Lattice orientation and crack size effect on the mechanical properties of Graphene

The effect of lattice orientation and crack length on the mechanical properties of Graphene are studied based on molecular dynamics simulations. Bond breaking and crack initiation in an initial edge crack model with 13 different crack lengths, in 10 different lattice orientations of Graphene are examined. In all the lattice orientations, three recurrent fracture patterns are reported. The influence of the lattice orientation and crack length on yield stress and yield strain of Graphene is also investigated. The arm-chair fracture pattern is observed to possess the lowest yield properties. A sudden decrease in yield stress and yield strain can be noticed for crack sizes <10 nm. However, for larger crack sizes, a linear decrease in yield stress is observed, whereas a constant yield strain of ≈≈0.05 is noticed. Therefore, the yield strain of ≈≈0.05 can be considered as a critical strain value below which Graphene does not show failure. This information can be utilized as a lower bound for the design of nano-devices for various strain sensor applications. Furthermore, the yield data will be useful while developing the Graphene coating on Silicon surface in order to enhance the mechanical and electrical characteristics of solar cells and to arrest the growth of micro-cracks in Silicon cells

Parametric studies on buckling of thin walled channel beams

Abstract The lateral buckling analysis of cold-formed thin walled beams subjected to pure bending moments has been performed. The critical buckling loads are estimated based an optimization criteria. The estimated critical buckling stresses are compared with the published results, they show excellent agreement. The effect of the beam length, radius and thickness of the flanges and the length of the extended open flanges, on the critical buckling stresses have been studied for several combinations of the geometric parameters of the beam. Among the three beams, the critical buckling moments for the beam with the extended open flanges are found to be the maximum. However, considering the material and manufacturing costs, beams with rounded cross section are efficient in resisting the buckling loads

Buckling analysis of thin wall stiffened composite panels

Abstract We present the pre and post buckling analysis of stiffened composite panels based on the finite element models. Individual buckling studies are conducted on the stiffened composite panel madeup of woven fabric CFC/epoxy, E-glass/epoxy and the Kevlar/epoxy composites. Straight, T shaped and I shaped stiffeners are considered to stiffen the panel. The panel is fabricated with 8 layers and the stiffeners are madeup of 16 layers, of equal thickness arranged in different orientations. The panel is subjected to a uniform axial compression load of 10&#xa0;kN. The distribution of the buckling stresses and the buckling loads with different panel and stiffener combinations are estimated for three different layup sequences. The variation of the buckling stresses and the buckling loads from the numerical model are compared with the experiment. The results are in excellent agreement

Directionality of sound radiation from rectangular panels

Abstract In this paper, the directionality of sound radiated from a rectangular panel, attached with masses/springs, set in a baffle, is studied. The attachment of masses/springs is done based on the receptance method. The receptance method is used to generate new mode shapes and natural frequencies of the coupled system, in terms of the old mode shapes and natural frequencies. The Rayleigh integral is then used to compute the sound field. The point mass/spring locations are arbitrary, but chosen with the objective of attaining a unique directionality. The excitation frequency to a large degree decides the sound field variations. However, the size of the masses and the locations of the masses/springs do influence the new mode shapes and hence the sound field. The problem is more complex when the number of masses/springs are increased and/or their values are made different. The technique of receptance method is demonstrated through a steel plate with attached point masses in the first example. In the second and third examples, the present method is applied to estimate the sound field from a composite panel with attached springs and masses, respectively. The layup sequence of the composite panel considered in the examples corresponds to the multifunctional structure battery material system, used in the micro air vehicle (MAV) (Thomas and Qidwai, 2005). The demonstrated receptance method does give a reasonable estimate of the new modes

A nonlocal adaptive discrete empirical interpolation method combined with modified hp-refinement for order reduction of molecular dynamics systems

Model order reduction is an emerging technique to tackle the computational complexities of molecular dynamics (MD) simulations. Different strategies are required to adequately obtain the reduced solutions of different classes of molecular dynamics systems. In this work, a proper orthogonal decomposition (POD) is combined with the discrete empirical interpolation method (DEIM) to study atomic systems. Due to the limitations of the DEIM in capturing the nonlocal response of the nonlinear force field of MD systems, a nonlocal adaptive discrete empirical interpolation method (ADEIM) is proposed. Furthermore, a modified hp-refinement algorithm is introduced to extend the application of the PODDEIM approach to order reduction of multi-dimensional MD systems. In the DEIM, the distance between atoms and hence the reduced internal force vector is estimated based on a local interpolation of the state variables. The internal forces of a multi-dimensional MD system depend on the distance between the atoms, represented in space by more than one coordinate. Therefore, the ADEIM approach seeks to obtain a nonlocal interpolation of the state variables to accurately predict the distance between the interpolated atoms and hence the reduced force vector. Simulation of MD systems with frequently changing neighbour atoms leads to change in the system dynamics, which further leads to change of properties of the snapshots. Therefore, the temporal domain is adaptively subdivided into smaller sub-domains using the adopted hp-refinement procedure. The reduced system parameters are effectively derived over the sub-domains. Considering the computational cost, a modified hp-refinement algorithm is developed in this study, which is further coupled with the POD-ADEIM approach to obtain the reduced-order solution of the MD systems. The results of the proposed approach demonstrate the efficiency and accuracy of the reduced solutions

Studies on ballistic impact of the composite panels

Abstract The ballistic impact of the composite materials is studied using the numerical models. Individual impact studies are conducted on the composite plate made-up of woven fabric CFRP, E-glass/epoxy and the Kevlar/epoxy composites. The plate is fabricated with 8 layers of equal thickness arranged in different orientations. A spherical steel projectile is considered for the high velocity impact. The projectile is placed very close to the plate, at the center and impacted with a velocity of 100&#xa0;m/s. The displacement and the stress distribution in each layer are studied for the layup sequence +45/−45/+45/−45/−45/+45/−45/+45. The variation of the kinetic energy, the increase in the internal energy of the laminate and the decrease in velocity of the projectile with time are also studied. Based on the results, the best layup sequence for the ballistic impact of each material is suggested

An adaptive multiscale method for quasi-static crack growth

This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom–atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement

Vibration analysis of multi-walled carbon nanotubes embedded in elastic medium

We propose a method to estimate the natural frequencies of the multi-walled carbon nanotubes (MWCNTs) embedded in an elastic medium. Each of the nested tubes is treated as an individual bar interacting with the adjacent nanotubes through the inter-tube Van der Waals forces. The effect of the elastic medium is introduced through an elastic model. The mathematical model is finally reduced to an eigen value problem and the eigen value problem is solved to arrive at the inter-tube resonances of the MWCNTs. Variation of the natural frequencies with different parameters are studied. The estimated results from the present method are compared with the literature and results are observed to be in close agreement

Efficient coarse graining in multiscale modeling of fracture

Abstract We propose a coarse-graining technique to reduce a given atomistic model into an equivalent coarse grained continuum model. The developed technique is tailored for problems involving complex crack patterns in 2D and 3D including crack branching and coalescence. Atoms on the crack surface are separated from the atoms not on the crack surface by employing the centro symmetry parameter. A rectangular grid is superimposed on the atomistic model. Atoms on the crack surface in each cell are used to estimate the equivalent coarse-scale crack surface of that particular cell. The crack path in the coarse model is produced by joining the approximated crack paths in each cell. The developed technique serves as a sound basis to study the crack propagation in multiscale methods for fracture