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 Young's modulus, the shear modulus and Poisson's 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.

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 Poisson's 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.

The paper describes the manufacturing and tensile testing of auxetic (negative Poisson's ratio) thermoplastic polyurethane foams, both under constant strain rate and sinusoidal excitation. The foams are produced from conventional flexible polyurethane basis following a manufacturing route developed in previous works. The Poisson's ratio behaviour over tensile strain has been analyzed using an Image Data processing technique based on Edge Detection from digital images recorded during quasi-static tensile test. The samples have been subjected to tensile and compressive tests at quasi-static and constant strain-rate values (up to 12 s -1 ). Analogous tests have been performed over iso-volumetric foams samples, i.e., foams subjected to the same volumetric compression of the auxetic ones, exhibiting a near zero Poisson's ratio behaviour. The auxetic and non-auxetic foams have been also tested under sinusoidal cycling load up to 10 Hz, with maximum pre-strain applied of 12%. The hysteresis of the cycling loading curve has been measured to determine the damping hysteretic loss factor for the various foams. The measurements indicate that auxetic foams have increased damping loss factor of 20% compared to the conventional foams. The energy dissipation is particularly relevant in the tensile segment of the curve, with effects given by the pre-strain level imposed on the samples.

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.

No abstract