A Continuum Model for Circular Graphene Membranes Under Uniform Lateral Pressure

Despite the numerous applications of pressurized graphene membranes in new technologies, there is still a lack of accurate mechanical models. In this work we develop a continuum model for circular graphene membranes subjected to uniform lateral pressure. We adopt a semi-inverse method by defining a simplified kinematics of deformation and we describe the material behavior with a stored energy function that takes into account both nonlinearity and anisotropy of graphene. An expression of the applied pressure as a function of the deflection of the membrane is obtained from an approximate solution of the equilibrium. The simplifying hypotheses of the analytical model are verified by a finite element (FE) analysis in nonlinear elasticity. In addition, a numerical solution of the differential equilibrium equations of the exact theory is presented. The pressure-deflection response from FE and numerical solutions agree well with the prediction of the analytical formula, demonstrating its accuracy. The analytical solution is then employed for the response of a two-layered composite membrane made of graphene deposited onto a soft substrate. This application is of great interest since new nanotechnologies make use of layered nanocomposites. Differently from our entirely nonlinear approach, most continuum models in the literature are based on the assumption of linear elastic material, which is suitable only when deformations are small. The present work gives a comprehensive description of the mechanics of pressurized graphene membranes

Effect of compressibility on the mechanics of hyperelastic membranes

Elastic membranes are usually studied assuming material incompressibility. However, in several applications they are made of compressible materials such as polymeric foams, hydrogels, and certain kinds of elastomers. Only a few works attempted to incorporate volume changes into membrane problems, but with significant limitations. The models proposed were designed for nearly incompressible materials and lacked a foundation in experimental data, leading to results of limited value. In this work, we investigate the effect of compressibility in membrane problems adopting a consistent model based on the real response of materials to large volume changes. We consider three benchmark problems of nonlinear elasticity: (i) inflation of a circular flat membrane; (ii) inflation of a thin-walled cylindrical tube; (iii) inflation of a thin-walled spherical balloon. Four types of materials divided by increasing degree of compressibility are studied. The results indicate that volumetric deformations have a significant impact on both the limit pressure and the deformed shape. The proposed solutions represent benchmarks for developing new applications of compressible membranes made of polymeric foams and hydrogels, playing an increasingly important role in engineering technologies

Analytical, numerical and experimental study of the finite inflation of circular membranes

In the present work we derive an analytical expression for the pressure–deflection curve of circular membranes subjected to inflation. This problem has been studied mostly from a numerical point of view and there is still a lack of accurate closed-form solutions in nonlinear elasticity. The analytical formulation is developed with a semi-inverse method by setting a priori the kinematics of deformation of the membrane. A compressible Mooney–Rivlin material model is considered and a pressure–deflection relation is derived from the equilibrium. The kinematics is approximated and therefore the obtained solution is not exact. Consequently, the formulation is adjusted by introducing an additional polynomial function in the pressure–deflection equation. The polynomial is calibrated by fitting numerical solutions of the exact system of differential equilibrium equations. The calibration is done over a wide range of constitutive parameters that covers the response of all rubber materials for technological applications. As a result, a definitive and accurate expression of the applied pressure as a function of the deflection of the membrane is obtained. The formula is validated with finite element (FE) simulations and compared with other solutions available in the literature. The comparison shows that the present model is more accurate. In addition, unlike the other models, it can be applied to compressible materials. Experimental uniaxial and bulge tests are carried out on rubber materials and the model proposed is used to characterize the Mooney–Rivlin constitutive parameters. Since the pressure–deflection formula is accurate and easy-to-use, it is an innovative tool in engineering applications of inflated membranes

Active shape correction of a thin glass/plastic X-ray mirror

Optics for future X-ray telescopes will be characterized by very large aperture and focal length, and will be made of lightweight materials like glass or plastic in order to keep the total mass within acceptable limits. Optics based on thin slumped glass foils are currently in use in the NuSTAR telescope and are being developed at various institutes like INAF/OAB, aiming at improving the angular resolution to a few arcsec HEW. Another possibility would be the use of thin plastic foils, being developed at SAO and the Palermo University. Even if relevant progresses in the achieved angular resolution were recently made, a viable possibility to further improve the mirror figure would be the application of piezoelectric actuators onto the non-optical side of the mirrors. In fact, thin mirrors are prone to deform, so they require a careful integration to avoid deformations and even correct forming errors. This however offers the possibility to actively correct the residual deformation. Even if other groups are already at work on this idea, we are pursuing the concept of active integration of thin glass or plastic foils with piezoelectric patches, fed by voltages driven by the feedback provided by X-rays, in intra-focal setup at the XACT facility at INAF/OAPA. In this work, we show the preliminary simulations and the first steps taken in this project

Buckling capacity model for timber screws loaded in compression: Experimental, analytical and FE investigations

This paper investigates the buckling of screws loaded in compression inserted into timber members. Screws are often used as a reinforcement in timber structures. However, under compression forces, they are prone to axial buckling. The current model for the screw buckling, enclosed in the EC5 proposal, is based on the general framework of EC3 for the instability of compressed steel members. The main shortcomings of the current formulation for the buckling of screws are the following. (1) The analytical expression for calculating the theoretical buckling load does not follow the observed modes. (2) Due to the need for dedicated studies, the value of the imperfection coefficient is arbitrarily chosen. This paper fills the above gaps. Firstly, a simple analytical expression for predicting the buckling of screws is proposed and validated against experimental and finite element (FE) findings. Furthermore, the formulation adopts a more accurate expression for lateral deformation based on experimental observation. Secondly, a FE model calibrated on experimental tests is used to estimate the defect coefficients of the instability curves as a function of the amplitude of the geometric defects of the screw, expressed as a fraction of its length. Finally, a Markov chain Monte Carlo analysis is carried out to simulate the capacity of screws with different sizes, assuming the uncertainty of all input parameters sampled from suitable probability distributions. The results are used to validate the proposed deterministic capacity model and estimate the uncertainty factors of the design equation

Design and advancement status of the Beam Expander Testing X-ray facility (BEaTriX)

The BEaTriX (Beam Expander Testing X-ray facility) project is an X-ray apparatus under construction at INAF/OAB to generate a broad (200 x 60 mm2), uniform and low-divergent X-ray beam within a small lab (6 x 15 m2). BEaTriX will consist of an X-ray source in the focus a grazing incidence paraboloidal mirror to obtain a parallel beam, followed by a crystal monochromation system and by an asymmetrically-cut diffracting crystal to perform the beam expansion to the desired size. Once completed, BEaTriX will be used to directly perform the quality control of focusing modules of large X-ray optics such as those for the ATHENA X-ray observatory, based on either Silicon Pore Optics (baseline) or Slumped Glass Optics (alternative), and will thereby enable a direct quality control of angular resolution and effective area on a number of mirror modules in a short time, in full X-ray illumination and without being affected by the finite distance of the X-ray source. However, since the individual mirror modules for ATHENA will have an optical quality of 3-4 arcsec HEW or better, BEaTriX is required to produce a broad beam with divergence below 1-2 arcsec, and sufficient flux to quickly characterize the PSF of the module without being significantly affected by statistical uncertainties. Therefore, the optical components of BEaTriX have to be selected and/or manufactured with excellent optical properties in order to guarantee the final performance of the system. In this paper we report the final design of the facility and a detailed performance simulation.Comment: Accepted paper, pre-print version. The finally published manuscript can be downloaded from http://dx.doi.org/10.1117/12.223895

Resolving the nature of electronic excitations in resonant inelastic x-ray scattering

The study of elementary bosonic excitations is essential toward a complete description of quantum electronic solids. In this context, resonant inelastic X-ray scattering (RIXS) has recently risen to becoming a versatile probe of electronic excitations in strongly correlated electron systems. The nature of the radiation-matter interaction endows RIXS with the ability to resolve the charge, spin and orbital nature of individual excitations. However, this capability has been only marginally explored to date. Here, we demonstrate a systematic method for the extraction of the character of excitations as imprinted in the azimuthal dependence of the RIXS signal. Using this novel approach, we resolve the charge, spin, and orbital nature of elastic scattering, (para-)magnon/bimagnon modes, and higher energy dd excitations in magnetically-ordered and superconducting copper-oxide perovskites (Nd2CuO4 and YBa2Cu3O6.75). Our method derives from a direct application of scattering theory, enabling us to deconstruct the complex scattering tensor as a function of energy loss. In particular, we use the characteristic tensorial nature of each excitation to precisely and reliably disentangle the charge and spin contributions to the low energy RIXS spectrum. This procedure enables to separately track the evolution of spin and charge spectral distributions in cuprates with doping. Our results demonstrate a new capability that can be integrated into the RIXS toolset, and that promises to be widely applicable to materials with intertwined spin, orbital, and charge excitations

Electronic and magnetic excitations in the "half-stuffed" Cu--O planes of Ba2_2Cu3_3O4_4Cl2_2 measured by resonant inelastic x-ray scattering

We use resonant inelastic x-ray scattering (RIXS) at the Cu L$_3$ edge to measure the charge and spin excitations in the "half-stuffed" Cu--O planes of the cuprate antiferromagnet Ba$_2$Cu$_3$O$_4$Cl$_2$. The RIXS line shape reveals distinct contributions to the $dd$ excitations from the two structurally inequivalent Cu sites, which have different out-of-plane coordinations. The low-energy response exhibits magnetic excitations. We find a spin-wave branch whose dispersion follows the symmetry of a CuO$_2$ sublattice, similar to the case of the "fully-stuffed" planes of tetragonal CuO (T-CuO). Its bandwidth is closer to that of a typical cuprate material, such as Sr$_2$CuO$_2$Cl$_2$, than it is to that of T-CuO. We interpret this result as arising from the absence of the effective four-spin inter-sublattice interactions that act to reduce the bandwidth in T-CuO.Comment: 10 pages, 8 figure