A. Srikantha Phani

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.

Wave propagation in two-dimensional periodic lattices

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagomé lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.

Influence of temperature and free edges on the mechanical properties of graphene

A systematic molecular dynamics simulation study is performed to assess the effects of temperature and free edges on the ultimate tensile strength and Youngs modulus of a single-layer graphene sheet. It is observed that graphene sheets at higher temperatures fail at lower strains, due to the high kinetic energy of atoms. A numerical model, based on kinetic analysis, is used to predict the ultimate strength of the graphene under various temperatures and strain rates. As the width of a graphene reduces, the excess edge energy associated with free edge atoms induces an initial strain on the relaxed configuration of the sheets. This initial strain has a greater influence on the Youngs modulus of the zigzag sheet compared with that of the armchair sheets. The simulations reveal that the carbon–carbon bond length and amplitude of intrinsic ripples of the graphene increases with temperature. The initial out-of-plane displacement of carbon atoms is necessary to simulate the physical behaviour of a graphene when the Nose–Hoover or Berendsen thermostat is used.

Position-Dependent Multibody Dynamic Modeling of Machine Tools Based on Improved Reduced Order Models

Dynamic response of a machine tool structure varies along the tool path depending on the changes in its structural configurations. The productivity of the machine tool varies as a function of its frequency response function (FRF) which determines its chatter stability and productivity. This paper presents a computationally efficient reduced order model to obtain the FRF at the tool center point of a machine tool at any desired position within its work volume. The machine tool is represented by its position invariant substructures. These substructures are assembled at the contacting interfaces by using novel adaptations of constraint formulations. As the tool moves to a new position, these constraint equations are updated to predict the FRFs efficiently without having to use computationally costly full order finite element or modal models. To facilitate dynamic substructuring, an improved variant of standard component mode synthesis method is developed which automates reduced order determination by retaining only the important modes of the subsystems. Position-dependent dynamic behavior and chatter stability charts are successfully simulated for a virtual three axis milling machine, using the substructurally synthesized reduced order model. Stability lobes obtained using the reduced order model agree well with the corresponding full-order system.

Local resonance bandgaps in periodic media: Theory and experiment

Periodic composites such as acoustic metamaterials use local resonance phenomenon in designing low frequency sub-Bragg bandgaps. These bandgaps emerge from a resonant scattering interaction between a propagating wave and periodically arranged resonators. This paper develops a receptance coupling technique to combine the dynamics of the resonator with the unit cell dynamics of the background medium to analyze flexural wave transmission in a periodic structure, involving a single degree of freedom coupling between the medium and the resonator. Receptance techniques allow for a straightforward extension to higher dimensional systems with multiple degrees of freedom coupling and for easier experimental measurements. Closed-form expressions for the location and width of sub-Bragg bandgaps are obtained. Rigid body modes of the unit cell of the background medium are shown to set the bounding frequencies for local resonance bandgaps. Results from the receptance analysis compare well with Bloch wave analysis and experiments performed on a finite structural beam with periodic masses and resonators. Stronger coupling and inertia of the resonator increase the local resonance bandgap width. Two-fold periodicity widens the Bragg bandgap, narrowed by local resonators, thus expanding the design space and highlighting the advantages of hierarchical periodicity.

Experimental Identification of Generalized Proportional Viscous Damping Matrix

A simple and easy-to-implement algorithm to identify a generalized proportional viscous damping matrix is developed in this work. The chief advantage of the proposed technique is that only a single drive-point frequency response function (FRF) measurement is needed. Such FRFs are routinely measured using the standard techniques of an experimental modal analysis, such as impulse test. The practical utility of the proposed identification scheme is illustrated on three representative structures: (1) a free-free beam in flexural vibration, (2) a quasiperiodic three-cantilever structure made by inserting slots in a plate in out-of-plane flexural vibration, and (3) a point-coupled-beam system. The finite element method is used to obtain the mass and stiffness matrices for each system, and the damping matrix is fitted to a measured variation of the damping (modal damping factors) with the natural frequency of vibration. The fitted viscous damping matrix does accommodate for any smooth variation of damping with frequency, as opposed to the conventional proportional damping matrix. It is concluded that a more generalized viscous damping matrix, allowing for a smooth variation of damping as a function of frequency, can be accommodated within the framework of standard finite element modeling and vibration analysis of linear systems.

Elastic Boundary Layers in Two-Dimensional Isotropic Lattices

The phenomenon of elastic boundary layers under quasistatic loading is investigated using the Floquet–Bloch formalism for two-dimensional, isotropic, periodic lattices. The elastic boundary layer is a region of localized elastic deformation, confined to the free edge of a lattice. Boundary layer phenomena in three isotropic lattice topologies are investigated: the semiregular Kagome lattice, the regular hexagonal lattice, and the regular fully triangulated lattice. The boundary layer depth is on the order of the strut length for the hexagonal and the fully triangulated lattices. For the Kagome lattice, the depth of boundary layer scales inversely with the relative density. Thus, the boundary layer in a Kagome lattice of low relative density spans many cells.

Young's modulus measurement of thin-film materials using micro-cantilevers

The need for a simple and effective characterization technique for thin-film materials which are widely used in MEMS (micro-electro-mechanical systems), using commonly available equipment, has prompted consideration of cantilever beam-based methods. The advantages of this class of techniques which employ a scanning surface profiler to deform micro-cantilevers are simplicity, speed, cost and wide applicability. A technique for extracting Youngs modulus from static deflection data is developed in this paper and validated in experiments on thin-film specimens of silicon nitride deposited on a silicon substrate under different conditions. Finite element analysis is used to assess the influence of factors affecting the bending of thin films, and thus guide the analysis of micro-cantilever deflection data for reliable characterization of the material.

Bending and Stretching Actuation of Soft Materials through Surface- Initiated Polymerization**

Shape–memory materials (SMMs) and actuators possess the ability to respond to external stimuli such as temperature, electricity, magnetic field, and light, and change their shapes. During the process, energy is converted into mechanical deformation which makes them attractive for various applications in biomedical devices, deployable structures, artificial muscles, microdevices, sensors, etc. Traditional SMMs and actuators rely on the properties of bulk material irrespective of their nature (e.g. polymers, metallic alloys, composite materials). Very recently, polymer-brush-based nanoscale bending actuators were reported. As a consequence of the strong interchain repulsion, the overcrowded polymer chains within the polymer brush can exert forces onto the underlying substrate and deform the substrate. However, there is no empirical evidence that bending observed on the nanoscale can be adapted for actuator applications on the macroscale. Furthermore, bending alone may not be sufficient to provide the desired macroscopic actuation; axial stretching may also be required. Herein we demonstrate the bending and stretching of a soft polymeric substrate, plasticized poly(vinyl chloride) (pPVC, thickness 400 mm, Young!s Modulus 6.89 MPa), on the macroscale by grafting a model hydrophilic polymer, poly(N,N-dimethylacrylamide) (PDMA), at high graft density on the pPVC surface. As shown in Figure 1A, when PDMA

Compliance and Longitudinal Strain of Cardiovascular Stents: Influence of Cell Geometry

A systematic study on the influence of the cell geometry of a cardiovascular stent on its radial compliance and longitudinal strain is presented. Eight stent cell geometries—based on common lattice cells—are compared using finite element analysis. It is found that, for a given strut thickness, the radial compliance depends on the shape of the cell and is intimately connected with the longitudinal strain through effective Poisson’s ratio, which depends on the cell geometry. It is demonstrated experimentally that a hybrid stent containing both positive and negative Poisson’s ratio cell lattice geometries exhibited very low values of longitudinal strain. This study indicates that cell geometries may be tailored to minimize longitudinal stresses imposed by the stent onto the artery wall.