Fabrizio Scarpa

Effective elastic mechanical properties of single layer graphene sheets.

The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Youngs modulus, the shear modulus and Poissons ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

Structural health monitoring using scanning laser vibrometry: I. Lamb wave sensing

Structural health monitoring using Lamb waves is based on guided waves introduced to a structure at one point and sensed at a different location. Actuation and sensing can be accomplished using various types of transducer. The paper demonstrates a non-contact method for low-frequency Lamb wave sensing. The technique utilizes a laser Doppler velocimeter. Lamb wave responses are enhanced using data smoothing and filtering procedures. The results are validated using classical piezoceramic-based sensing and numerical simulations. The study shows the potential of laser vibrometry for Lamb wave sensing.

Wave beaming effects in two-dimensional cellular structures

Cellular structures like honeycombs or reticulated micro-frames are widely used in sandwich construction because of their superior structural static and dynamic properties. The aim of this study is to evaluate the dynamic behavior of two-dimensional cellular structures, with the focus on the effect of the geometry of unit cells on the dynamics of the propagation of elastic waves within the structure. The characteristics of wave propagation for the considered class of cellular solids are analyzed through the finite element model of the unit cell and the application of the theory of periodic structures. This combined analysis yields the phase constant surfaces, which define the directions of waves propagating in the plane of the structure for the assigned frequency values. The analysis of iso-frequency contour lines in the phase constant surfaces allows the prediction of the location and extension of angular ranges, and therefore regions within the structures where waves do not propagate. The performance of honeycomb grids of regular hexagonal topology is compared with that of grids of various geometries, with the emphasis on configurations featuring a negative Poissons ratio behavior. The harmonic response of the considered structures at specified frequencies confirms the predictions from the analysis of the phase constant surfaces and demonstrates the strongly spatially-dependent characteristics of periodic cellular structures. The numerical results presented indicate the potentials of the phase constant surfaces as tools for the evaluation of the wave propagation characteristics of this class of two-dimensional periodic structures. Optimal design configurations can be identified in order to achieve the desired transmissibility levels in specified directions and to obtain efficient vibration isolation capabilities. The findings from the presented investigations and the described analysis methodology will provide invaluable guidelines for the prototyping of future concepts of honeycombs or cellular structures with enhanced vibro-acoustics performance.

Dynamic properties of high structural integrity auxetic open cell foam

This paper illustrates various dynamic characteristics of open cell compliant polyurethane foam with auxetic (negative Poissons ratio) behaviour. The foam is obtained from off-the-shelf open cell polyurethane grey foam with a manufacturing process based on mechanical deformation on a mould in a temperature-controlled oven. The Poissons ratio is measured with an image processing technique based on edge detection with wavelet methods. Foam samples have been tested in a viscoelastic analyser tensile test machine to determine the Youngs modulus and loss factor for small dynamic strains. The same samples have also been tested in an acoustic impedance tube to measure acoustic absorption and specific acoustic resistance and reactance with a transmissibility technique. Another set of tests has been set up on a cam plastometer machine for constant strain rate dynamic crushing analysis. All the tests have been carried out on auxetic and normal foam samples to provide a comparison between the two types of cellular solids. The results from the experimental tests are discussed and interpreted using microstructure models for cellular materials existing in the literature. The negative Poissons ratio foam presented in this paper shows an overall superiority regarding damping and acoustic properties compared to the original conventional foam. Its dynamic crushing performance is also significantly superior to the normal foam, suggesting a possible use in structural integrity compliant elements.

Structural health monitoring using scanning laser vibrometry: II. Lamb waves for damage detection

Guided ultrasonic waves have shown great potential for structural health monitoring. Various types of transducer can be used for actuating and sensing of these waves. This includes non-contact approaches such as optical/laser techniques. Classical laser methods usually involve high energy interferometers. The paper demonstrates that a commercial laser vibrometer, designed for vibration/modal analysis, can be used for crack detection in metallic structures. The study involves a simple fatigue test in order to initiate and grow a crack. Lamb waves generated by one bonded piezoceramic transducer were sensed using a multi-point scanning laser vibrometer. The results demonstrate the potential of laser vibrometry for simple, rapid and robust detection of fatigue cracks in metallic structures.

Effective mechanical properties of hexagonal boron nitride nanosheets

We propose an analytical formulation to extract from energy equivalence principles the equivalent thickness and in-plane mechanical properties (tensile and shear rigidity, and Poissons ratio) of hexagonal boron nitride (h-BN) nanosheets. The model developed provides not only very good agreement with existing data available in the open literature from experimental, density functional theory (DFT) and molecular dynamics (MD) simulations, but also highlights the specific deformation mechanisms existing in boron nitride sheets, and their difference with carbon-based graphitic systems.

Numerical and experimental uniaxial loading on in-plane auxetic honeycombs

Auxetic honeycombs show in-plane negative Poissons ratio properties; they expand in all directions when pulled in only one, and contract when compressed. This characteristic is due to the reentrant shape of the honeycomb unit cell. The cell convoluteness gives a geometric stiffening effect that affects the linear elastic properties of the whole cellular solid. In this paper finite element simulations are carried out to calculate the in-plane Poissons ratio and Youngs moduli of re-entrant cell honeycombs for different geometric layout combinations (side cell aspect ratio, relative thickness and internal cell angle) subjected to uniaxial loading. The results show a high sensitivity of the mechanical properties for particular ranges of the geometric cell parameters. An image data detection technique is used to extract displacements and strains from an aramid paper re-entrant honeycomb sample in a tensile test. The comparison between numerical and experimental results shows good agreement.

Passive and MR fluid-coated auxetic PU foam - Mechanical, acoustic, and electromagnetic properties

This paper deals with a comparative study on the mechanical, acoustic, and electromagnetic properties of a novel class of auxetic (negative Poisson’s ratio) rigid polyurethane (PU) foam with a magnetorheological (MR) fluid coating. An auxetic solid expands in all directions when pulled in only one, thus behaving in an opposite manner compared to ‘classical’ solids. When compared with the conventional PU foam, the auxetic PU foam shows enhanced crashworthiness properties and increased sound absorption characteristics (at low frequencies). Samples of auxetic foam coated with MR fluid are examined in this work. While the tensile mechanical properties of the MR fluid-coated samples are affected mainly by surface effects, the acoustic absorption characteristics show almost constant values beyond the cut-off frequency level of the original uncoated auxetic foam. With regard to the foams’ electromagnetic properties, the auxetic structure and MR coating cause an increase in the refractive index and loss factor compared to the conventional foams. These electromagnetic effects are due to the presence of a high relative density and metal particulates in the foam material.

The bending of single layer graphene sheets: the lattice versus continuum approach

The out-of-plane bending behaviour of single layer graphene sheets (SLGSs) is investigated using a special equivalent atomistic-continuum model, where the C-C bonds are represented by deep shear bending and axial stretching beams and the graphene properties by a homogenization approach. SLGS models represented by circular and rectangular plates are subjected to linear and nonlinear geometric point loading, similar to what is induced by an atomic force microscope (AFM) tip. The graphene models are developed using both a lattice and a continuum finite element discretization of the partial differential equations describing the mechanics of the graphene. The minimization of the potential energy allows us to identify the thickness, elastic parameters and force/displacement histories of the plates, in good agreement with other molecular dynamic (MD) and experimental results. We note a substantial equivalence of the linear elastic mechanical properties exhibited by circular and rectangular sheets, while some differences in the nonlinear geometric elastic regime for the two geometrical configurations are observed. Enhanced flexibility of SLGSs is observed by comparing the nondimensional force versus displacement relations derived in this work and the analogous ones related to equivalent plates with conventional isotropic materials.

Dynamic crushing of auxetic open-cell polyurethane foam

Abstract A high strain rate compression test with a constant speed of 1.5 m/s has been performed on samples of negative Poissons ratio and normal open-cell polyurethane foam. The tests show that the transformation of the normal foam into the auxetic phase greatly increases the crashworthiness qualities of the open-cell foam.