Engineering of atomic-scale flexoelectricity at grain boundaries

Flexoelectricity is a type of ubiquitous and prominent electromechanical coupling, pertaining to the electrical polarization response to mechanical strain gradients that is not restricted by the symmetry of materials. However, large elastic deformation is usually difficult to achieve in most solids, and the strain gradient at minuscule is challenging to control. Here, we exploit the exotic structural inhomogeneity of grain boundary to achieve a huge strain gradient (~1.2 nm−1) within 3–4-unit cells, and thus obtain atomic-scale flexoelectric polarization of up to ~38 μC cm−2 at a 24° LaAlO3 grain boundary. Accompanied by the generation of the nanoscale flexoelectricity, the electronic structures of grain boundaries also become different. Hence, the flexoelectric effect at grain boundaries is essential to understand the electrical activities of oxide ceramics. We further demonstrate that for different materials, altering the misorientation angles of grain boundaries enables tunable strain gradients at the atomic scale. The engineering of grain boundaries thus provides a general and feasible pathway to achieve tunable flexoelectricity.

A Concise and Geometrically Exact Planar Beam Model for Arbitrarily Large Elastic Deformation Dynamics

The potential of large elastic deformations in control applications, e.g., robotic manipulation, is not yet fully exploited, especially in dynamic contexts. Mainly because essential geometrically exact continuum models are necessary to express these arbitrarily large deformation dynamics, they typically result in a set of nonlinear, coupled, partial differential equations that are unsuited for control applications. Due to this lack of appropriate models, current approaches that try to exploit elastic properties are limited to either small deflection assumptions or quasistatic considerations only. To promote further exploration of this exciting research field of large elastic deflection control, we propose a geometrically exact, but yet concise a beam model for a planar, shear-, and torsion-free case without elongation. The model is derived by reducing the general geometrically exact the 3D Simo–Reissner beam model to this special case, where the assumption of inextensibility allows expressing the couple of planar Cartesian parameters in terms of the curve tangent angle of the beam center line alone. We further elaborate on how the necessary coupling between position-related boundary conditions (i.e., clamped and hinged ends) and the tangent angle parametrization of the beam model can be incorporated in a finite element method formulation and verify all derived expressions by comparison to analytic initial value solutions and an energy analysis of a dynamic simulation result. The presented beam model opens the possibility of designing online feedback control structures for accessing the full potential that elasticity in planar beam dynamics has to offer.

Theoretical modeling and experimental research on the depth of radial material removal for flexible grinding

Abrasive belt flap wheel has large elastic deformation, which can better fit the surface of aero-engine blades. Reasonable control of the depth of radial material removal can effectively improve the grinding efficiency and profile accuracy of the blade surface. The depth of radial material removal for flexible grinding was studied through the process parameters in this article. First, the material removal rate model was established based on Hertz elastic contact theory and Preston equation. Then, according to the principle of equivalent material removal volume, a noval approach to determine the depth of radial material removal was proposed. Finally, the experiments for both plane and surface were implemented on a vertical machining center. The results indicate that the proposed method can improve the accuracy and consistency for flexible grinding.

Beyond linearity: bent crystalline copper nanowires in the small-to-moderate regime

The model proposed here adequately describes the bending phenomenon with terms accounting for the geometrical- and mechanical non-linearity as global features of a moderately large elastic deformation.

Large elastic deformation of micromorphic shells. Part I: Variational formulation

We aimed to study the static deformation of geometrically nonlinear shell-type structures on the basis of micromorphic theory. Employing the most comprehensive model in the micro-continuum field, shells in low-dimensions and made of inhomogeneous materials are precisely investigated. The seven-parameter two-dimensional (2D) kinematic model is used which satisfies three-dimensional (3D) constitutive relations and represents the macro-deformation components in mid-surface area of the shell. Also, in the framework of micromorphic continua with three deformable director vectors, nine micro-deformation degrees of freedom, including micro-scale rotations, shears and stretches, are taken into account. Utilizing the energy approach in the convected curvilinear coordinate system leads to the general derivation of the variational formulations in Lagrangian description. High-order stress–strain relations are obtained via introducing the size-dependent as well as size-independent elasticity tensors for the isotropic micromorphic solid. Finally, an equivalent matrix–vector form of representation is proposed to facilitate the solution procedure of the extracted tensor-based formulation. Determining the kinetic and kinematic fields in terms of 16 macro and micro-deformation components, provides the opportunity to directly implement the interpolation-based solution methodologies, such as the finite element isogeometric analysis presented in Part II of this study. Two parts of the article, that are organized to be independent, contribute to the literature respectively from theoretical and computational perspectives.

Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis

In Part I of this study, a variational formulation was presented for the large elastic deformation problem of micromorphic shells. Using the novel matrix-vector format presented for the kinematic model, constitutive relations, and energy functions, an isogeometric analysis (IGA)-based solution strategy is developed, which appropriately estimates the macro- and micro-deformation field components. Due to the capability of constructing exact geometries and the powerful mesh refinement tools, IGA can be successfully applied to solve the equilibrium equations with dominant nonlinear terms. It is known that different types of locking phenomena take place in the conventional finite element analysis of thin shells based on low-order elements. Non-standard finite element models with mixed interpolation schemes and additional degrees of freedom (DOFs) or the ones used the high-order Lagrangian shell elements which require high computational costs, are the available solutions to tackle locking issues. The present 16-DOFs IGA is found to be efficient because of possessing a good rate of convergence and providing locking-free stable responses for micromorphic shells. Such a conclusion is found from several comparative studies with available data in the well-known macro-scale benchmark problems based on the classical elasticity as well as the corresponding numerical examples studied in nano-scale beam-, plate-, cylindrical shell- and spherical shell-type structures on the basis of the micromorphic continuum theory.