Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Impact of the Economic Recession on Toll Highway Concessions in Spain

After joining the European Union in 1986, Spain experienced steady economic growth that enabled the country to grow at a greater pace than other European countries. During this period, the government of Spain opted for major investments in public infrastructure by taking advantage both of the funding provided by the European Union and of several types of public-private-partnership (PPP) approaches. Within this framework, the government of Spain between 1996 and 2004 procured a series of toll highway concessions. These concessions entered into operation a few years before the global economic recession made itself felt in Spain. The concession contracts signed between the government and some private consortia allocated most of the risks (expropriation, construction, and traffic) to the private sector. In this paper the impact that the economic recession has had on the business performance of the concessionaires is assessed, and the effectiveness of the measures adopted by the government to help the concessionaire to avoid bankruptcy is analyzed. It was found that some of the guarantees offered by the legal framework to the concessionaires in case of bankruptcy are prompting an outcome that could negatively affect the users. In addition to that, some suggestions as to how to better allocate risk in toll highway concessions in the future are provided.

Risk Allocation in Toll Highway Concessions in Spain: Lessons from Economic Recession

Spain has a long tradition of encouraging toll highways by granting concessions to private companies. Concessions in Spain have been characterized by a willingness to transfer considerable risk to the private sector. Traffic demand, acquisition of the right-of-way, and financial risk have often been allocated to the private sector. From 1996 to 2011, 16 toll highway concessions, covering a total distance of 835 km, were awarded by the central government of Spain with this approach. Some of those highways started their operations just before the economic recession began. The recession had negative consequences for Spain's economy. The gross domestic product per capita plummeted, and the unemployment rate increased from 9% to 20% of the working population in just 2 years. The recession also had severe consequences for the economic performance of toll highway concessions. Traffic levels declined at a much greater rate than did the gross domestic product. In addition, the conditions imposed by the financial markets on borrowers became much stricter because of the liquidity crisis. This study analyzes the impact that the economic recession ultimately had on the performance of toll highway concessions in Spain and the actions that the government adopted to avoid the bankruptcy of the concessionaires. It was found that the economic recession helped identify some deficiencies in how risk had been allocated in Spain. The measures that both Spain and the European Union are adopting so as to improve risk allocation are discussed.

A comparative analysis of road financing approaches in Europe and the United States

• The viability of the present system of road funding has in recent years been widely questioned, for it has proved insufficient to support spending programs at their current levels. • Some transfers from the general fund have been needed since 2008 to keep the HTF solvent. • Fuel taxes, the primary source for funding roads in the US, have not kept pace with inflation for years. • A wide variety of measures to increase revenue has been presented: raising fuel taxes, extending toll highways, implementing a VMT fee, etc.

Crisis and the city: neoliberalism, austerity planning and the production of space

The current crisis, with its particularly severe configuration in Southern European countries, provides an opportunity to probe the interrelation of economic crunches and the production of space, and also to imagine potential paths of sociospatial emancipation from the dictates of global markets. This introductory chapter offers a preliminary interpretive framework exploring the fundamental role of urban and territorial restructuring in the formation, management and resolution of capitalist crises and, conversely, periods of crisis as key stages in the history of urbanization. I will begin by contextualizing the 2007-8 economic slump, the subsequent global recession and its uneven impact on states and cities in the longue durée of capitalist productions of space, studying the transformation of spatial configurations in previous episodes of economic stagnation. This broader perspective will then be used to analyze currently emerging formations of austerity urbanism, showing how the practices of crisis management incorporate a strategy for economic and institutional restructuring that eventually impacts on urban policy, and indeed in the production of urban space itself.