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.

A bayesian model for mixed responses and skew laten variable to measure HRQoL in children

The aim of the thesi is to formulate a suitable Item Response Theory (IRT) based model to measure HRQoL (as latent variable) using a mixed responses questionnaire and relaxing the hypothesis of normal distributed latent variable. The new model is a combination of two models already presented in literature, that is, a latent trait model for mixed responses and an IRT model for Skew Normal latent variable. It is developed in a Bayesian framework, a Markov chain Monte Carlo procedure is used to generate samples of the posterior distribution of the parameters of interest. The proposed model is test on a questionnaire composed by 5 discrete items and one continuous to measure HRQoL in children, the EQ-5D-Y questionnaire. A large sample of children collected in the schools was used. In comparison with a model for only discrete responses and a model for mixed responses and normal latent variable, the new model has better performances, in term of deviance information criterion (DIC), chain convergences times and precision of the estimates.

Microscopic Modeling on complex networks

The field of complex systems is a growing body of knowledge, It can be applied to countless different topics, from physics to computer science, biology, information theory and sociology. The main focus of this work is the use of microscopic models to study the behavior of urban mobility, which characteristics make it a paradigmatic example of complexity. In particular, simulations are used to investigate phase changes in a finite size open Manhattan-like urban road network under different traffic conditions, in search for the parameters to identify phase transitions, equilibrium and non-equilibrium conditions . It is shown how the flow-density macroscopic fundamental diagram of the simulation shows,like real traffic, hysteresis behavior in the transition from the congested phase to the free flow phase, and how the different regimes can be identified studying the statistics of road occupancy.

Low Correlated Sequences & Architectures and Algorithms for Analog-to-Information Converters: Theory, Design, Implementation and Applications.

Most electronic systems can be described in a very simplified way as an assemblage of analog and digital components put all together in order to perform a certain function. Nowadays, there is an increasing tendency to reduce the analog components, and to replace them by operations performed in the digital domain. This tendency has led to the emergence of new electronic systems that are more flexible, cheaper and robust. However, no matter the amount of digital process implemented, there will be always an analog part to be sorted out and thus, the step of converting digital signals into analog signals and vice versa cannot be avoided. This conversion can be more or less complex depending on the characteristics of the signals. Thus, even if it is desirable to replace functions carried out by analog components by digital processes, it is equally important to do so in a way that simplifies the conversion from digital to analog signals and vice versa. In the present thesis, we have study strategies based on increasing the amount of processing in the digital domain in such a way that the implementation of analog hardware stages can be simplified. To this aim, we have proposed the use of very low quantized signals, i.e. 1-bit, for the acquisition and for the generation of particular classes of signals.

Evaluation of Human Exposure to Magnetic Fields Generated by Electric Power Systems in Complex Configurations

The international growing concern for the human exposure to magnetic fields generated by electric power lines has unavoidably led to imposing legal limits. Respecting these limits, implies being able to calculate easily and accurately the generated magnetic field also in complex configurations. Twisting of phase conductors is such a case. The consolidated exact and approximated theory regarding a single-circuit twisted three-phase power cable line has been reported along with the proposal of an innovative simplified formula obtained by means of an heuristic procedure. This formula, although being dramatically simpler, is proven to be a good approximation of the analytical formula and at the same time much more accurate than the approximated formula found in literature. The double-circuit twisted three-phase power cable line case has been studied following different approaches of increasing complexity and accuracy. In this framework, the effectiveness of the above-mentioned innovative formula is also examined. The experimental verification of the correctness of the twisted double-circuit theoretical analysis has permitted its extension to multiple-circuit twisted three-phase power cable lines. In addition, appropriate 2D and, in particularly, 3D numerical codes for simulating real existing overhead power lines for the calculation of the magnetic field in their vicinity have been created. Finally, an innovative ‘smart’ measurement and evaluation system of the magnetic field is being proposed, described and validated, which deals with the experimentally-based evaluation of the total magnetic field B generated by multiple sources in complex three-dimensional arrangements, carried out on the basis of the measurement of the three Cartesian field components and their correlation with the field currents via multilinear regression techniques. The ultimate goal is verifying that magnetic induction intensity is within the prescribed limits.

Multidimensional item response theory models with general and specific latent traits for ordinal data

The aim of the thesis is to propose a Bayesian estimation through Markov chain Monte Carlo of multidimensional item response theory models for graded responses with complex structures and correlated traits. In particular, this work focuses on the multiunidimensional and the additive underlying latent structures, considering that the first one is widely used and represents a classical approach in multidimensional item response analysis, while the second one is able to reflect the complexity of real interactions between items and respondents. A simulation study is conducted to evaluate the parameter recovery for the proposed models under different conditions (sample size, test and subtest length, number of response categories, and correlation structure). The results show that the parameter recovery is particularly sensitive to the sample size, due to the model complexity and the high number of parameters to be estimated. For a sufficiently large sample size the parameters of the multiunidimensional and additive graded response models are well reproduced. The results are also affected by the trade-off between the number of items constituting the test and the number of item categories. An application of the proposed models on response data collected to investigate Romagna and San Marino residents' perceptions and attitudes towards the tourism industry is also presented.

Modelling and analysis of thin-walled beams in the context of the Generalized Beam Theory

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.

Flow of Complex Fluids in Geological Fractures

In this study, the lubrication theory is used to model flow in geological fractures and analyse the compound effect of medium heterogeneity and complex fluid rheology. Such studies are warranted as the Newtonian rheology is adopted in most numerical models because of its ease of use, despite non-Newtonian fluids being ubiquitous in subsurface applications. Past studies on Newtonian and non-Newtonian flow in single rock fractures are summarized in Chapter 1. Chapter 2 presents analytical and semi-analytical conceptual models for flow of a shear-thinning fluid in rock fractures having a simplified geometry, providing a first insight on their permeability. in Chapter 3, a lubrication-based 2-D numerical model is first implemented to solve flow of an Ellis fluid in rough fractures; the finite-volumes model developed is more computationally effective than conducting full 3-D simulations, and introduces an acceptable approximation as long as the flow is laminar and the fracture walls relatively smooth. The compound effect of shear-thinning fluid nature and fracture heterogeneity promotes flow localization, which in turn affects the performance of industrial activities and remediation techniques. In Chapter 4, a Monte Carlo framework is adopted to produce multiple realizations of synthetic fractures, and analyze their ensemble statistics pertaining flow for a variety of real non-Newtonian fluids; the Newtonian case is used as a benchmark. In Chapter 5 and Chapter 6, a conceptual model of the hydro-mechanical aspects of backflow occurring in the last phase of hydraulic fracturing is proposed and experimentally validated, quantifying the effects of the relaxation induced by the flow.

How to explain: from theory to practice

Today we live in an age where the internet and artificial intelligence allow us to search for information through impressive amounts of data, opening up revolutionary new ways to make sense of reality and understand our world. However, it is still an area of improvement to exploit the full potential of large amounts of explainable information by distilling it automatically in an intuitive and user-centred explanation. For instance, different people (or artificial agents) may search for and request different types of information in a different order, so it is unlikely that a short explanation can suffice for all needs in the most generic case. Moreover, dumping a large portion of explainable information in a one-size-fits-all representation may also be sub-optimal, as the needed information may be scarce and dispersed across hundreds of pages. The aim of this work is to investigate how to automatically generate (user-centred) explanations from heterogeneous and large collections of data, with a focus on the concept of explanation in a broad sense, as a critical artefact for intelligence, regardless of whether it is human or robotic. Our approach builds on and extends Achinstein’s philosophical theory of explanations, where explaining is an illocutionary (i.e., broad but relevant) act of usefully answering questions. Specifically, we provide the theoretical foundations of Explanatory Artificial Intelligence (YAI), formally defining a user-centred explanatory tool and the space of all possible explanations, or explanatory space, generated by it. We present empirical results in support of our theory, showcasing the implementation of YAI tools and strategies for assessing explainability. To justify and evaluate the proposed theories and models, we considered case studies at the intersection of artificial intelligence and law, particularly European legislation. Our tools helped produce better explanations of software documentation and legal texts for humans and complex regulations for reinforcement learning agents.

Weak reasoning argumentative theory. A dialogical approach for the discovery of philosophy in high schools

In the literature on philosophical practices, despite the crucial role that argumentation plays in these activities, no specific argumentative theories have ever been proposed to assist the figure of the facilitator in conducting philosophical dialogue and to enhance student’s critical thinking skills. The dissertation starts from a cognitive perspective that challenges the classic Cartesian notion of rationality by focusing on limits and biases of human reasoning. An argumentative model (WRAT – Weak Reasoning Argumentative Theory) is then outlined in order to respond to the needs of philosophical dialogue. After justifying the claim that this learning activity, among other inductive methodologies, is the most suitable for critical thinking education, I inquired into the specific goal of ‘arguing’ within this context by means of the tools provided by Speech Act Theory: the speaker’s intention is to construct new knowledge by questioning her own and other’s beliefs. The model proposed has been theorized on this assumption, starting from which the goals, and, in turn, the related norms, have been pinpointed. In order to include all the epistemic attitudes required to accomplish the complex task of arguing in philosophical dialogue, I needed to integrate two opposed cognitive accounts, Dual Process Theory and Evolutionary Approach, that, although they provide incompatible descriptions of reasoning, can be integrated to provide a normative account of argumentation. The model, apart from offering a theoretical contribution to argumentation studies, is designed to be applied to the Italian educational system, in particular to classes in technical and professional high schools belonging to the newly created network Inventio. This initiative is one of the outcomes of the research project by the same name, which also includes an original Syllabus, research seminars, a monitoring action and publications focused on introducing philosophy, in the form of workshop activities, into technical and professional schools.

Potential theory on metric spaces

This work revolves around potential theory in metric spaces, focusing on applications of dyadic potential theory to general problems associated to functional analysis and harmonic analysis. In the first part of this work we consider the weighted dual dyadic Hardy's inequality over dyadic trees and we use the Bellman function method to characterize the weights for which the inequality holds, and find the optimal constant for which our statement holds. We also show that our Bellman function is the solution to a stochastic optimal control problem. In the second part of this work we consider the problem of quasi-additivity formulas for the Riesz capacity in metric spaces and we prove formulas of quasi-additivity in the setting of the tree boundaries and in the setting of Ahlfors-regular spaces. We also consider a proper Harmonic extension to one additional variable of Riesz potentials of functions on a compact Ahlfors-regular space and we use our quasi-additivity formula to prove a result of tangential convergence of the harmonic extension of the Riesz potential up to an exceptional set of null measure

Response times in computerized adaptive testing: a method for cheating detection

In the field of educational and psychological measurement, the shift from paper-based to computerized tests has become a prominent trend in recent years. Computerized tests allow for more complex and personalized test administration procedures, like Computerized Adaptive Testing (CAT). CAT, following the Item Response Theory (IRT) models, dynamically generates tests based on test-taker responses, driven by complex statistical algorithms. Even if CAT structures are complex, they are flexible and convenient, but concerns about test security should be addressed. Frequent item administration can lead to item exposure and cheating, necessitating preventive and diagnostic measures. In this thesis a method called "CHeater identification using Interim Person fit Statistic" (CHIPS) is developed, designed to identify and limit cheaters in real-time during test administration. CHIPS utilizes response times (RTs) to calculate an Interim Person fit Statistic (IPS), allowing for on-the-fly intervention using a more secret item bank. Also, a slight modification is proposed to overcome situations with constant speed, called Modified-CHIPS (M-CHIPS). A simulation study assesses CHIPS, highlighting its effectiveness in identifying and controlling cheaters. However, it reveals limitations when cheaters possess all correct answers. The M-CHIPS overcame this limitation. Furthermore, the method has shown not to be influenced by the cheaters’ ability distribution or the level of correlation between ability and speed of test-takers. Finally, the method has demonstrated flexibility for the choice of significance level and the transition from fixed-length tests to variable-length ones. The thesis discusses potential applications, including the suitability of the method for multiple-choice tests, assumptions about RT distribution and level of item pre-knowledge. Also limitations are discussed to explore future developments such as different RT distributions, unusual honest respondent behaviors, and field testing in real-world scenarios. In summary, CHIPS and M-CHIPS offer real-time cheating detection in CAT, enhancing test security and ability estimation while not penalizing test respondents.