Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is most noticeable for nanoscale objects, where strain gradients are higher. Simulations are important to understand flexoelectricity because experiments at very small scales are difficult, and analytical solutions are scarce. Here, we computationally evaluate the role of flexoelectricity in the electromechanical response of linear dielectric solids in two-dimensions. We deal with the higher-order coupled partial differential equations using smooth meshfree basis functions in a Galerkin method, which allows us to consider general geometries and boundary conditions. We focus on the most common setups to quantify the flexoelectric response, namely, bending of cantilever beams and compression of truncated pyramids, which are generally interpreted through approximate solutions. While these approximations capture the sizedependent flexoelectric electromechanical coupling, we show that they only provide order-of-magnitude estimates as compared with a solution fully accounting for the multidimensional nature of the problem. We discuss the flexoelectric mechanism behind the enhanced size-dependent elasticity in beam configurations. We show that this mechanism is also responsible for the actuation of beams under purely electrical loading, supporting the idea that a mechanical flexoelectric sensor also behaves as an actuator. The predicted actuation-induced curvature is in a good agreement with experimental results. The truncated pyramid configuration highlights the critical role of geometry and boundary conditions on the effective electromechanical response. Our results suggest that computer simulations can help understanding and quantifying the physical properties of flexoelectric devices. (c) 2014 AIP Publishing LLC.Postprint (published version

Flexoelectricity allows a dielectric material to polarize in response to a mechanical bending moment and, conversely, to bend in response to an electric field. Compared with piezoelectricity, flexoelectricity is a weak effect of little practical significance in bulk materials. However, the roles can be reversed at the nanoscale. Here, we demonstrate that flexoelectricity is a viable route to lead-free microelectromechanical and nanoelectromechanical systems. Specifically, we have fabricated a silicon-compatible thin-film cantilever actuator with a single flexoelectrically active layer of strontium titanate with a figure of merit (curvature divided by electric field) of 3.33 MV(-1), comparable to that of state-of-the-art piezoelectric bimorph cantilevers.

a b s t r a c tWe present a family of phase field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase fields. The main challenge addressed here is encoding various electromechanical crack models (introduced as crack face boundary conditions in sharp models) into the phase field framework. The proposed models are verified through comparisons with the corresponding sharp crack models. We also perform two dimensional finite element simulations to demonstrate the effect of the different crack face conditions, the electromechanical loading and the media filling the crack gap on the crack propagation and the microstructure evolution. Salient features of the results are compared with experiments.

Bones generate electricity under pressure, and this electromechanical behavior is thought to be essential for bone's self-repair and remodeling properties. The origin of this response is attributed to the piezoelectricity of collagen, which is the main structural protein of bones. In theory, however, any material can also generate voltages in response to strain gradients, thanks to the property known as flexoelectricity. In this work, the flexoelectricity of bone and pure bone mineral (hydroxyapatite) are measured and found to be of the same order of magnitude; the quantitative similarity suggests that hydroxyapatite flexoelectricity is the main source of bending-induced polarization in cortical bone. In addition, the measured flexoelectric coefficients are used to calculate the (flexo)electric fields generated by cracks in bone mineral. The results indicate that crack-generated flexoelectricity is theoretically large enough to induce osteocyte apoptosis and thus initiate the crack-healing process, suggesting a central role of flexoelectricity in bone repair and remodeling.

Converse flexoelectricity is a mechanical stress induced by an electric polarization gradient. It can appear in any material, irrespective of symmetry, whenever there is an inhomogeneous electric field distribution. This situation invariably happens in piezoresponse force microscopy (PFM), which is a technique whereby a voltage is delivered to the tip of an atomic force microscope in order to stimulate and probe piezoelectricity at the nanoscale. While PFM is the premier technique for studying ferroelectricity and piezoelectricity at the nanoscale, here we show, theoretically and experimentally, that large effective piezoelectric coefficients can be measured in non-piezoelectric dielectrics due to converse flexoelectricity.