Growth and shape control of disks by bending and extension

Differential growth of thin elastic bodies furnishes a surprisingly simple explanation of the complex and intriguing shapes of many biological systems, such as plant leaves and organs. Similarly, inelastic strains induced by thermal effects or active materials in layered plates are extensively used to control the curvature of thin engineering structures. Such behaviour inspires us to distinguish and to compare two possible modes of differential growth not normally compared to each other, in order to reveal the full range of out-of-plane shapes of an initially flat disk. The first growth mode, frequently employed by engineers, is characterised by direct bending strains through the thickness, and the second mode, mainly apparent in biological systems, is driven by extensional strains of the middle surface. When each mode is considered separately, it is shown that buckling is common to both modes, leading to bistable shapes: growth from bending strains results in a double-curvature limit at buckling, followed by almost developable deformation in which the Gaussian curvature at buckling is conserved; during extensional growth, out-of-plane distortions occur only when the buckling condition is reached, and the Gaussian curvature continues to increase. When both growth modes are present, it is shown that, generally, larger displacements are obtained under in-plane growth when the disk is relatively thick and growth strains are small, and vice versa. It is also shown that shapes can be mono-, bi-, tri- or neutrally stable, depending on the growth strain levels and the material properties: furthermore, it is shown that certain combinations of growth modes result in a free, or natural, response in which the doubly curved shape of disk exactly matches the imposed strains. Such diverse behaviour, in general, may help to realise more effective actuation schemes for engineering structures. © 2012 Elsevier Ltd. All rights reserved.

Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials

The paper presents a multiscale procedure for the linear analysis of components made of lattice materials. The method allows the analysis of both pin-jointed and rigid-jointed microtruss materials with arbitrary topology of the unit cell. At the macroscopic level, the procedure enables to determine the lattice stiffness, while at the microscopic level the internal forces in the lattice elements are expressed in terms of the macroscopic strain applied to the lattice component. A numeric validation of the method is described. The procedure is completely automated and can be easily used within an optimization framework to find the optimal geometric parameters of a given lattice material. © 2011 Elsevier Ltd. All rights reserved.

Capillary bending of Janus carbon nanotube micropillars.

We present a scalable process for the fabrication of slanted carbon nanotube micropillar arrays by inclined metal deposition and capillary self-assembly. Local control of the micropillar angle from vertical to nearly horizontal is achieved, and is explained using a finite element model. These structures may be useful for microscale contacts and anisotropic smart surfaces.

Bending of nanoscale filament assemblies by elastocapillary densification

We report a mechanism by which nanoscale filaments self-assemble into asymmetric aggregates by elastocapillary action. Specifically, capillary rise of liquid into an asymmetric pattern of vertically aligned filaments causes the filaments to deflect laterally during elastocapillary densification. We quantitatively show that the lateral deflection can be controlled precisely by the pattern shape and the coupling strength among the filaments. We exploit this mechanism to fabricate asymmetric micropillars and multidirectional bridges of densely packed carbon nanotubes. Analogous behavior occurs as biological filaments interact with liquids, and these findings enable scalable fabrication of anisotropic filament assemblies for manipulating surface interactions between solids and liquids. © 2010 The American Physical Society.

Influence of band bending and polarization on the valence band offset measured by x-ray photoelectron spectroscopy

The influence of band bending and polarization on the valence band offset measured by x-ray photoelectron spectroscopy (XPS) is discussed, and a modification method based on a modified self-consistent calculation is proposed to eliminate the influence and thus increasing the precision of XPS. Considering the spontaneous polarization at the surfaces and interfaces and the different positions of Fermi levels at the surfaces, we compare the energy band structures of Al/Ga-polar AlN/GaN and N-polar GaN/AlN heterojunctions, and give corrections to the XPS-measured valence band offsets. Other AlN/GaN heterojunctions and the piezoelectric polarization are also introduced and discussed in this paper.

Bending of jets in the QSO NRAO 530

We present radio images of NRAO 530 on scales ranging from pc to kpc. The observations include the EVN at 5 GHz, the VLBA at 1.6, 8.6 and 15 GHz, the MERLIN at 1.6 and 5 GHz, and the VLA at 5, 8.4, 15, 22, and 43 GHz. The VLBI images show a core-jet structure with an oscillating trajectory on a scale of about 30 mas north of the strongest compact component (core). Superluminal motions are detected in five of the jet components with apparent velocities in the range of 13.6 to 25.2c. A new component is detected at 15 GHz with the VLBA observations, which appears to be associated with the outburst in 2002. Significant polarized emission is detected around the core with the VLBA observations at 15 GHz. Rapid variations of the polarization intensity and angle are found between the epochs in 2002 and 2004. On the kpc-scale, a distant component (labelled as WL) located 11 aresec west (PA=-86 degrees) of the core is detected beyond the core-jet structure which extended to several hundreds of mas in the north-west direction (-50 degrees). A significant emission between the core-jet structure and the WL is revealed. A clump of diffuse emission (labelled EL, 12 arcsec long) at PA 70 degrees to the core, is also detected in the VLA observations, suggesting the presence of double lobes in the source. The core component shows a flat spectrum, while the distant components WL and EL have steep spectra. The steep spectra of the distant components and the detection of the arched emission suggest that the distant components are lobes or hot-spots powered by the core of NRAO 530. The morphologies from pc- to kpc-scales and the bending of jets are investigated. The observed radio morphology from pc to kcp appears to favor the model in which precession or wobbling of the nuclear disk drives the helical motion of the radio plasma and produces the S-shaped structure on kpc scale.

LOCAL BENDING OF THIN FILM ON VISCOUS LAYER

Effects of deposition layer position and number/density on local bending of a thin film are systematically investigated. Because the deposition layer interacts with the thin film at the interface and there is an offset between the thin film neutral surface and the interface, the deposition layer generates not only axial stress but also bending moment. The bending moment induces an instant out-of-plane deflection of the thin film, which may or may not cause the so-called local bending. The deposition layer is modeled as a local stressor, whose location and density are demonstrated to be vital to the occurrence of local bending. The thin film rests on a viscous layer, which is governed by the Navier-Stokes equation and behaves like an elastic foundation to exert transverse forces on the thin film. The unknown feature of the axial constraint force makes the governing equation highly nonlinear even for the small deflection case. The constraint force and film transverse deflection are solved iteratively through the governing equation and the displacement constraint equation of immovable edges. This research shows that in some special cases, the deposition density increase does not necessarily reduce the local bending. By comparing the thin film deflections of different deposition numbers and positions, we also present the guideline of strengthening or suppressing the local bending.

Study of Anisotropic Conductive Adhesive Joint Behaviour under 3-Point Bending

Flip chip interconnections using anisotropic conductive film (ACF) are now a very attractive technique for electronic packaging assembly. Although ACF is environmentally friendly, many factors may influence the reliability of the final ACF joint. External mechanical loading is one of these factors. Finite element analysis (FEA) was carried out to understand the effect of mechanical loading on the ACF joint. A 3-dimensional model of adhesively bonded flip chip assembly was built and simulations were performed for the 3-point bending test. The results show that the stress at its highest value at the corners, where the chip and ACF were connected together. The ACF thickness was increased at these corner regions. It was found that higher mechanical loading results in higher stress that causes a greater gap between the chip and the substrate at the corner position. Experimental work was also carried out to study the electrical reliability of the ACF joint with the applied bending load. As per the prediction from FEA, it was found that at first the corner joint failed. Successive open joints from the corner towards the middle were also noticed with the increase of the applied load.