Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators

Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100¿nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.Peer ReviewedPostprint (author's final draft

An efficacious method to assemble a modern multi-modal robotic team: dilemmas, challenges, possibilities and solutions

A modern multiagent robotic platform consists of a cooperative team of humans which develop a collaborative team of robots. The multi-modal nature of both the system and the team causes a complex problem which needs to be solved for optimum performance. Both the management and the technical aspect of a modern robotic team are explored in this Chapter in the platform of the RoboCup Competition. RoboCup is an example of such an environment where researchers from different disciplines join to develop a robotic team for completion as an evaluation challenge (Robocup, 2011). RoboCup competitions were first proposed by Mackworth in 1993. The main goal of this scientific competition is to exploit, improve and integrate the methods and techniques from robotics, machine vision and artificial intelligence disciplines to create an autonomous team of soccer playing robots(Kitano, 1997a; Kitano, 1997b; Kitano et al., 1997). Such experiment includes several challenges, from inviting an expert of specific field to the team to choosing bolts and nuts for each part of the robots. Usually each challenge has several possible solutions and choosing the best one is often challenging. We have participated in several world wide RoboCup competitions (Abdollahi, Samani et al. 2002, 2003 & 2004) and share our experience as an extensive instruction for setting up a modern robotic team including management and technical issues.Peer ReviewedPostprint (published version

Modeling and simulation of conducting crack propagation in ferroelectric single crystals under purely electrical loading

We present a phase-field model of fracture in ferroelectric single crystals for the simulation of conducting crack propagation under purely electrical loading. This is done by introducing the electrical enthalpy of a diffuse conducting layer into the phase-field formulation. Simulation results show an oblique crack propagation and crack branching from a conducting notch in a ferroelectric sample under applied electric fields. Microstructure evolution indicates the formation of 90 domains which results in a charge accumulation around the crack. The charge accumulation, in turn, induces a high electric field and hence a high electrostatic energy for driving the conducting crack.Peer ReviewedPostprint (published version

Numerical simulations of vickers indentation crack growth in ferroelectric single crystals: effect of microstructure on the fracture process

Ferroelectric materials exhibit strong electro-mechanical coupling which make them ideal materials for use in electro-mechanical devices such as sensors, actuators and transducers. To assure optimum reliability of these devices, understanding of the fracture behavior in these materials is essential. The complex nonlinear interactions of the mechanical and electrical fields in the vicinity of the crack, with localized switching phenomena, govern the fracture behavior of ferroelectric materials. Experimental techniques have been used to study fracture in ferroelectrics, including Vickers indentation to investigate the fracture toughness anisotropy [1–5]. Experiments show that cracking along the poling direction of the material has a shorter length and consequently a higher effective fracture toughness than that normal to the poling direction. In this paper we introduce a model able to capture the anisotropic crack growth under Vickers indentation loading. This anisotropy is obtained by linking the crack propagation with the microstructural phenomena. The model treats in a coupled phase-field energetic fashion both the brittle crack propagation and the microstructure evolution. We have recently presented a model, showing that the interaction of the microstructure and the crack leads to a slow-fast crack propagation behavior observed in experiment [6]. In Ref. [7], we have introduced a modification in the formulation to endow the phase-field model with the ability to simulate the aforementioned anisotropic crack growth. We present here the highlights of that work. The theory of the coupled phase-field model is summarized in Section 2. Simulation results are presented and discussed in Section 3. The last Section is the conclusion of this paper

Crack initiation patterns at electrode edges in multilayer ferroelectric actuators

Peer ReviewedPostprint (author's final draft

Phase-field modeling of the coupled microstructure and fracture evolution in ferroelectric single crystals

We propose a phase-field model for the coupled simulation of microstructure formation and evolution, and the nucleation and propagation of cracks in single-crystal ferroelectric materials. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The finite-element implementation of the theory in two dimensions (plane-polarization and plane-strain) is described. We perform, to the best of our knowledge, the first crack propagation calculations of ferroelectric single crystals, simultaneously allowing general microstructures to develop. Previously, the microstructure calculations were performed at fixed crack configurations or under the assumption of small-scale switching. Our simulations show that this assumption breaks down as soon as the crack-tip field interacts with the boundaries of the test sample (or, in general, obstacles such as defects or grain boundaries). Then, the microstructure induced by the presence of the crack propagates beyond its vicinity, leading to the formation of twins. Interactions between the twins and the crack are investigated under mechanical and electromechanical loadings, both for permeable and impermeable cracks, with an emphasis on fracture toughening due to domain switching, and compared with experiments.Peer ReviewedPostprint (published version

Ferroelectrics as smart mechanical materials

This is the peer reviewed version of the following article: Cordero, K., Domingo Marimon, Neus, Abdollahi, A., Sort Viñas, Jordi, Catalan, G. Ferroelectrics as smart mechanical materials. "Advanced materials", 21 Juliol 2017, vol. 29, núm. 37, p. 1-6, which has been published in final form at DOI: 10.1002/adma.201702210. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The mechanical properties of materials are insensitive to space inversion, even when they are crystallographically asymmetric. In practice, this means that turning a piezoelectric crystal upside down or switching the polarization of a ferroelectric should not change its mechanical response. Strain gradients, however, introduce an additional source of asymmetry that has mechanical consequences. Using nanoindentation and contact-resonance force microscopy, this study demonstrates that the mechanical response to indentation of a uniaxial ferroelectric (LiNbO3) does change when its polarity is switched, and use this mechanical asymmetry both to quantify its flexoelectricity and to mechanically read the sign of its ferroelectric domains.Peer ReviewedPostprint (author's final draft

Phase-field modeling of fracture in ferroelectric materials

Tesi per compendi de publicacions. La consulta íntegra de la tesi, inclosos els articles no comunicats públicament per drets d'autor, es pot realitzar prèvia petició a l'Arxiu de la UPCPremi extraordinari doctorat 2012-2013The unique electro-mechanical coupling properties of ferroelectrics make them ideal materials for use in micro-devices as sensors, actuators and transducers. Nevertheless, because of the intrinsic brittleness of ferroelectrics, the optimal design of the electro-mechanical devices is strongly dependent on the understanding of the fracture behavior in these materials. Fracture processes in ferroelectrics are notoriously complex, mostly due to the interactions between the crack tip stress and electric fields and the localized switching phenomena in this zone (formation and evolution of domains of different crystallographic variants). Phase-field models are particularly interesting for such a complex problem, since a single partial differential equation governing the phase-field accomplishes at once (1) the tracking of the interfaces in a smeared way (cracks, domain walls) and (2) the modeling of the interfacial phenomena such as domain-wall energies or crack face boundary conditions. Such a model has no difficulty for instance in describing the nucleation of domains and cracks or the branching and merging of cracks. Furthermore, the variational nature of these models makes the coupling of multiple physics (electrical and mechanical fields in this case) very natural. The main contribution of this thesis is to propose a phase-field model for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in single crystal ferroelectric materials. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The finite element implementation of the theory is described. Simulations show the interactions between the microstructure and the crack under mechanical and electro-mechanical loadings. Another objective of this thesis is to encode different crack face boundary conditions into the phase-field framework since these conditions strongly affect the fracture behavior of ferroelectrics. The smeared imposition of these conditions are discussed and the results are compared with that of sharp crack models to validate the proposed approaches. Simulations show the effects of different conditions, electro-mechanical loadings and media filling the crack gap on the crack propagation and the microstructure of the material. In a third step, the coupled model is modified by introducing a crack non-interpenetration condition in the variational approach to fracture accounting for the asymmetric behavior in tension and compression. The modified model makes it possible to explain anisotropic crack growth in ferroelectrics under Vickers indentation loading. This model is also employed for the fracture analysis of multilayer ferroelectric actuators, which shows the potential of the model for future application. The coupled phase-field model is also extended to polycrystals by introducing realistic polycrystalline microstructures in the model. Inter- and trans-granular crack propagation modes are observed in the simulations. Finally and for completeness, the phase-field theory is extended for the simulation of conducting cracks and some preliminary simulations are also performed in three dimensions. Salient features of the crack propagation phenomenon predicted by the simulations of this thesis are directly compared with experimental observations.Los materiales ferroeléctricos poseen únicas propiedades electro-mecánicas y por eso se utilizan para los micro-dispositivos como sensores, actuadores y transductores. No obstante, debido a la fragilidad intrínseca de los ferroeléctricos, el diseño óptimo de los dispositivos electro-mecánicos es altamente dependiente de la comprensión del comportamiento de fractura en estos materiales. Los procesos de fractura en ferroeléctricos son notoriamente complejos, sobre todo debido a las interacciones entre campos de tensión y eléctricos y los fenómenos localizados en zona de fractura (formación y evolución de los dominios de las diferentes variantes cristalográficas). Los modelos de campo de fase son particularmente útiles para un problema tan complejo, ya que una sola ecuación diferencial parcial que gobierna el campo de fase lleva a cabo a la vez (1) el seguimiento de las interfaces de una manera suave (grietas, paredes de dominio) y (2) la modelización de los fenómenos interfaciales como las energías de la pared de dominio o las condiciones de las caras de grieta. Tal modelo no tiene ninguna dificultad, por ejemplo en la descripción de la nucleación de los dominios y las grietas o la ramificación y la fusión de las grietas. Además, la naturaleza variacional de estos modelos facilita el acoplamiento de múltiples físicas (campos eléctricos y mecánicos en este caso). La principal aportación de esta tesis es la propuesta de un modelo campo de fase para la simulación de la formación y evolución de la microestructura y la nucleación y propagación de grietas en materiales ferroeléctricos. El modelo aúna dos modelos de campo de fase para la fractura frágil y para la formación de dominios ferroeléctricos. La aplicación de elementos finitos a la teoría es descrita. Las simulaciones muestran las interacciones entre la microestructura y la fractura del bajo cargas mecánicas y electro-mecánicas. Otro de los objetivos de esta tesis es la codificación de diferentes condiciones de contorno de grieta porque estas condiciones afectan en gran medida el comportamiento de la fractura de ferroeléctricos. La imposición de estas condiciones se discuten y se comparan con los resultados de modelos clasicos para validar los modelos propuestos. Las simulaciones muestran los efectos de diferentes condiciones, cargas electro-mecánicas y medios que llena el hueco de la grieta en la propagación de las fisuras y la microestructura del material. En un tercer paso, el modelo se modifica mediante la introducción de una condición que representa el comportamiento asimétrico en tensión y compresión. El modelo modificado hace posible explicar el crecimiento de la grieta anisotrópica en ferroeléctricos. Este modelo también se utiliza para el análisis de la fractura de los actuadores ferroeléctricos, lo que demuestra el potencial del modelo para su futura aplicación. El modelo se extiende también a policristales mediante la introducción de microestructuras policristalinas realistas en el modelo. Modos de fractura inter y trans-granulares de propagación se observan en las simulaciones. Por último y para completar, la teoría del campo de fase se extiende para la simulación de las grietas conductivas y algunas simulaciones preliminares también se realizan en tres dimensiones. Principales características del fenómeno de la propagación de la grieta predicho por las simulaciones de esta tesis se comparan directamente con las observaciones experimentales.Award-winningPostprint (published version

Rational analysis of the traditional and conventional building materials and techniques in house construction With particular reference to Zambia

SIGLELD:D49755/84(2vols) / BLDSC - British Library Document Supply CentreGBUnited Kingdo

An efficacious method to assemble a modern multi-modal robotic team: dilemmas, challenges, possibilities and solutions

A modern multiagent robotic platform consists of a cooperative team of humans which develop a collaborative team of robots. The multi-modal nature of both the system and the team causes a complex problem which needs to be solved for optimum performance. Both the management and the technical aspect of a modern robotic team are explored in this Chapter in the platform of the RoboCup Competition. RoboCup is an example of such an environment where researchers from different disciplines join to develop a robotic team for completion as an evaluation challenge (Robocup, 2011). RoboCup competitions were first proposed by Mackworth in 1993. The main goal of this scientific competition is to exploit, improve and integrate the methods and techniques from robotics, machine vision and artificial intelligence disciplines to create an autonomous team of soccer playing robots(Kitano, 1997a; Kitano, 1997b; Kitano et al., 1997). Such experiment includes several challenges, from inviting an expert of specific field to the team to choosing bolts and nuts for each part of the robots. Usually each challenge has several possible solutions and choosing the best one is often challenging. We have participated in several world wide RoboCup competitions (Abdollahi, Samani et al. 2002, 2003 & 2004) and share our experience as an extensive instruction for setting up a modern robotic team including management and technical issues.Peer Reviewe