A materially non-linear layered beam super element is developed for the analysis of RC beams and columns strengthened by externally bonded steel/FRP plates. The elasto-plastic behavior of RC member is incorporated by its internally generated or externally supplied moment-curvature diagram. The steel plate is assumed to be elasto-plastic and the FRP laminate is assumed to behave linearly elastic up to rupture. The thin epoxy layer between the RC member and the externally bonded lamina is simulated by a special interface element which allows for the changing failure modes from steel plate yielding/FRP plate rupture to separation of the bonded plates as a result of bond failure in the epoxy layer. An empirical failure criterion based on test results is used for the epoxy material of the interface. The most critical aspect of such applications in real life frame structures is the anchorage conditions at the member ends and junctions. This has direct influence on the success and the effectiveness of the application. Therefore, a special corner piece anchorage element is also considered in the formulation of the joint super element, which establishes the fixity and continuity conditions at the member ends and the joints.

A nonlinear finite element analysis was performed for an existing road bridge in order to see if that could show a higher load bearing capacity, as an alternative to repairing or replacing. The regular linear analysis had shown that the bridge could not take any traffic load due to the effects from large and uneven support settlements. It is a five-span reinforced concrete bridge with a continuous slab on supports made out of rows of columns. The width-to-span ratio was around 1 and the supports were angled up to about 30°, giving rise to a complex three-dimensional behaviour, which was seen and studied in the nonlinear results. Since the bending moment was the limiting factor, the nonlinear analysis focused on that. The direct result was that the load bearing capacity was 730 kN for the traffic vehicle boogie load, B, in the ultimate limit state. This was however only for the load case tested, and several more disadvantageous vehicle positions may exist. Other aspects also became limiting, as the maximum allowed vertical deflection in the serviceability limit state was reached at 457 kN. The most restraining though, was the shear capacity from the linear analysis; 78 kN, since it was not possible to simulate that type of failure with the shell elements used in the nonlinear finite element analysis. The main aim of the thesis was nonetheless reached, since the nonlinear analysis was able to show a significant increase in load bearing capacity.  A comparison was made with the settlements for the nonlinear case, to see how much influence they had on the load bearing capacity for traffic load. This was performed for both the bridge and a simple two-span beam. Both showed that there was no effect on the load bearing capacity in the ultimate limit. One thing to note was that the full settlements were applied, and with no relaxation due to creep.  Another aim of the thesis was to make comments on the practical usability of the nonlinear finite element method in load bearing capacity assessments. A linear analysis was performed before the nonlinear in order to be able to determine the load case to be used in the latter. This worked well, as the strengths of the two methods could then be utilized. Convergence problems were however encountered for the nonlinear when using the regular static solver. Due to this, the dynamic explicit calculation scheme was used instead, treating the case as quasi-static. This managed to produce enough usable results. It was concluded that the nonlinear finite element method is useable for assessment calculations, but that its strengths and weaknesses must be known in order to make it an efficient method.

A nonlinear finite element analysis was performed for an existing road bridge in order to see if that could show a higher load bearing capacity, as an alternative to repairing or replacing. The regular linear analysis had shown that the bridge could not take any traffic load due to the effects from large and uneven support settlements. It is a five-span reinforced concrete bridge with a continuous slab on supports made out of rows of columns. The width-to-span ratio was around 1 and the supports were angled up to about 30°, giving rise to a complex three-dimensional behaviour, which was seen and studied in the nonlinear results. Since the bending moment was the limiting factor, the nonlinear analysis focused on that. The direct result was that the load bearing capacity was 730 kN for the traffic vehicle boogie load, B, in the ultimate limit state. This was however only for the load case tested, and several more disadvantageous vehicle positions may exist. Other aspects also became limiting, as the maximum allowed vertical deflection in the serviceability limit state was reached at 457 kN. The most restraining though, was the shear capacity from the linear analysis; 78 kN, since it was not possible to simulate that type of failure with the shell elements used in the nonlinear finite element analysis. The main aim of the thesis was nonetheless reached, since the nonlinear analysis was able to show a significant increase in load bearing capacity. A comparison was made with the settlements for the nonlinear case, to see how much influence they had on the load bearing capacity for traffic load. This was performed for both the bridge and a simple two-span beam. Both showed that there was no effect on the load bearing capacity in the ultimate limit. One thing to note was that the full settlements were applied, and with no relaxation due to creep. Another aim of the thesis was to make comments on the practical usability of the nonlinear finite element method in load bearing capacity assessments. A linear analysis was performed before the nonlinear in order to be able to determine the load case to be used in the latter. This worked well, as the strengths of the two methods could then be utilized. Convergence problems were however encountered for the nonlinear when using the regular static solver. Due to this, the dynamic explicit calculation scheme was used instead, treating the case as quasi-static. This managed to produce enough usable results. It was concluded that the nonlinear finite element method is useable for assessment calculations, but that its strengths and weaknesses must be known in order to make it an efficient method.

<div>Excessive deformation and stress of skin following reconstructive surgery plays a crucial role in wound healing, often leading to complications. Yet, despite of this concern, surgeries are still planned and executed based on each surgeon's training and experience rather than quantitative engineering tools. The limitations of current treatment planning and execution stem in part from the difficulty in predicting the mechanical behavior of skin, challenges in directly measuring stress in the operating room, and inability to predict the long term adaptation of skin following reconstructive surgery. Computational modeling of soft tissue mechanics has emerged as an ideal candidate to determine stress contours over sizable skin regions in realistic situations. Virtual surgeries with computational mechanics tools will help surgeons explore different surgeries preoperatively, make prediction of stress contours, and eventually aid the surgeon in planning for optimal wound healing. While there has been significant progress on computational modeling of both reconstructive surgery and skin mechanical and mechanobiological behavior, there remain major gaps preventing computational mechanics to be widely used in the clinical setting. At the preoperative stage, better calibration of skin mechanical properties for individual patients based on minimally invasive mechanical tests is still needed. One of the key challenges in this task is that skin is not stress-free in vivo. In many applications requiring large skin flaps, skin is further grown with the tissue expansion technique. Thus, better understanding of skin growth and the resulting stress-free state is required. The other most significant challenge is dealing with the inherent variability of mechanical properties and biological response of biological systems. Skin properties and adaptation to mechanical cues changes with patient demographic, anatomical location, and from one individual to another. Thus, the precise model parameters can never be known exactly, even if some measurements are available. Therefore, rather than expecting to know the exact model describing a patient, a probabilistic approach is needed. To bridge the gaps, this dissertation aims to advance skin biomechanics and computational mechanics tools in order to make virtual surgery for clinical use a reality in the near future. In this spirit, the dissertation constitutes three parts: skin growth and its incompatibility, acquisition of patient-specific geometry and skin mechanical properties, and uncertainty analysis of virtual surgery scenarios.</div><div>Skin growth induced by tissue expansion has been widely used to gain extra skin before reconstructive surgery. Within continuum mechanics, growth can be described with the split of the deformation gradient akin to plasticity. We propose a probabilistic framework to do uncertainty analysis of growth and remodeling of skin in tissue expansion. Our approach relies on surrogate modeling through multi-fidelity Gaussian process regression. This work is being used calibrate the computational model against animal model data. Details of the animal model and the type of data obtained are also covered in the thesis. One important aspect of the growth and remodeling process is that it leads to residual stress. It is understood that this stress arises due to the nonhomogeneous growth deformation. In this dissertation we characterize the geometry of incompatibility of the growth field borrowing concepts originally developed in the study of crystal plasticity. We show that growth produces unique incompatibility fields that increase our understanding of the development of residual stress and the stress-free configuration of tissues. We pay particular attention to the case of skin growth in tissue expansion.</div><div>Patient-specific geometry and material properties are the focus on the second part of the thesis. Minimally invasive mechanical tests based on suction have been developed which can be used in vivo, but these tests offer only limited characterization of an individual's skin mechanics. Current methods have the following limitations: only isotropic behavior can be measured, the calibration problem is done with inverse finite element methods or simple analytical calculations which are inaccurate, the calibration yields a single deterministic set of parameters, and the process ignores any previous information about the mechanical properties that can be expected for a patient. To overcome these limitations, we recast the calibration problem in a Bayesian framework. To sample from the posterior distribution of the parameters for a patient given a suction test, the method relies on an inexpensive Gaussian process surrogate. For the patient-specific geometry, techniques such as magnetic resonance imaging or computer tomography scans can be used. Such approaches, however, require specialized equipment and set up and are not affordable in many scenarios. We propose to use multi-view stereo (MVS) to capture patient-specific geometry.</div><div>The last part of the dissertation focuses on uncertainty analysis of the reconstructive procedure itself. To achieve uncertainty analysis in the clinical setting we propose to create surrogate and reduced order models, especially principal component analysis and Gaussian process regression. We first show the characterization of stress profiles under uncertainty for the three most common flap designs. For these examples we deal with idealized geometries. The probabilistic surrogates enable not only tasks such as fast prediction and uncertainty quantification, but also optimization. Based on a global sensitivity analysis we show that the direction of anisotropy of skin with respect to the flap geometry is the most important parameter controlled by the surgeon, and we show hot to optimize the flap in this idealized setting. We conclude with the application of the probabilistic surrogates to perform uncertainty analysis in patient-specific geometries. In summary, this dissertation focuses on some of the fundamental challenges that needed to be addressed to make virtual surgery models ready for clinical use. We anticipate that our results will continue to shape the way computational models continue to be incorporated in reconstructive surgery plans.</div>

As of now, the most common way in Sweden, to address the issue of local buckling of steelstructures is through the procedure called the effective width method. A less commonprocedure for dealing with local buckling is the reduced stress method. The benefit of thelatter method is that, when combined with finite element analysis, results in a less tediousdesign process. However, this method is often labelled as a method that results in anoverconservative design. Therefore, the purpose of this report is to compare and evaluate thereduced stress method against the effective width method and nonlinear finite elementmethod. The nonlinear FE-analyses are performed with intention of simulating the realbehaviour of the structure and serve as a reference for the other two methods. The comparisonis conducted through a series of analyses, on different steel members with various loadconfigurations and slenderness in order to include the most common cases in the constructionindustry. This report resulted in recommendations for when the reduced stress method couldbe a relevant design procedure, with emphasis on providing reliable and accurate resultscompared to FE-analyses. Furthermore, the report resulted in proposed further studies, bothregarding the improvement of the reduced stress method and other structural elements thatshould be studied. The result from the report indicates that the reduced stress method can beused when the effect of patch loading is small. Furthermore, it is recommended to obtain thecritical stresses from a linear finite element analysis rather than from hand calculations, as tonot end up with over-conservative results. / I Sverige behandlas problemet med lokal buckling av stålkonstruktioner vanligtvis med hjälpav den effektiva bredd metoden, vilket är en dimensionergsmetod som återfinns i Eurocode.En ytterligare dimensionerings metod för lokal buckling som presenteras i Eurocode är denreducerade spänningsmetoden. Den senare nämnda metoden är fördelaktig då den kombinerasmed linjära finita element analyser, vilket resulterar i en mindre tidskrävandedimensioneringsprocess. Dock är metoden känd för att ofta resultera i överdimensioneradekonstruktioner, vilket bidragit till att mindre antal konstruktörer använder sig av denna metod.Syftet med denna rapport blir därmed att jämföra och utvärdera den reduceradespänningsmetoden gentemot den effektiva bredd metoden och olinjär finita element metoden.De olinjära finita element analyserna genomfördes med syfte att simulera det verkligabeteendet och för att sedan jämföra dessa resultat med de två andra metoderna. Analyser harutförts på flera stålbalkar med olika lastkombinationer och slankhet för att inkludera devanligaste fallen inom byggindustrin. Dessutom har det tagits fram några rekommendationerför användningen av metoderna och dessa är presenterade med avseende på de erhållnaresultaten. Rekommendationer för den reducerade spänningsmetoden har presenterats ochytterligare studier gällande dessa metoder och andra konstruktionselement har föreslagits. Deslutsatser som kunde dras är att den reducerade spänningsmetoden kan användas förkonstruktioner som inte påverkas i allt för stor grad av intryckning. För att ge tillförliterligaresultat så rekommenderas att kritiska spänningar erhålles från linjära finita element analyser.