Numerical simulation of some viscoelastic fluids

Numerical simulation of the Oldroyd-B type viscoelastic fluids is a very challenging problem. rnThe well-known High Weissenberg Number Problem" has haunted the mathematicians, computer scientists, and rnengineers for more than 40 years. rnWhen the Weissenberg number, which represents the ratio of elasticity to viscosity, rnexceeds some limits, simulations done by standard methods break down exponentially fast in time. rnHowever, some approaches, such as the logarithm transformation technique can significantly improve rnthe limits of the Weissenberg number until which the simulations stay stable. rnrnWe should point out that the global existence of weak solutions for the Oldroyd-B model is still open. rnLet us note that in the evolution equation of the elastic stress tensor the terms describing diffusive rneffects are typically neglected in the modelling due to their smallness. However, when keeping rnthese diffusive terms in the constitutive law the global existence of weak solutions in two-space dimension rncan been shown. rnrnThis main part of the thesis is devoted to the stability study of the Oldroyd-B viscoelastic model. rnFirstly, we show that the free energy of the diffusive Oldroyd-B model as well as its rnlogarithm transformation are dissipative in time. rnFurther, we have developed free energy dissipative schemes based on the characteristic finite element and finite difference framework. rnIn addition, the global linear stability analysis of the diffusive Oldroyd-B model has also be discussed. rnThe next part of the thesis deals with the error estimates of the combined finite element rnand finite volume discretization of a special Oldroyd-B model which covers the limiting rncase of Weissenberg number going to infinity. Theoretical results are confirmed by a series of numerical rnexperiments, which are presented in the thesis, too.

Eliminating Adhesion Errors in Nanoindentation of Compliant Polymers and Hydrogels

Nanoindentation is a valuable tool for characterization of biomaterials due to its ability to measure local properties in heterogeneous, small or irregularly shaped samples. However, applying nanoindentation to compliant, hydrated biomaterials leads to many challenges including adhesion between the nanoindenter tip and the sample. Although adhesion leads to overestimation of the modulus of compliant samples when analyzing nanoindentation data using traditional analysis techniques, most studies of biomaterials have ignored its effects. This paper demonstrates two methods for managing adhesion in nanoindentation analysis, the nano-JKR force curve method and the surfactant method, through application to two biomedically-relevant compliant materials, poly(dimethyl siloxane) (PDMS) elastomers and poly(ethylene glycol) (PEG) hydrogels. The nano-JKR force curve method accounts for adhesion during data analysis using equations based on the Johnson-Kendall-Roberts (JKR) adhesion model, while the surfactant method eliminates adhesion during data collection, allowing data analysis using traditional techniques. In this study, indents performed in air or water resulted in adhesion between the tip and the sample, while testing the same materials submerged in Optifree Express() contact lens solution eliminated tip-sample adhesion in most samples. Modulus values from the two methods were within 7% of each other, despite different hydration conditions and evidence of adhesion. Using surfactant also did not significantly alter the properties of the tested material, allowed accurate modulus measurements using commercial software, and facilitated nanoindentation testing in fluids. This technique shows promise for more accurate and faster determination of modulus values from nanoindentation of compliant, hydrated biological samples. Copyright 2013 Elsevier Ltd. All rights reserved.

The long-term mechanical integrity of non-reinforced PEEK-OPTIMA polymer for demanding spinal applications: experimental and finite-element analysis

Polyetheretherketone (PEEK) is a novel polymer with potential advantages for its use in demanding orthopaedic applications (e.g. intervertebral cages). However, the influence of a physiological environment on the mechanical stability of PEEK has not been reported. Furthermore, the suitability of the polymer for use in highly stressed spinal implants such as intervertebral cages has not been investigated. Therefore, a combined experimental and analytical study was performed to address these open questions. A quasi-static mechanical compression test was performed to compare the initial mechanical properties of PEEK-OPTIMA polymer in a dry, room-temperature and in an aqueous, 37 degrees C environment (n=10 per group). The creep behaviour of cylindrical PEEK polymer specimens (n=6) was measured in a simulated physiological environment at an applied stress level of 10 MPa for a loading duration of 2000 hours (12 weeks). To compare the biomechanical performance of different intervertebral cage types made from PEEK and titanium under complex loading conditions, a three-dimensional finite element model of a functional spinal unit was created. The elastic modulus of PEEK polymer specimens in a physiological environment was 1.8% lower than that of specimens tested at dry, room temperature conditions (P<0.001). The results from the creep test showed an average creep strain of less than 0.1% after 2000 hours of loading. The finite element analysis demonstrated high strain and stress concentrations at the bone/implant interface, emphasizing the importance of cage geometry for load distribution. The stress and strain maxima in the implants were well below the material strength limits of PEEK. In summary, the experimental results verified the mechanical stability of the PEEK-OPTIMA polymer in a simulated physiological environment, and over extended loading periods. Finite element analysis supported the use of PEEK-OPTIMA for load-bearing intervertebral implants.

Investigation into the enhancement of polycarbonate with conductive nanomaterials

Polymers are typically electrically and thermally insulating materials. The electrical and thermal conductivities of polymers can be increased by the addition conductive fillers such as carbons. Once the polymer composites have been made electrically and thermally conductive, they can be used in applications where these conductivities are desired such as electromagnetic shielding and static dissipation. In this project, three carbon nanomaterials are added to polycarbonate to enhance the electrical and thermal conductivity of the resulting composite. Hyperion Catalysis FIBRILs carbon nanotubes were added to a maximum loading of 8 wt%. Ketjenblack EC-600 JD carbon black was added to a maximum loading of 10 wt%. XG Sciences xGnP™ graphene nanoplatelets were added to a maximum loading of 15 wt%. These three materials have drastically different morphologies and will have varying effects on the various properties of polycarbonate composites. It was determined that carbon nanotubes have the largest effect on electrical conductivity with an 8 wt% carbon nanotube in polycarbonate composite having an electrical conductivity of 0.128 S/cm (from a pure polycarbonate value of 10-17 S/cm). Carbon black has the next largest effect with an 8 wt% carbon black in polycarbonate composite having an electrical conductivity of 0.008 S/cm. Graphene nanoplatelets have the least effect with an 8 wt% graphene nanoplatelet in polycarbonate having an electrical conductivity of 2.53 x 10-8 S/cm. Graphene nanoplatelets show a significantly higher effect on increasing thermal conductivity than either carbon nanotubes or carbon black. Mechanically, all three materials have similar effects with graphene nanoplatelets being somewhat more effective at increasing the tensile modulus of the composite than the other fillers. Carbon black and graphene nanoplatelets show standard carbon-filler rheology where the addition of filler increases the viscosity of the resulting composite. Carbon nanotubes, on the other hand, show an unexpected rheology. As carbon nanotubes are added to polycarbonate the viscosity of the composite is reduced below that of the original polycarbonate. It was seen that the addition of carbon nanotubes offsets the increased viscosity from a second filler, such as carbon black or graphene nanoplatelets.

Variation of the mechanical properties of PMMA to suit osteoporotic cancellous bone

Poly(methyl methacrylate) (PMMA) is by far the most frequently used bone substitute material for vertebroplasty. However, there are serious complications, such as cement leakage and an increased fracture rate of the adjacent vertebral bodies. The latter may be related to the mechanical properties of the augmented segment within the osteoporotic spine. A possible counter-measure is prophylactic augmentation at additional levels, but this aggravates the risk for the patient. Introduction of pores is a possible method to reduce the inherent high stiffness of PMMA. This study investigates the effect of porosity on the mechanical properties of PMMA bone cement. Different fractions of a highly viscous liquid were mixed into the PMMA during preparation. An open-porous material with adjustable mechanical properties resulted after removal of the aqueous phase. Different radiopacifiers were admixed to investigate their suitability for vertebroplasty. The final material was characterized mechanically by compressive testing, microscopically and radiologically. In addition, the monomer release subsequent to hardening was measured by means of gas chromatography. The Young's modulus in compression could be varied between 2800 +/- 70 MPa and 120 +/- 150 MPa, and the compression ultimate strength between 170 +/- 5 MPa and 8 +/- 9 MPa for aqueous fractions ranging between 0 and 50% of volume. Only a slight decrease of the Young's modulus and small changes of ultimate strength were found when the mixing time was increased. An organic hydrophilic and lipophilic radiopacifier led to a higher Young's modulus of the porous material; however, the ultimate strength was not significantly affected by adding different radiopacifiers to the porous cement. The radiopacity was lost after washing the aqueous phase out of the pores. No separation occurred between the aqueous and the PMMA phase during injection into an open porous ceramic material. The monomer released was found to increase for increasing aqueous fractions, but remained comparable in magnitude to standard PMMA. This study demonstrates that a conventional PMMA can be modified to obtain a range of mechanical properties, including those of osteoporotic bone.

Performance of vertebral cancellous bone augmented with compliant PMMA under dynamic loads

Increased fracture risk has been reported for the adjacent vertebral bodies after vertebroplasty. This increase has been partly attributed to the high Young's modulus of commonly used polymethylmethacrylate (PMMA). Therefore, a compliant bone cement of PMMA with a bulk modulus closer to the apparent modulus of cancellous bone has been produced. This compliant bone cement was achieved by introducing pores in the cement. Due to the reduced failure strength of that porous PMMA cement, cancellous bone augmented with such cement could deteriorate under dynamic loading. The aim of the present study was to assess the potential of acute failure, particle generation and mechanical properties of cancellous bone augmented with this compliant cement in comparison to regular cement. For this purpose, vertebral biopsies were augmented with porous- and regular PMMA bone cement, submitted to dynamic tests and compression to failure. Changes in Young's modulus and height due to dynamic loading were determined. Afterwards, yield strength and Young's modulus were determined by compressive tests to failure and compared to the individual composite materials. No failure occurred and no particle generation could be observed during dynamical testing for both groups. Height loss was significantly higher for the porous cement composite (0.53+/-0.21%) in comparison to the biopsies augmented with regular cement (0.16+/-0.1%). Young's modulus of biopsies augmented with porous PMMA was comparable to cancellous bone or porous cement alone (200-700 MPa). The yield strength of those biopsies (21.1+/-4.1 MPa) was around two times higher than for porous cement alone (11.6+/-3.3 MPa).

Characterization of thermal and mechanical properties of polypropylene-based composites for fuel cell bipolar plates and development of educational tools in hydrogen and fuel cell technologies

In this project we developed conductive thermoplastic resins by adding varying amounts of three different carbon fillers: carbon black (CB), synthetic graphite (SG) and multi-walled carbon nanotubes (CNT) to a polypropylene matrix for application as fuel cell bipolar plates. This component of fuel cells provides mechanical support to the stack, circulates the gases that participate in the electrochemical reaction within the fuel cell and allows for removal of the excess heat from the system. The materials fabricated in this work were tested to determine their mechanical and thermal properties. These materials were produced by adding varying amounts of single carbon fillers to a polypropylene matrix (2.5 to 15 wt.% Ketjenblack EC-600 JD carbon black, 10 to 80 wt.% Asbury Carbon's Thermocarb TC-300 synthetic graphite, and 2.5 to 15 wt.% of Hyperion Catalysis International's FIBRILTM multi-walled carbon nanotubes) In addition, composite materials containing combinations of these three fillers were produced. The thermal conductivity results showed an increase in both through-plane and in-plane thermal conductivities, with the largest increase observed for synthetic graphite. The Department of Energy (DOE) had previously set a thermal conductivity goal of 20 W/m·K, which was surpassed by formulations containing 75 wt.% and 80 wt.% SG, yielding in-plane thermal conductivity values of 24.4 W/m·K and 33.6 W/m·K, respectively. In addition, composites containing 2.5 wt.% CB, 65 wt.% SG, and 6 wt.% CNT in PP had an in–plane thermal conductivity of 37 W/m·K. Flexural and tensile tests were conducted. All composite formulations exceeded the flexural strength target of 25 MPa set by DOE. The tensile and flexural modulus of the composites increased with higher concentration of carbon fillers. Carbon black and synthetic graphite caused a decrease in the tensile and flexural strengths of the composites. However, carbon nanotubes increased the composite tensile and flexural strengths. Mathematical models were applied to estimate through-plane and in-plane thermal conductivities of single and multiple filler formulations, and tensile modulus of single-filler formulations. For thermal conductivity, Nielsen's model yielded accurate thermal conductivity values when compared to experimental results obtained through the Flash method. For prediction of tensile modulus Nielsen's model yielded the smallest error between the predicted and experimental values. The second part of this project consisted of the development of a curriculum in Fuel Cell and Hydrogen Technologies to address different educational barriers identified by the Department of Energy. By the creation of new courses and enterprise programs in the areas of fuel cells and the use of hydrogen as an energy carrier, we introduced engineering students to the new technologies, policies and challenges present with this alternative energy. Feedback provided by students participating in these courses and enterprise programs indicate positive acceptance of the different educational tools. Results obtained from a survey applied to students after participating in these courses showed an increase in the knowledge and awareness of energy fundamentals, which indicates the modules developed in this project are effective in introducing students to alternative energy sources.

CHARACTERIZATION OF ASPHALT MATERIALS CONTAINING BIO OIL FROM MICHIGAN WOOD

The objective of this research is to develop sustainable wood-blend bioasphalt and characterize the atomic, molecular and bulk-scale behavior necessary to produce advanced asphalt paving mixtures. Bioasphalt was manufactured from Aspen, Basswood, Red Maple, Balsam, Maple, Pine, Beech and Magnolia wood via a 25 KWt fast-pyrolysis plant at 500 °C and refined into two distinct end forms - non-treated (5.54% moisture) and treated bioasphalt (1% moisture). Michigan petroleum-based asphalt, Performance Grade (PG) 58-28 was modified with 2, 5 and 10% of the bioasphalt by weight of base asphalt and characterized with the gas chromatography-mass spectroscopy (GC-MS), Fourier Transform Infra-red (FTIR) spectroscopy and the automated flocculation titrimetry techniques. The GC-MS method was used to characterize the Carbon-Hydrogen-Nitrogen (CHN) elemental ratio whiles the FTIR and the AFT were used to characterize the oxidative aging performance and the solubility parameters, respectively. For rheological characterization, the rotational viscosity, dynamic shear modulus and flexural bending methods are used in evaluating the low, intermediate and high temperature performance of the bio-modified asphalt materials. 54 5E3 (maximum of 3 million expected equivalent standard axle traffic loads) asphalt paving mixes were then prepared and characterized to investigate their laboratory permanent deformation, dynamic mix stiffness, moisture susceptibility, workability and constructability performance. From the research investigations, it was concluded that: 1) levo, 2, 6 dimethoxyphenol, 2 methoxy 4 vinylphenol, 2 methyl 1-2 cyclopentandione and 4-allyl-2, 6 dimetoxyphenol are the dominant chemical functional groups; 2) bioasphalt increases the viscosity and dynamic shear modulus of traditional asphalt binders; 3) Bio-modified petroleum asphalt can provide low-temperature cracking resistance benefits at -18 °C but is susceptible to cracking at -24 °C; 3) Carbonyl and sulphoxide oxidation in petroleum-based asphalt increases with increasing bioasphalt modifiers; 4) bioasphalt causes the asphaltene fractions in petroleum-based asphalt to precipitate out of the solvent maltene fractions; 5) there is no definite improvement or decline in the dynamic mix behavior of bio-modified mixes at low temperatures; 6) bio-modified asphalt mixes exhibit better rutting performance than traditional asphalt mixes; 7) bio-modified asphalt mixes have lower susceptibility to moisture damage; 8) more field compaction energy is needed to compact bio-modified mixes.

The Laboratory Evaluation of Bio Oil Derived From Waste Resources as Extender for Asphalt Binder

A shortage of petroleum asphalt is creating opportunities for engineers to utilize alternative pavement materials. Three types of bio oils, original bio oil (OB), dewatered bio oil (DWB) and polymer-modified bio oil (PMB) were used to modify and partially replace petroleum asphalt in this research. The research investigated the procedure of producing bio oil, the rheological properties of asphalt binders modified and partially replaced by bio oil, and the mechanical performances of asphalt mixtures modified by bio oil. The analysis of variance (ANOVA) is conducted on the test results for the significance analysis. The main finding of the study includes: 1) the virgin bioasphalt is softer than the traditional asphalt binder PG 58-28 but stiffer after RTFO aging because bio oil ages much faster than the traditional asphalt binder during mixing and compaction; 2) the binder test showed that the addition of bio oil is expected to improve the rutting performance while reduce the fatigue and low temperature performance; 3) both the mass loss and the oxidation are important reasons for the bio oil aging during RTFO test; the mixture test showed that 1) most of the bio oil modified asphalt mixture had slightly higher rutting depth than the control asphalt mixture, but the difference is not statistically significant; 2) the dynamic modulus of some of the bio oil modified asphalt mixture were slightly lower than the control asphalt mixture, the E* modulus is also not statistically significant; 3) most of the bio oil modified asphalt mixture had higher fatigue lives than the control asphalt mixture; 4) the inconsistence of binder test results and mixture test results may be attributed to that the aging during the mixing and compaction was not as high as that in the RTFO aging simulation. 5) the implementation of Michigan wood bioasphalt is anticipated to reduce the emission but bring irritation on eyes and skins during the mixing and compaction.

Probing the mechanical properties of TNF-α stimulated endothelial cell with atomic force microscopy.

TNF-α (tumor necrosis factor-α) is a potent pro-inflammatory cytokine that regulates the permeability of blood and lymphatic vessels. The plasma concentration of TNF-α is elevated (> 1 pg/mL) in several pathologies, including rheumatoid arthritis, atherosclerosis, cancer, pre-eclampsia; in obese individuals; and in trauma patients. To test whether circulating TNF-α could induce similar alterations in different districts along the vascular system, three endothelial cell lines, namely HUVEC, HPMEC, and HCAEC, were characterized in terms of 1) mechanical properties, employing atomic force microscopy; 2) cytoskeletal organization, through fluorescence microscopy; and 3) membrane overexpression of adhesion molecules, employing ELISA and immunostaining. Upon stimulation with TNF-α (10 ng/mL for 20 h), for all three endothelial cells, the mechanical stiffness increased by about 50% with a mean apparent elastic modulus of E ~5 ± 0.5 kPa (~3.3 ± 0.35 kPa for the control cells); the density of F-actin filaments increased in the apical and median planes; and the ICAM-1 receptors were overexpressed compared with controls. Collectively, these results demonstrate that sufficiently high levels of circulating TNF-α have similar effects on different endothelial districts, and provide additional information for unraveling the possible correlations between circulating pro-inflammatory cytokines and systemic vascular dysfunction.

The impact of ocean acidification and warming on the skeletal mechanical properties of the sea urchin Paracentrotus lividus from laboratory and field observations

Increased atmospheric CO2 concentration is leading to changes in the carbonate chemistry and the temperature of the ocean. The impact of these processes on marine organisms will depend on their ability to cope with those changes, particularly the maintenance of calcium carbonate structures. Both a laboratory experiment (long-term exposure to decreased pH and increased temperature) and collections of individuals from natural environments characterized by low pH levels (individuals from intertidal pools and around a CO2 seep) were here coupled to comprehensively study the impact of near-future conditions of pH and temperature on the mechanical properties of the skeleton of the euechinoid sea urchin Paracentrotus lividus. To assess skeletal mechanical properties, we characterized the fracture force, Young's modulus, second moment of area, material nanohardness, and specific Young's modulus of sea urchin test plates. None of these parameters were significantly affected by low pH and/or increased temperature in the laboratory experiment and by low pH only in the individuals chronically exposed to lowered pH from the CO2 seeps. In tidal pools, the fracture force was higher and the Young's modulus lower in ambital plates of individuals from the rock pool characterized by the largest pH variations but also a dominance of calcifying algae, which might explain some of the variation. Thus, decreases of pH to levels expected for 2100 did not directly alter the mechanical properties of the test of P. lividus. Since the maintenance of test integrity is a question of survival for sea urchins and since weakened tests would increase the sea urchins' risk of predation, our findings indicate that the decreasing seawater pH and increasing seawater temperature expected for the end of the century should not represent an immediate threat to sea urchins vulnerability

Influence of the molecular architecture on the secondary relaxations of Poly(styrene-co-methylmethacrylate) copolymers

The processes of adsorption of grafted copolymers onto negatively charged surfaces were studied using a dissipative quartz crystal microbalance (D-QCM) and ellipsometry. The control parameters in the study of the adsorption are the existence or absence on the molecular architecture of grafted polyethyleneglycol (PEG) chains with different lengths and the chemical nature of the main chain, poly(allylamine) (PAH) or poly(L-lysine) (PLL). It was found out that the adsorption kinetics of the polymers showed a complex behavior. The total adsorbed amount depends on the architecture of the polymer chains (length of the PEG chains), on the polymer concentration and on the chemical nature of the main chain. The comparison of the thicknesses of the adsorbed layers obtained from D-QCM and from ellipsometry allowed calculation of the water content of the layers that is intimately related to the grafting length. The analysis of D-QCM results also provides information about the shear modulus of the layers, whose values have been found to be typical of a rubber-like polymer system. It is shown that the adsorption of polymers with a charged backbone is not driven exclusively by the electrostatic interactions, but the entropic contributions as a result of the trapping of water in the layer structure are of fundamental importance.

Nanoindentation of Bridgman YBCO samples

In this study, the mechanical properties of YBa2Cu3O7−x, obtained by the Bridgman technique, were examined using a Berkovich tip indenter on the basal plane (0 0 1). Intrinsic hardness was measured by nanoindentation tests and corrected using the Nix and Gao model for this material. Furthermore, Vickers hardness tests were performed, in order to determine the possible size effect on these measurements. The results showed an underestimation of the hardness value when the tests were performed with large loads. Moreover, the elastic modulus of the Bridgman samples was 128 ± 5 GPa. Different residual imprints were visualised by atomic force microscopy and a focused ion beam, in order to observe superficial and internal fracturing. Mechanical properties presented a considerable reduction at the interface. This effect could be attributed to internal stress generated during the texturing process. In order to corroborate this hypothesis, an observation using transmission electron microscopy was performed.

Experimental and numerical study of cracking of concrete due to reinforcement corrosion

La corrosión del acero es una de las patologías más importantes que afectan a las estructuras de hormigón armado que están expuestas a ambientes marinos o al ataque de sales fundentes. Cuando se produce corrosión, se genera una capa de óxido alrededor de la superficie de las armaduras, que ocupa un volumen mayor que el acero inicial; como consecuencia, el óxido ejerce presiones internas en el hormigón circundante, que lleva a la fisuración y, ocasionalmente, al desprendimiento del recubrimiento de hormigón. Durante los últimos años, numerosos estudios han contribuido a ampliar el conocimiento sobre el proceso de fisuración; sin embargo, aún existen muchas incertidumbres respecto al comportamiento mecánico de la capa de óxido, que es fundamental para predecir la fisuración. Por ello, en esta tesis se ha desarrollado y aplicado una metodología, para mejorar el conocimiento respecto al comportamiento del sistema acero-óxido-hormigón, combinando experimentos y simulaciones numéricas. Se han realizado ensayos de corrosión acelerada en condiciones de laboratorio, utilizando la técnica de corriente impresa. Con el objetivo de obtener información cercana a la capa de acero, como muestras se seleccionaron prismas de hormigón con un tubo de acero liso como armadura, que se diseñaron para conseguir la formación de una única fisura principal en el recubrimiento. Durante los ensayos, las muestras se equiparon con instrumentos especialmente diseñados para medir la variación de diámetro y volumen interior de los tubos, y se midió la apertura de la fisura principal utilizando un extensómetro comercial, adaptado a la geometría de las muestras. Las condiciones de contorno se diseñaron cuidadosamente para que los campos de corriente y deformación fuesen planos durante los ensayos, resultando en corrosión uniforme a lo largo del tubo, para poder reproducir los ensayos en simulaciones numéricas. Se ensayaron series con varias densidades de corriente y varias profundidades de corrosión. De manera complementaria, el comportamiento en fractura del hormigón se caracterizó en ensayos independientes, y se midió la pérdida gravimétrica de los tubos siguiendo procedimientos estándar. En todos los ensayos, la fisura principal creció muy despacio durante las primeras micras de profundidad de corrosión, pero después de una cierta profundidad crítica, la fisura se desarrolló completamente, con un aumento rápido de su apertura; la densidad de corriente influye en la profundidad de corrosión crítica. Las variaciones de diámetro interior y de volumen interior de los tubos mostraron tendencias diferentes entre sí, lo que indica que la deformación del tubo no fue uniforme. Después de la corrosión acelerada, las muestras se cortaron en rebanadas, que se utilizaron en ensayos post-corrosión. El patrón de fisuración se estudió a lo largo del tubo, en rebanadas que se impregnaron en vacío con resina y fluoresceína para mejorar la visibilidad de las fisuras bajo luz ultravioleta, y se estudió la presencia de óxido dentro de las grietas. En todas las muestras, se formó una fisura principal en el recubrimiento, infiltrada con óxido, y varias fisuras secundarias finas alrededor del tubo; el número de fisuras varió con la profundidad de corrosión de las muestras. Para muestras con la misma corrosión, el número de fisuras y su posición fue diferente entre muestras y entre secciones de una misma muestra, debido a la heterogeneidad del hormigón. Finalmente, se investigó la adherencia entre el acero y el hormigón, utilizando un dispositivo diseñado para empujar el tubo en el hormigón. Las curvas de tensión frente a desplazamiento del tubo presentaron un pico marcado, seguido de un descenso constante; la profundidad de corrosión y la apertura de fisura de las muestras influyeron notablemente en la tensión residual del ensayo. Para simular la fisuración del hormigón causada por la corrosión de las armaduras, se programó un modelo numérico. Éste combina elementos finitos con fisura embebida adaptable que reproducen la fractura del hormigón conforme al modelo de fisura cohesiva estándar, y elementos de interfaz llamados elementos junta expansiva, que se programaron específicamente para reproducir la expansión volumétrica del óxido y que incorporan su comportamiento mecánico. En el elemento junta expansiva se implementó un fenómeno de despegue, concretamente de deslizamiento y separación, que resultó fundamental para obtener localización de fisuras adecuada, y que se consiguió con una fuerte reducción de la rigidez tangencial y la rigidez en tracción del óxido. Con este modelo, se realizaron simulaciones de los ensayos, utilizando modelos bidimensionales de las muestras con elementos finitos. Como datos para el comportamiento en fractura del hormigón, se utilizaron las propiedades determinadas en experimentos. Para el óxido, inicialmente se supuso un comportamiento fluido, con deslizamiento y separación casi perfectos. Después, se realizó un ajuste de los parámetros del elemento junta expansiva para reproducir los resultados experimentales. Se observó que variaciones en la rigidez normal del óxido apenas afectaban a los resultados, y que los demás parámetros apenas afectaban a la apertura de fisura; sin embargo, la deformación del tubo resultó ser muy sensible a variaciones en los parámetros del óxido, debido a la flexibilidad de la pared de los tubos, lo que resultó fundamental para determinar indirectamente los valores de los parámetros constitutivos del óxido. Finalmente, se realizaron simulaciones definitivas de los ensayos. El modelo reprodujo la profundidad de corrosión crítica y el comportamiento final de las curvas experimentales; se comprobó que la variación de diámetro interior de los tubos está fuertemente influenciada por su posición relativa respecto a la fisura principal, en concordancia con los resultados experimentales. De la comparación de los resultados experimentales y numéricos, se pudo extraer información sobre las propiedades del óxido que de otra manera no habría podido obtenerse. Corrosion of steel is one of the main pathologies affecting reinforced concrete structures exposed to marine environments or to molten salt. When corrosion occurs, an oxide layer develops around the reinforcement surface, which occupies a greater volume than the initial steel; thus, it induces internal pressure on the surrounding concrete that leads to cracking and, eventually, to full-spalling of the concrete cover. During the last years much effort has been devoted to understand the process of cracking; however, there is still a lack of knowledge regarding the mechanical behavior of the oxide layer, which is essential in the prediction of cracking. Thus, a methodology has been developed and applied in this thesis to gain further understanding of the behavior of the steel-oxide-concrete system, combining experiments and numerical simulations. Accelerated corrosion tests were carried out in laboratory conditions, using the impressed current technique. To get experimental information close to the oxide layer, concrete prisms with a smooth steel tube as reinforcement were selected as specimens, which were designed to get a single main crack across the cover. During the tests, the specimens were equipped with instruments that were specially designed to measure the variation of inner diameter and volume of the tubes, and the width of the main crack was recorded using a commercial extensometer that was adapted to the geometry of the specimens. The boundary conditions were carefully designed so that plane current and strain fields were expected during the tests, resulting in nearly uniform corrosion along the length of the tube, so that the tests could be reproduced in numerical simulations. Series of tests were carried out with various current densities and corrosion depths. Complementarily, the fracture behavior of concrete was characterized in independent tests, and the gravimetric loss of the steel tubes was determined by standard means. In all the tests, the main crack grew very slowly during the first microns of corrosion depth, but after a critical corrosion depth it fully developed and opened faster; the current density influenced the critical corrosion depth. The variation of inner diameter and inner volume of the tubes had different trends, which indicates that the deformation of the tube was not uniform. After accelerated corrosion, the specimens were cut into slices, which were used in post-corrosion tests. The pattern of cracking along the reinforcement was investigated in slices that were impregnated under vacuum with resin containing fluorescein to enhance the visibility of cracks under ultraviolet lightening and a study was carried out to assess the presence of oxide into the cracks. In all the specimens, a main crack developed through the concrete cover, which was infiltrated with oxide, and several thin secondary cracks around the reinforcement; the number of cracks diminished with the corrosion depth of the specimen. For specimens with the same corrosion, the number of cracks and their position varied from one specimen to another and between cross-sections of a given specimen, due to the heterogeneity of concrete. Finally, the bond between the steel and the concrete was investigated, using a device designed to push the tubes of steel in the concrete. The curves of stress versus displacement of the tube presented a marked peak, followed by a steady descent, with notably influence of the corrosion depth and the crack width on the residual stress. To simulate cracking of concrete due to corrosion of the reinforcement, a numerical model was implemented. It combines finite elements with an embedded adaptable crack that reproduces cracking of concrete according to the basic cohesive model, and interface elements so-called expansive joint elements, which were specially designed to reproduce the volumetric expansion of oxide and incorporate its mechanical behavior. In the expansive joint element, a debonding effect was implemented consisting of sliding and separation, which was proved to be essential to achieve proper localization of cracks, and was achieved by strongly reducing the shear and the tensile stiffnesses of the oxide. With that model, simulations of the accelerated corrosion tests were carried out on 2- dimensional finite element models of the specimens. For the fracture behavior of concrete, the properties experimentally determined were used as input. For the oxide, initially a fluidlike behavior was assumed with nearly perfect sliding and separation; then the parameters of the expansive joint element were modified to fit the experimental results. Changes in the bulk modulus of the oxide barely affected the results and changes in the remaining parameters had a moderate effect on the predicted crack width; however, the deformation of the tube was very sensitive to variations in the parameters of oxide, due to the flexibility of the tube wall, which was crucial for indirect determination of the constitutive parameters of oxide. Finally, definitive simulations of the tests were carried out. The model reproduced the critical corrosion depth and the final behavior of the experimental curves; it was assessed that the variation of inner diameter of the tubes is highly influenced by its relative position with respect to the main crack, in accordance with the experimental observations. From the comparison of the experimental and numerical results, some properties of the mechanical behavior of the oxide were disclosed that otherwise could not have been measured.

Optimal boundary geometry in an elasticity problem: a systematic adjoint approach

In different problems of Elasticity the definition of the optimal gcometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables. Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.