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.

Simple deformation measures for discrete elastic rods and ribbons

The discrete elastic rod method (Bergou et al. 2008 ACM Trans. Graph . 27 , 63:1–63:12. ( doi:10.1145/1360612.1360662 )) is a numerical method for simulating slender elastic bodies. It works by representing the centreline as a polygonal chain, attaching two perpendicular directors to each segment and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulae for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.

Bending strain in 3D topological semi-metals

We present an experimental set-up for the controlled application of strain gradients by mechanical piezoactuation on 3D crystalline microcantilevers that were fabricated by focused ion beam machining. A simple sample design tailored for transport characterization under strain at cryogenic temperatures is proposed. The topological semi-metal Cd3As2 serves as a test bed for the method, and we report extreme strain gradients of up to 1.3% µm-1 at a surface strain value of ≈ 0.65% at 4K. Interestingly, the unchanged quantum transport of the cantilever suggests that the bending cycle does not induce defects via plastic deformation. This approach is a first step towards realizing transport phenomena based on structural gradients, such as artificial gauge fields in topological materials.

Size effect in piezoelectric semiconductor nanostructures

A gradient theory is applied to the mechanical constitutive equations for piezoelectric semiconductor nanostructures. This is achieved by considering the strain gradients in the constitutive equation with high-order stresses and electric displacements in advanced continuum model. The C1 continuous interpolations of displacements or a mixed formulation is required in the finite element method (FEM) due to the presence of the second-order derivative on the elastic displacements. A mixed FEM is then developed from the principle of virtual work. Numerical examples clearly show the significant effect of flexoelectricity on the induced electric potential and electric current in the piezoelectric semiconductor nanostructures.

Tuning crumpled sheets for an enhanced flexoelectric response

Flexoelectricity is a universal phenomenon present in all dielectrics that couples electrical polarization to strain gradients and vice-versa. Thus, structures and configurations that permit large strain gradients facilitate the design of an enhanced electromechanical coupling. In a recent work, we demonstrated the prospects for using crumpling of essentially arbitrary thin sheets for energy harvesting. Crumples, with their defect-like nature, admit singular and rapidly varying deformation fields and are thus ideal for engineering sharp non-uniformities in the strain field. In this work, we consider how to tune the design of crumpled sheets for a significant flexoelectric response. Specifically, we analytically derive the electromechanical coupling for a thin crumpled sheet with varying thickness and graded Young’s modulus as key design variables. We show that, the electromechanical coupling of such crumpled sheets can be tuned to be nearly five times those of the homogeneous film.

Validation of notch stress estimation schemes for different constraints, strain gradients and loading conditions on low C-Mn steel

The present study is aimed at validation of notch stress/ strain estimation schemes such as classical Neuber, Hoffmann-Seeger and recently developed Ince-Glinka method for Nuclear piping material (low C-Mn steel). The study has considered different constraints, loading conditions, various hole sizes to accommodate strain gradient variations and equivalent peak strains. The notch stress field evaluated using these schemes is compared with corresponding stress using elastic-plastic Finite Element (FE) analyses. The comparisons have brought out that the Hoffmann-Seeger scheme results in reasonably accurate assessment of stress localization nearly for all constraint geometries, loadings and strain gradients. However, the classical Neuber scheme is more suitable for low constraint geometries and intermediate constraint geometries whereas it results in under-estimation of maximum principal stress for high constraint geometries, thereby leading to over-prediction of fatigue life. Further, the suitability of energy equivalence equations of Ince-Glinka model for individual stress components, has been reviewed.

The evolution of triple junctions: from failure to success

Divergent triple junctions are stable plate margins where three spreading ridges meet. Although it is accepted that this configuration is inherited from an earlier phase of continental rifting, how post-breakup triple junctions emerge from the separation of two plates remains unclear. By documenting the strain rate history recorded in the three rift-arms of several modern and ancient triple junctions, we show that deformation is episodic and localized in only one or two rifts at any given time. We further investigate this behavior in three-dimensional (3D) analog experiments of rifting, under a range of kinematic boundary conditions and containing a variety of pre-existing lithospheric heterogeneities. Deformation in the experiments is characterized by strain jumps and rift abandonment, comparable to natural observations. Boundary rotation during extension induces oblique stretching directions, along-strike strain gradients and forces significant strain jump to reduce the number of rifts segments active. Models that comprise lithospheres ranging from homogenous to containing a triple junction-like pre-existing heterogeneities, never developed a three-armed rift, where all rift segments are active at same time, at any stage. Our experimental results indicate that, unlike mature, successful, and stable oceanic triple junctions, early-stage continental rifting progresses through unstable “double-junctions” characterized by repeated strain jumps and rift failures and reactivations.