four by applying quasi-static loading and four by applying dynamic loading, with a cylindrical indenter in the centre of the plate, transversal and longitudinal to the stiffeners. The dynamic experiments were conducted using the kicking machine at the Department of Structural Engineering, NTNU. The experiments were attempted simulated and validated using shell elements in a nonlinear element analysis in Abaqus/Explicit. In order to perform the laboratory experiments, a rig fixing the aluminium plates in the test machine was designed. In the experiments a good correlation was detected between the quasi-static and dynamic tests. This gave grounds to conclude that quasi-static experiments could give satisfying validation for this type of experiment on the aluminium alloy, AA6082-T6. The numerical model was implemented with two different criteria to detect fracture, the Cockcroft-Latham (CL) fracture criterion and the Bressan-Williams-Hill (BWH) instability criterion. The material implementation was simplified by using the von Mises yield criterion, where the anisotropic properties of the AA6082-T6 were neglected. The CL fracture criterion gave acceptable estimates of initiation of fracture when the mesh size is equal to the thickness of the plate. With a coarser mesh, the accuracy of this criterion decreased significantly. The BWH instability criterion gave acceptable estimates of initiation of fracture for mesh sizes varying from equal to the thickness to five times the thickness. The estimates showed to be somewhat conservative for this criterion, and a slight mesh sensitivity was detected. In the material tests, a large degree of anisotropy was detected for aluminium alloy AA6082-T6, and a large difference between the material properties in the plate, stiffeners and the friction stir welds was found. This made the material implementation more complicated than first assumed, and the simplification with an isotropic yield criterion less accurate. An anisotropic yield criterion would more accurately describe the material behavior in the experiments, and could therefore give improved estimates.

The purpose of this thesis is to study the behaviour of the connection between the guardrail and post in a steel road safety barrier subject to tensile, shear and combined loading conditions. This is accomplished by performing laboratory tests on a special-built test rig. Finite element models of the connection are created and validated in order to form a basis for large scale numerical simulations of road safety barriers.The laboratory tests all failed by thread stripping of the bolt in the connection. The ultimate failure load decreased by 15.9 and 17.3 percent when loading in 15\degree{} and 30\degree{} from pure tension respectively. A two-step finite element model was created to simulate the behaviour of the threaded bolt and nut assembly in question. The relative displacement between the bolt and the nut in an initial model of the guard rail and post with an unthreaded connection was enforced on a separate model of the bolt and nut with threads. A full model including the threaded connection was created and compared to the two-step model.The results indicate that the behaviour prior to failure is controlled by deformations in the guardrail, post and washers. Failure is controlled by the threaded bolt, and the ultimate load is highly dependent on the bolt material. It is possible to model the bolted connection, subject to combined tension and shear loading conditions, with an acceptable degree of accuracy. A consistent failure mode can be achieved with both the two-step model and the full model. The ultimate loads experienced in the two-step model were in close proximity to the experimental results in some load combinations. The full model was close to the laboratory results in most load combinations, where the deviation from the average failure load in pure tension was 1.1 - 2.7 percent.

This thesis presents an experimental and numerical study on the behaviour of Flow-Drilling Screw (FDS) connections under various quasi-static loading conditions. The behaviour and fracture of the connections were closely studied by means of tests on simple coupons joined with a single connector and component tests. Single-connector tests were performed on both two- and three-layered specimens. Cross tests in three loading directions, lap-joint tests and peeling tests were conducted for both configurations. The two-layered cross tests were used to calibrate two different macroscopic models. The first model was a point-connector model developed for self-piercing rivets (SPR), while the other was a material model developed for spot welds. Two different assemblies of three-layered cross tests were used to calibrate the SPR model for three-layered FDS connections. All models were validated by simulations of the lap-joint and peeling tests. A component test was performed to validate the two-layered macroscopic models for complex loading situations.In the single-connector tests, shear-dominated loading situations generally produced higher forces than tension-dominated. Failure in the connections were mostly caused by pull-out from the bottom sheet. For the three-layered crosses and lap-joint specimens failure due to fracture of the screw itself, near the screw-head, was observed. In the component, all screws experienced both rotation and one-sided thread stripping.The spotweld model was able to represent the stiffness and maximum force in some tests, but failure occurred too early in all simulations. The macroscopic model developed for SPR connections generally gave a good representation of the results, except under-predicting the force in peeling. The macroscopic model of the three-layered specimens showed some acceptable results, but under-estimated the forces in peeling, and over-estimated both force and displacement for the lap-joint. The macroscopic models gave an acceptable representation of maximum force in the component test, but were not able to accurately represent the stiffness observed in the experiments.To develop a point-connector model for FDS more work is necessary. The SPR model seems reliable for two-layered connections, but a model for three-layered connections requires further calibration, especially for shear-dominated loading cases. The spotweld model shows promising results, but further optimisation of the parameters must be conducted to conclude.

The structural impact laboratory (SIMLab) at NTNU have developed a constitutive material modelto represent the behavior of brittle and ductile polymeric materials. The material model can be implementedinto finite element solvers, e.g. LS-Dyna and Abaqus. In this thesis, the material model sability to describe the behavior of an injection molded polypropylene, provided by TOYOTA, hasbeen studied.The material had during previous experimental tests shown an inhomogeneous material behavior.As the material was loaded in uniaxial tensile, the core would fracture prior to it s outer section.This skin-core behavior has been observed for many injection molded polypropylenes, but theeffect varies substantially due to differences in the molding process and the material additives. Todetermine how the material parameters would vary through the material s cross section, the skincore effect had to be better understood.To be able to separate the core from the skin, experimental tests were conducted using specimenswith and without a reduction in its section thickness. The difference between the material parametersof the specimens with a full thickness and with a reduced thickness, was suggested to be thematerial parameters of the skin. The experimental tests showed that the main difference was linkedto the specimens yield stress and damage propagation. The specimens with a full section thicknesshad a higher yield stress and a lower damage propagation than the specimens with a reduced sectionsthickness.Experimental tests were also performed to determine how the material s molding thickness wouldaffect it s material properties. Three different molding thicknesses were used; 2mm, 3mm and 4mm.The tests indicated that the molding thickness mainly affected the damage propagation and yieldstress of the material, the damage propagation increased and the yield stress decreased with anincrease in the material s molding thickness. The tests suggested that the difference was larger forthe material s skin than for it s core, which may be due to the distribution of particles.To evaluate SIMLab polymer model s ability to describe the material s behavior, numerical simulationsof the experimental tests were conducted. The numerical simulations ability to reproducethe behavior of the experimental tests would be used to determine the accuracy of the materialmodel. The numerical models were composed of two sections; one for the core and one for the skin.Where the behavior of each section was controlled by it s own material card. The thickness of theskin was determined to be 0.2mm, based on visual evidence using an optical microscope.Drop-tower tests and tensile loaded notched specimens were used for validation of the materialmodel. The simulation results, indicated that SIMLab s polymer model could predict the material sbehavior well, but that improving the formulation of the plastic flow will yield better results. Thecurrent formulation is not able to capture the material s transverse behavior and the material sbehavior in compression.

Accurate and reliable models of connections are essential for the design of aluminium parts in cars. Today, there exist a few models customized for self-piercing rivets (SPR), but none for self-piercing screws (SPS). This thesis presents an experimental and numerical study on the behaviour of SPR and SPS connections for different loading situations. For the rolled base material, AA6016 in the T4 condition, uniaxial tension, plane strain tension and in-plane single shear tests were performed. The Voce isotropic hardening rule and the YLD-2004-18P anisotropic yield function were calibrated using MatPrePost. The calibration was validated by simulations of the material tests. Cross tests in three directions, single lap-joint tests and peeling tests were performed for SPR and SPS, and a point-connector model developed for self-piercing rivets was calibrated by a reverse engineering approach based on the cross tests. Single lap-joint and peeling tests were used for validation. Forming process simulations were performed to account for initial plastic deformations in bent specimens. In all tests except for pure normal loading, failure of SPR was initiated from the top sheet, while failure of SPS was caused by pull-out from the bottom sheet in all cases. For SPR, good predictions were found, except for over-prediction of the peeling resistance. The model was not able to describe mixed tension and shear loading accurately for SPS, but other tests were well reproduced. Static and dynamic crash box tests were performed and deformation and failure modes of SPR and SPS were characterized. The same progressive buckling mode was found in all tests. Higher force was observed for riveted crash boxes compared to the screwed. Relative movement between the sheets was observed for SPS. During dynamic testing, 7 % of the SPR and 19 % of the SPS connections failed. Simulations of dynamic crash box tests investigated effects of forming history, yield surface and mesh size. The deformation mode was well reproduced, but the force was under-predicted with 5 % to 20 %. The simulations predicted some connection failure for SPS, but not for SPR. A more fundamental understanding of the behaviour of SPS connections is required to develop a new point-connector model. Further studies could include investigation of the effects of screw diameter, sheet thickness, sheet material, screw material and dynamic effects of the connection.