<p>The surface of cell membranes can display a high degree of lateral heterogeneity. This non-uniform distribution of constituents is characterized by mobile nanodomain clusters called rafts. Enriched by saturated phospholipids, cholesterol and proteins, rafts are considered to be vital for several important cellular functions such as signalling and trafficking, morphological transformations associated with exocytosis and endocytosis and even as sites for the replication of viruses. Understanding the evolving distribution of these domains can provide significant insight into the regulation of cell function. Giant vesicles are simple prototypes of cell membranes. Microdomains on vesicles can be considered as simple analogues of rafts on cell membranes and offer a means to study various features of cellular processes in isolation. </p><p>In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles (GUVs). The interplay of species transport on the vesicle surface and the mechanics of vesicle shape change is captured using a chemo-mechanical model. Specifically, the approach focuses on the regime of vesicle dynamics where shape change occurs on a much faster time scale in comparison to species transport, as has been observed in several experimental studies on GUVs. In this study, shape changes are assumed to be instantaneous, while species transport, which is modeled by phase separation and domain coarsening, follows a natural time scale described by the Cahn--Hilliard dynamics.</p><p>The curvature energy of the vesicle membrane is defined by the classical Canham--Helfrich--Evans model. Dependence of flexural rigidity and spontaneous curvature on the lipid species is built into the energy functional. The chemical energy is characterized by a Cahn--Hilliard type density function that intrinsically captures the line energy of interfaces between two phases. Both curvature and chemical contributions to the vesicle energetics are consistently non-dimensionalized.</p><p>The coupled model is cast in a diffuse-interface form using the phase-field framework. The phase-field form of the governing equations describing shape equilibrium and species transport are both fourth-order and nonlinear. The system of equations is discretized using the finite element method with a uniform cubic-spline basis that satisfies global higher-order continuity. For shape equilibrium, geometric constraints of constant internal volume and constant surface area of the vesicle are imposed weakly using the penalty approach. A time-stepping scheme based on the unconditionally gradient-stable convexity-splitting technique is employed for explicit time integration of nonlocal integrals arising from the geometric constraints.</p><p>Numerical examples of axisymmetric stationary shapes of uniform vesicles are presented. Further, two- and three-dimensional numerical examples of domain formation and growth coupled to vesicle shape changes are discussed. Simulations qualitatively depicting curvature-dependent domain sorting and shape changes to minimize line tension are presented. The effect of capturing the difference in time scales is also brought out in a few numerical simulations that predict a starkly different pathway to equilibrium.</p> / Dissertation

Prestressed concrete is a popular construction material for highway bridges. A variety of girder span values, cross-sectional shapes, and prestressing strand layouts has been used in bridges across the United States. A major concern for such bridges is the possibility of corrosion damage in the prestressing strands or reinforcing bars, which is commonly caused by the use of deicing salts on the deck or saltwater spray in coastal regions. The present study aims at establishing analytical tools for the accurate simulation of chloride ingress, corrosion and mechanical damage (cracking) in the concrete, and for the evaluation of the impact of corrosion on the flexural and shear strength of bridge girders. First, an efficient and accurate analytical scheme is formulated to enable the calculation of the load-carrying capacity of corrosion-damaged girders. The analyses rely on two types of models, namely, beam models and nonlinear truss models. The latter are deemed necessary to obtain reliable estimates of the shear capacity, as beam models are not well-tailored for capturing shear failures. A procedure to account for the reduction in area and deformability of corroded strands, based on visually observed corrosion damage, is proposed and implemented. The models are calibrated and validated with the results of experimental tests on prestressed girders which exhibited varying levels of corrosion damage. Further analyses allow the comparison of the capacity of corrosion-damaged girders to that of their undamaged counterparts. The accuracy of a simplified procedure, using equations in the AASHTO code to determine the flexural and shear capacity of the damaged girders, is also determined. Subsequently, a computation scheme was proposed to describe the intrusion of chloride ions in prestressed bridge girder sections. The approach accounts for multiple, coupled processes, i.e., heat transfer, moisture transport, and chloride advective and diffusive transport. The constitutive models for moisture and chloride transport rely on previous pertinent work, with several necessary enhancements. The modeling scheme is calibrated with data from previous experimental tests on concrete cylindrical and prismatic specimens. The calibrated models are then validated using data from chloride titration tests conducted on girders removed from two bridges in Virginia after 34 and 49 years of service. The results indicate that the proposed framework can accurately reproduce the experimentally measured chloride content. The modeling approach also allows the evaluation of the accuracy of simplified, design-oriented tools for estimating the evolution of chloride content with time. The multi-physics simulation scheme is further refined to account for the corrosion-induced mechanical damage (cracking), by incorporating a phenomenological description of the electrochemical reaction kinetics, generation of expansive corrosion products, and subsequent development of tensile stresses and cracking in the surrounding concrete. The impact of cracking on the chloride and moisture transport mechanisms is also taken into account. The last part of this dissertation pursues the quantification of the uncertainty governing the chloride ingress in bridge girders, through the use of a stochastic collocation approach. The focus is on understanding how the inherent uncertainty in the value of input parameters (e.g., material transport parameters, ambient conditions etc.) is propagated, leading to uncertainty in the evolution of chloride content and the expected corrosion initiation time for a given bridge. / Doctor of Philosophy / Prestressed concrete is widely utilized in the construction of highway bridges in the United States. A significant concern arises regarding potential corrosion damage in the prestressing strands or reinforcing bars, which is commonly attributed to the application of deicing salts on the deck or exposure to saltwater spray in coastal regions. This study aims to develop analytical tools that can accurately simulate the intrusion of corrosive agents (namely chloride ions), and subsequent damage (cracking) in concrete. Furthermore, the research seeks to assess the impact of corrosion on the bearing capacity of bridge girders. Two different classes of analytical approaches are pursued. The first class employs purely mechanical (stress/deformation) models for capturing the strength, deformability and failure modes of girders with visual corrosion damage. These models rely on two approaches to capture the flexural and shear capacity of specimens, namely, beam-based models and truss-based models. The impact of corrosion is established through appropriate modification of the model parameters, based on the extent of visually observed corrosion damage. The analytical approaches are validated through a series of experimental tests previously conducted on corrosion-damaged girders. The second class of analytical approaches employs multi-physics models, to describe the mechanisms leading to corrosion-induced damage. The models account for heat transfer, moisture transport, and chloride transport in prestressed beam sections. Model parameters are calibrated with experimental tests in literature. The computational scheme is used to quantitatively describe the chloride ingress on bridge girders decommissioned from two different bridges in Virginia, after 34 and 49 years of service. The analysis results are found capable of capturing the actual chloride content at various depths from the exposure surface, as determined by chloride titration tests. The temporal evolution of chloride on the surface of prestressing strands indicates that corrosion has been taking place over a period of time for the two bridges. The multi-physics simulation approach is further enhanced to account for the corrosion-induced mechanical damage (cracking), by explicitly incorporating a description of the reaction kinetics, generation of expansive corrosion products and subsequent development of cracking in the surrounding concrete. The last part of this dissertation pursues the quantification of the uncertainty in the expected service life of prestressed concrete bridge structures. Given the inherent uncertainty to key values of model parameters, a parametric study is employed to investigate the propagation of uncertainty to the time history of chloride content at particular locations of the section and the probability of corrosion initiation at specific age values.

Afin de répondre aux questions des propriétaires de structures atteintes de réaction alcali-silice (RAS), ce travail se concentre sur une partie d'une méthodologie globale, proposée initialement par le LMDC et EDF, et dont le but est l'étude du comportement mécanique des constructions endommagées par la RAS. Pour atteindre cet objectif, l'avancement chimique de la RAS des granulats récupérés dans les structures affectées doit être évalué. Ainsi, ce travail est consacré à la quantification de la silice potentiellement réactive des granulats, par l'utilisation de deux approches : une approche indirecte par un test d'expansion et une approche directe par des méthodes chimiques. La présentation du manuscrit s'articule autour des points suivants :• Un test d'expansion pertinent et rapide sur mortiers pour relier la quantité de silice réactive à l'expansion mesurée. Les conditions expérimentales suivantes ont été choisies pour tester différentes tailles et natures de granulats, ainsi que différentes tailles d'éprouvettes : solution de NaOH à 1 mol/l et température de conservation de 60°C.• Une méthode chimique rapide de dissolution sélective pour mesurer directement la quantité de silice réactive disponible pour la RAS. La méthode HF / HF+HCl a été trouvé comme étant la plus efficace.• Un modèle chemo-mécanique pour analyser les effets de la taille des granulats et des éprouvettes, et évaluer l'avancement chimique de la réaction.Finalement, une méthodologie est proposée pour calculer la constante cinétique de la réaction dans le cadre de la requalification des structures atteintes de RAS. / In order to answer the questions of the ASR-affected structures owners, this work focused on a part of a global methodology, which is proposed originally by the LMDC and EDF, aiming to reassess the mechanical behavior of ASR-damaged constructions. To achieve this purpose, the chemical advancement of ASR in the aggregates recovered from the structure should be evaluated. Thus, this work focuses on the assessment of the potentially reactive silica content with two main methods: indirectly by expansion test and directly by chemical methods. The presentation of this manuscript is around the following points: • A relevant and rapid expansion test on mortars to link the reactive silica content to measured expansion. The experimental condition: 1 mol/l NaOH solution conserved at 60°C is chosen to test different aggregate sizes, specimen sizes and natures of aggregate. • A fast chemical method of selective dissolution to measure directly the silica available for ASR. Acid/basic methods are tested and compared; HF / HF+HCl method is found to be the most effective. • A chemo-mechanical model to analyze the effect of aggregate size and specimen size, and evaluate the chemical advancement of ASR. Finally, a methodology is proposed to calculate the kinetics constant in the framework of structural requalification. Key words: alkali-silica reaction (ASR), chemical advancement, reactive silica, expansion test, chemical test, chemo-mechanical model, kinetic constant, selective dissolution