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.

On Designing Compliant Actuators Based On Dielectric Elastomers

Dielectric Elastomers (DE) are incompressible dielectrics which can experience deviatoric (isochoric) finite deformations in response to applied large electric fields. Thanks to the strong electro-mechanical coupling, DE intrinsically offer great potentialities for conceiving novel solid-state mechatronic devices, in particular linear actuators, which are more integrated, lightweight, economic, silent, resilient and disposable than equivalent devices based on traditional technologies. Such systems may have a huge impact in applications where the traditional technology does not allow coping with the limits of weight or encumbrance, and with problems involving interaction with humans or unknown environments. Fields such as medicine, domotic, entertainment, aerospace and transportation may profit. For actuation usage, DE are typically shaped in thin films coated with compliant electrodes on both sides and piled one on the other to form a multilayered DE. DE-based Linear Actuators (DELA) are entirely constituted by polymeric materials and their overall performance is highly influenced by several interacting factors; firstly by the electromechanical properties of the film, secondly by the mechanical properties and geometry of the polymeric frame designed to support the film, and finally by the driving circuits and activation strategies. In the last decade, much effort has been focused in the devolvement of analytical and numerical models that could explain and predict the hyperelastic behavior of different types of DE materials. Nevertheless, at present, the use of DELA is limited. The main reasons are 1) the lack of quantitative and qualitative models of the actuator as a whole system 2) the lack of a simple and reliable design methodology. In this thesis, a new point of view in the study of DELA is presented which takes into account the interaction between the DE film and the film supporting frame. Hyperelastic models of the DE film are reported which are capable of modeling the DE and the compliant electrodes. The supporting frames are analyzed and designed as compliant mechanisms using pseudo-rigid body models and subsequent finite element analysis. A new design methodology is reported which optimize the actuator performances allowing to specifically choose its inherent stiffness. As a particular case, the methodology focuses on the design of constant force actuators. This class of actuators are an example of how the force control could be highly simplified. Three new DE actuator concepts are proposed which highlight the goodness of the proposed method.

Inverse Static Analysis of Massive Parallel Arrays of Three-State Actuators via Artificial Intelligence

Massive parallel robots (MPRs) driven by discrete actuators are force regulated robots that undergo continuous motions despite being commanded through a finite number of states only. Designing a real-time control of such systems requires fast and efficient methods for solving their inverse static analysis (ISA), which is a challenging problem and the subject of this thesis. In particular, five Artificial intelligence methods are proposed to investigate the on-line computation and the generalization error of ISA problem of a class of MPRs featuring three-state force actuators and one degree of revolute motion.

Arbitrary Waveform Multilevel Generator for High Voltage High Frequency Plasma Actuators

This dissertation presents the theory and the conducted activity that lead to the construction of a high voltage high frequency arbitrary waveform voltage generator. The generator has been specifically designed to supply power to a wide range of plasma actuators. The system has been completely designed, manufactured and tested at the Department of Electrical, Electronic and Information Engineering of the University of Bologna. The generator structure is based on the single phase cascaded H-bridge multilevel topology and is comprised of 24 elementary units that are series connected in order to form the typical staircase output voltage waveform of a multilevel converter. The total number of voltage levels that can be produced by the generator is 49. Each level is 600 V making the output peak-to-peak voltage equal to 28.8 kV. The large number of levels provides high resolution with respect to the output voltage having thus the possibility to generate arbitrary waveforms. Maximum frequency of operation is 20 kHz. A study of the relevant literature shows that this is the first time that a cascaded multilevel converter of such dimensions has been constructed. Isolation and control challenges had to be solved for the realization of the system. The biggest problem of the current technology in power supplies for plasma actuators is load matching. Resonant converters are the most used power supplies and are seriously affected by this problem. The manufactured generator completely solves this issue providing consistent voltage output independently of the connected load. This fact is very important when executing tests and during the comparison of the results because all measures should be comparable and not dependent from matching issues. The use of the multilevel converter for power supplying a plasma actuator is a real technological breakthrough that has provided and will continue to provide very significant experimental results.

New Application of Piezoelectric Ultrasounds in Maxillo-facial bone surgery

Background: Piezoelectric instrumentation seems to offer 3 important advantages for cutting bone structures. Be more precise because it is produced by micro-vibrations from the cutting insert. Be safer because the ultrasonic frequency used does not affect soft tissue. Thirdly, the less invasive cutting action produces minor tissue damage and consequently probably a better healing Aim of the Study: The aim of this study is to evaluate the effectiveness of piezoelectric device capability in maxillo-facial surgery, in order to take advantage of these favourable capacity. Material and Methods: Considering the several potential application of the piezoelectric technology in Orthognathic, Oncologic and Extractive surgery, we would like to design protocols in order to verify how this new device can modify the surgical technique, the surgical time, the patients healing and its quality of life. Results: Due to the precise Piezosurgery cut, we can manage the Cad-Cam-Custom Made plates protocol in Oncologic Surgery and in Orthognatic Surgery increasing our percentage of comparison between the 3D preoperative plan and the surgical execution. We also found a better quality of life impaction in Patient who underwent and extractive surgery Conclusion: Piezosurgery device seems to be a strong surgical aid were safe and precise cut are needed and its capability to reduce the discomfort Patients need to be study in deep also in major surgery like Orthognatic and Oncologic surgery.