Deep soil mixing to construct stiff columns is one of the methods used today to improve performance of loose ground and remediate liquefaction problems. This research adopts a numerical approach to study seismic performance of soil-cement columnar reinforcements in loose sandy profiles. Different constitutive models were investigated in order to find a model that can properly predict soil behavior during seismic excitations. These models included NorSand, Dafalias-Manzari, Plasticity Model for Sands (PM4Sand) and Pressure-Dependent-Multi-Yield-02 (PDMY02) model. They were employed to predict behavior of soils with different relative densities and under different confining pressures during monotonic and cyclic loading. PDMY02 was identified as the most suitable model to represent soil seismic behavior for the system studied herein. The numerical aspects of the finite element approach were investigated to minimize the unintended numerical miscalculations. The focus was put on convergence tolerance, solver time-step, constraint definition, and, integration, material and Rayleigh damping. This resulted in forming a robust numerical configuration for 3-D nonlinear models that were later used for studying behavior of the reinforced grounds. Nonlinear finite element models were developed to capture the seismic response of columnar reinforced ground during dynamic centrifuge testing. The models were calibrated with results from tests with unreinforced profiles. Thereafter, they were implemented to predict the response of two reinforced profiles during seismic excitations with different intensities and liquefaction triggering. Model predictions were compared with recordings and the possible effects from the reinforcements were discussed. Finally, parametric studies were performed to further evaluate the efficiency of the reinforcements with different extension depths and area replacement ratios. The results collectively showed that the stiff elements, if constructed appropriately, can withstand seismic excitations with different intensities, and provide a firm base for overlying structures. However, the presence of the stiff elements within the loose ground resulted in stronger seismic intensities on the soil surface. The columns were not able to considerably reduce pore water pressure generation, nor prevent liquefaction triggering. The reinforced profiles, comparing to the free-field profiles, had larger settlements on the soil surface but smaller settlements on the columns. The results concluded that utilization of the columnar reinforcements requires great attention as these reinforcements may result in larger seismic intensities at the ground surface, while not considerably reducing the ground deformations. / Ph. D. / The mitigation of seismic damage potential of soft soil sites remains one of the leading challenges in geotechnical earthquake engineering. It is well-established that structures located on these sites generally experience more damage due to excessive ground deformation during earthquakes. Ground reinforcements are often required to improve these sites for support of overlying structures. A remediating approach is to construct stiff columns within these sites by mechanically mixing soil with cementitious materials. Cemented soil has higher strength, and thereby, undergoes less deformations. Moreover, stiff columns can provide resistance against movement of their surrounding soil providing a firm base for possible above foundations. The primary focus of this research is to evaluate the effect of stiff column reinforcements on seismic behavior of loose ground. For this purpose, a numerical model was developed for the reinforced ground, and it was validated with results from experiments. The model was then used to study the performance of the reinforced ground during earthquake excitations with different intensities. The observed behavior was discussed and compared with findings from previous studies in literature. Finally, the numerical model was employed to evaluate efficiency of the reinforcements with different extension depths and occupied area. The results collectively showed that stiff columns, if constructed appropriately, can withstand different shaking levels, and provide a firm support for overlying structures. However, they were not efficient in reducing deformation of the surrounding soils. The presence of the stiff elements within the loose ground resulted in stronger seismic intensities on the soil surface. The study concluded that utilization of stiff columns requires great attention and understanding of the reinforcing mechanism. These columns might increase seismic intensity below foundations, while not considerably reducing the ground deformations.

Two types of connection are generally considered in the design of steel structures in practice. These are classified as completely rigid (moment) and simple (shear) connections. In theory, completely rigid connections can not undergo rotation and simple connections can not transfer moment. However, in reality rigid connections have a relative flexibility which makes them to rotate and simple connections have some reserve capacity to transfer moments. In many modern design specifications, this fact is realized and another type which is called partially restrained or semi-rigid connection is introduced. These types of connections have got the transfer of some beam moment to column together with shear. However, there is a lack of information on the amount of moment transferred and rotation of connection during the action of the moment transfer. The only way to quantify the moment and rotation of the partially restrained connections is to draw momentrotation curves. Nevertheless, drawing such curves requires great amount of expenses for experiments. Taking these into account, the use of finite elements with the help of increased computational power is one way to obtain moment-rotation curves of connections. Available test results guides the finite element analysis for justifications. So these analyses can be further implemented into design functions. This thesis is intended to conduct 3-D non-linear finite element analyses to compliment with tests results for different types of semi-rigid connections with angles and compare them with mathematical models developed by different researchers.

The incorporation of inflatable structures into aerospace systems can produce significant advantages in stowed volume to mechanical effectiveness and overall weight. Many applications of these ultra-lightweight systems are designed to precisely control internal or external surfaces, or both, to achieve desired performance. The modeling of these structures becomes complex due to the material nonlinearities inherent to the majority of construction materials used in inflatable structures. Furthermore, accurately modeling the response and behavior of the interfacing boundaries that are common to many inflatable systems will lead to better understanding of the entire class of structures. The research presented involved using nonlinear finite element simulations correlated with photogrammetry testing to develop a procedure for defining material properties for commercially available polyurethane-coated woven nylon fabric, which is representative of coated materials that have been proven materials for use in many inflatable systems. Further, the new material model was used to design and develop an inflatable pathfinder system which employs only internal pressure to control an assembly of internal membranes. This canonical inflatable system will be used for exploration and development of general understanding of efficient design methodology and analysis of future systems. Canonical structures are incorporated into the design of the phased pathfinder system to allow for more universal insight. Nonlinear finite element simulations were performed to evaluate the effect of various boundary conditions, loading configurations, and material orientations on the geometric precision of geometries representing typical internal/external surfaces commonly incorporated into inflatable pathfinder system. The response of the inflatable system to possible damage was also studied using nonlinear finite element simulations. Development of a correlated material model for analysis of the inflatable pathfinder system has improved the efficiency of design and analysis techniques of future inflatable structures.

<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>

With increasing age of the concrete road bridges, the highly topical question is to determine their reliability and load-bearing capacity level required for the residual life of the structure. Doctoral thesis presents a comprehensive methodology for assessing the reliability of reinforced and prestressed concrete bridges based on non-linear finite element method damage and failure virtual simulations at both deterministic and stochastic levels. Load-bearing capacity values are specified by the structure’s design load capacity estimation by global safety factor methods or they are based on a fully probabilistic load capacity analysis using the direct resistance estimation. For the fully probabilistic calculations, the simulation technique Latin Hypercube Sampling is used.

The main topic of this thesis concerns the behavior of concrete pile cap supported by four piles with two varying positions of longitudinal reinforcements. The positions include top of piles and bottom of the pile cap. For this purpose, non-linear finite element models of a pile cap are created using software ATENA 3D. The goal was to observe which position of reinforcement yields the higher bearing capacity and to observe the failure modes in the models. To achieve the above goals, a short review of theoretical background concerning shear phenomena is performed. This, in order to enhance the knowledge regarding shear stresses, shear transfer mechanism, factors affecting shear capacity, modes of shear failure and relate them to the behavior of pile cap. Furthermore, the calculation of shear resistance capacity based on Eurocode 2 using strut and tie method and sectional approach is presented. The numerical analysis started by creating four pile cap models in ATENA 3D. The difference between the models being the position and ratio of longitudinal reinforcement. The purpose behind two reinforcement ratios were to observe the behavior of pile cap model in two cases: a) when failure occurs prior to yielding of reinforcement; b) when failure occurs while reinforcement is yielding. The models are then analyzed using software ATENA Studio. The results revealed that placing the reinforcement on top of piles in case (a) increased the capacity of the model by 23.5 % and in case (b) increased the capacity by 18.5 %. This because the tensile stresses were found to be concentrated on top of piles rather than the bottom of the pile cap. The final failure mode in the model with top reinforcement position was crushing of the inclined compressive strut at the node beneath the column and in the model with bottom reinforcement position, the splitting of the compressive strut due to tensile stresses developed perpendicular to the inclined strut. The potential advantage of placing the reinforcement at the bottom were a better crack control in serviceability limit state and a slightly less fragile failure mode compared to the top position of reinforcement. A parametric study was performed in the model as well to observe the effects of various parameters on the results obtained. It was found that fracture energy had the most significant effect on the results obtained. Finally, a comparison between the results of numerical analysis and analytical design approaches based on strut and tie method and sectional approach was performed. The comparison reveals that the design values obtained based on strut and tie method for the model were very conservative. In particular, the equation for the strength of inclined compressive strut based on Eurocode 2 was very general. / Det huvudsakliga ämnet för den här avhandlingen handlar om beteendet hos pålfundament som stöds av fyra pålar med två olika positioner av längsgående armering. Positionerna inkluderar toppen av pålarna och botten av slagdynan. För detta ändamål skapas icke-linjära finita elementmodeller av en slagdyna med mjukvaran ATENA 3D. Målet var att observera vilket armeringsläge som ger den högre bärkapaciteten och att identifiera brottmekanismen i modellerna. För att uppnå ovanstående mål utförs en kort genomgång av teoretisk bakgrund rörande skjuvningsfenomen. Detta för att förbättra kunskapen om skjuvspänningar, skjuvöverföringsmekanism, faktorer som påverkar skjuvkapacitet, skjuvbrott och relaterar dem till beteendet hos slagdynan. Beräkningen av skjuvmotståndet baserad på Eurocode2 med hjälp av Srut and tie-metod och sektionsmetod. Den numeriska analysen började med att skapa fyra pålfundament i ATENA 3D. Skillnaden mellan modellerna är positionen och förhållandet mellan längsgående armering. Syftet bakom två armeringsförhållanden var att observera beteendet hos slagdynan i två fall: a) när brott inträffar innan armering plasticeras; b) när brott inträffar medan armeringen plasticeras. Modellerna analyseras sedan med hjälp av programvaran ATENA Studio. Resultaten visade att placering av armeringen ovanpå pålarna i fall a) ökade modellens kapacitet med 23,5% och i fall (b) ökade kapaciteten med 18,5%. Detta på grund av att dragspänningarna visade sig vara koncentrerade på toppen av pålarna snarare än på botten av slagdynan. Det slutliga brottet i modellen med topparmeringsposition var krossning av det lutande tryckstaget vid noden under pelaren. I modellen med bottenarmeringsposition delades kompressionsstaget på grund av dragspänningar vinkelrätt mot det lutande staget. The potential advantage of placing the reinforcement at the bottom were a better crack control and slightly less fragile failure mode compared to the top position of reinforcement. En parametrisk studie genomfördes också i modellen för att observera effekterna av olika parametrar på de erhållna resultaten. Det visade sig att brottenergi hade den mest signifikanta effekten på de erhållna resultaten. Slutligen genomfördes en jämförelse mellan resultaten från numerisk analys och analytiska designmetoder baserade på strut and tie-metoden och sektionsmetoden. Jämförelsen avslöjar att de designvärden som erhölls baserat på strut and tie-metoden för modellen var mycket konservativa. I synnerhet var ekvationen för kapaciteten hos det lutande tryckstag baserad på Eurocode 2 mycket generell.

Implementing pre-stressing cables is a viable option aiming at controlling deformation and cracking of concrete flat slabs in serviceability limit state. The pre-stressing cables also contribute to punching shear capacity of the slab when they are located in vicinity of the column. The positive influence of pre-stressing cables on punching capacity of the concrete slabs is mainly due to the vertical component of inclined cables, compressive in-plane stresses and counter acting bending moments near the support region. The method presented in Eurocode 2 to determine the punching capacity of the pre-stressed concrete flat slabs considers the in-plane compressive stresses but totally neglects the effect of counter acting moments. The effect of vertical forces introduced by inclined cables is only considered when they are within the distance 2d from the face of the column. This area is called basic control area in the Eurocode 2. In this master thesis nonlinear finite element analysis is carried out to study the effect of pre-stressing cables on punching shear capacity of concrete slabs respecting the distance of cables from the face of the column. To attain this objective, the concrete damage plasticity model is implemented to model the concrete. The results indicate that until the distance of 6d from the face of the column the contribution of pre-stressing cables in punching shear capacity of slabs is significant. Furthermore, comparing the numerical results with the punching shear capacity of slabs predicted by Eurocode 2 reveals that Eurocode tremendously underestimates the punching shear capacity when the cables are located outside the basic control area.

In Nonlinear Finite Element Analysis (FEA) applied to structures, displacements at which the tangent stiffness matrix KT becomes singular are called critical points, and correspond to instabilities such as buckling or elastoplastic softening (e.g., necking). Prior to the introduction of Arc Length Methods (ALMs), critical points posed severe computational challenges, which was unfortunate since behavior at instabilities is of great interest as a precursor to structural failure. The original ALM was shown to be capable in some circumstances of continued computation at critical points, but limited success and unattractive features of the formulation were noted and addressed in extensive subsequent research. The widely used Crisfield Cylindrical and Spherical ALMs may be viewed as representing the 'state-of-the-art'. The more recent Stiff Arc Length method, which is attractive on fundamental grounds, was introduced in 2004, but without implementation, benchmarking or performance assessment. The present thesis addresses (a) implementation and (b) performance comparisons for the Crisfield and Stiff methods, using simple benchmarks formulated to incorporate elastoplastic softening. It is seen that, in contrast to the Crisfield methods, the Stiff ALM consistently continues accurate computation at, near and beyond critical points.

A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure.The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.

Nonlinear finite element models of functionally graded beams with power-law variation of material, accounting for the von-Karman geometric nonlinearity and temperature dependent material properties as well as microstructure dependent length scale have been developed using the Euler-Bernoulli as well as the first-order and third- order beam theories. To capture the size effect, a modified couple stress theory with one length scale parameter is used. Such theories play crucial role in predicting accurate deflections of micro- and nano-beam structures. A general third order beam theory for microstructure dependent beam has been developed for functionally graded beams for the first time using a modified couple stress theory with the von Karman nonlinear strain. Finite element models of the three beam theories have been developed. The thermo-mechanical coupling as well as the bending-stretching coupling play significant role in the deflection response. Numerical results are presented to show the effect of nonlinearity, power-law index, microstructural length scale, and boundary conditions on the bending response of beams under thermo-mechanical loads. In general, the effect of microstructural parameter is to stiffen the beam, while shear deformation has the effect of modeling more realistically as a flexible beam.