Elastic Propagation in random media: applications to the imaging of volcano structures

High-frequency seismograms contain features that reflect the random inhomogeneities of the earth. In this work I use an imaging method to locate the high contrast small- scale heterogeneity respect to the background earth medium. This method was first introduced by Nishigami (1991) and than applied to different volcanic and tectonically active areas (Nishigami, 1997, Nishigami, 2000, Nishigami, 2006). The scattering imaging method is applied to two volcanic areas: Campi Flegrei and Mt. Vesuvius. Volcanic and seismological active areas are often characterized by complex velocity structures, due to the presence of rocks with different elastic properties. I introduce some modifications to the original method in order to make it suitable for small and highly complex media. In particular, for very complex media the single scattering approximation assumed by Nishigami (1991) is not applicable as the mean free path becomes short. The multiple scattering or diffusive approximation become closer to the reality. In this thesis, differently from the ordinary Nishigami’s method (Nishigami, 1991), I use the mean of the recorded coda envelope as reference curve and calculate the variations from this average envelope. In this way I implicitly do not assume any particular scattering regime for the "average" scattered radiation, whereas I consider the variations as due to waves that are singularly scattered from the strongest heterogeneities. The imaging method is applied to a relatively small area (20 x 20 km), this choice being justified by the small length of the analyzed codas of the low magnitude earthquakes. I apply the unmodified Nishigami’s method to the volcanic area of Campi Flegrei and compare the results with the other tomographies done in the same area. The scattering images, obtained with frequency waves around 18 Hz, show the presence of high scatterers in correspondence with the submerged caldera rim in the southern part of the Pozzuoli bay. Strong scattering is also found below the Solfatara crater, characterized by the presence of densely fractured, fluid-filled rocks and by a strong thermal anomaly. The modified Nishigami’s technique is applied to the Mt. Vesuvius area. Results show a low scattering area just below the central cone and a high scattering area around it. The high scattering zone seems to be due to the contrast between the high rigidity body located beneath the crater and the low rigidity materials located around it. The central low scattering area overlaps the hydrothermal reservoirs located below the central cone. An interpretation of the results in terms of geological properties of the medium is also supplied, aiming to find a correspondence of the scattering properties and the geological nature of the material. A complementary result reported in this thesis is that the strong heterogeneity of the volcanic medium create a phenomenon called "coda localization". It has been verified that the shape of the seismograms recorded from the stations located at the top of the volcanic edifice of Mt. Vesuvius is different from the shape of the seismograms recorded at the bottom. This behavior is justified by the consideration that the coda energy is not uniformly distributed within a region surrounding the source for great lapse time.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Advanced polymeric materials for applications in technical equipment for snow sports

The thesis is divided in three chapters, each one covering one topic. Initially, the thermo-mechanical and impact properties of materials used for back protectors have been analysed. Dynamical mechanical analysis (DMTA) has shown that materials used for soft-shell protectors present frequency-sensitive properties. Furthermore, through impact tests, the shock absorbing characteristics of the materials have been investigated proving the differences between soft and hard-shell protectors; moreover it has been demonstrated that the materials used for soft-shell protectors maintain their protective properties after multi-impacts. The second chapter covers the effect of the visco-elastic properties of the thermoplastic polymers on the flexural and rebound behaviours of ski boots. DMTA analysis on the materials and flexural and rebound testing on the boots have been performed. A comparison of the results highlighted a correlation between the visco-elastic properties and the flexural and rebound behaviour of ski boots. The same experimental methods have been used to investigate the influence of the design on the flexural and rebound behaviours. Finally in the third chapter the thermoplastic materials employed for the construction of ski boots soles have been characterized in terms of chemical composition, hardness, crystallinity, surface roughness and coefficient of friction (COF). The results showed a relation between material hardness and grip, in particular softer materials provide more grip with respect to harder materials. On the contrary, the surface roughness has a negative effect on friction because of the decrease in contact area. The measure of grip on inclined wet surfaces showed again a relation between hardness and grip. The performance ranking of the different materials has been the same for the COF and for the slip angle tests, indicating that COF can be used as a parameter for the choice of the optimal material to be used for the soles of ski boots.

Vulnerable users' protection with advanced recycling paving materials. Design and characterisation of rubber-based impact-absorbing pavement materials for bike lanes and sidewalks

Our cities are constantly evolving, and the necessity to improve the condition and safety of the urban infrastructures is fundamental. However, on the roads, the specific needs of cyclists and pedestrians are often neglected. The Vulnerable Road Users (VRUs), among whom cyclists and pedestrians are, rarely benefit from the most innovative safety measures. Inspired by playgrounds and aiming to reduce VRUs injuries, the Impact-Absorbing Pavements (IAP) developed as novel sidewalks, and bike lanes surface layers may help decrease injuries, fatalities, and the related societal costs. To achieve this goal, the End-of-Life Tyres (ELTs) crumb rubber (CR) is used as a primary resource, bringing its elastic properties into the surface layer. The thesis is divided into five main chapters. The first concerns the formulation and the definition of a feasible mix. The second explores the mechanical and environmental properties in detail, and the ageing effect is also assessed. The third describes the modelling of the material to simulate accidents and measure the injury reduction, especially on the head. The fourth chapter is reserved for the field trial. The last gives some perspectives on the research and proposes a way to optimize and improve the data and results collected during the doctoral research. It was observed that the specimens made with cold protocol have noticeable performances and reduce the overall carbon footprint impact of this material. The material modelling and the accident simulation proved the performance of the IAP against head injuries, and the field trial confirmed the good results obtained in the laboratory for the cold-made material. Finally, the outcomes of this thesis opened many prospective to the IAP development, such as the use of a plant-based binder or recycled aggregates and gave a positive prospect of an innovative material to the urban road infrastructures.