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Experimental characterization of Graphene NanoRibbons (GNRs) is still an expensive task and computational simulations are therefore seen a practical option to study the properties and mechanical response of GNRs. Design of GNR in various nanotechnology devices can be approached through molecular dynamics simulations. This study demonstrates that the Atomic-scale Finite Element Method (AFEM) based on the second generation REBO potential is an efficient and accurate alternative to the molecular dynamics simulation of GNRs. Special atomic finite elements are proposed to model graphene edges. Extensive comparisons are presented with MD solutions to establish the accuracy of AFEM. It is also shown that the Tersoff potential is not accurate for GNR modeling. The study demonstrates the influence of chirality and size on design parameters such as tensile strength and stiffness. A GNR is stronger and stiffer in the zigzag direction compared to the armchair direction. Armchair GNRs shows a minor dependence of tensile strength and elastic modulus on size whereas in the case of zigzag GNRs both modulus and strength show a significant size dependency. The sizedependency trend noted in the present study is different from the previously reported MD solutions for GNRs but qualitatively agrees with experimental results. Based on the present study, AFEM can be considered a highly efficient computational tool for analysis and design of GNRs.

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This article analyzes the transient wave propagation phenomena that take place at 2D viscoelastic half-spaces subjected to spatially distributed surface loadings and to distinct temporal excitations. It starts with a fairly detailed review of the existing strategies to describe transient analysis for elastic and viscoelastic continua by means of the Boundary Element Method (BEM). The review explores the possibilities and limitations of the existing transient BEM procedures to describe dynamic analysis of unbounded viscoelastic domains. It proceeds to explain the strategy used by the authors of this article to synthesize numerically fundamental solutions or auxiliary states that allow an accurate analysis of transient wave propagation phenomena at the surface of viscoelastic half-spaces. In particular, segments with spatially constant and linear stress distributions over a halfspace surface are considered. The solution for the superposition of constant and discontinuous adjacent elements as well as linear and continuous stress distributions is addressed. The influence of the temporal excitation type and duration on the transient response is investigated. The present study is based on the numerical solution of stress boundary value problems of (visco)elastodynamics. In a first stage, the solution is obtained in the frequency domain. A numerical integration strategy allows the stationary solutions to be determined for very high frequencies. The transient solutions are obtained, in a second stage, by applying the Fast Fourier Transform (FFT) algorithm to the previously synthesized frequency domain solutions. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. By analyzing the transient solution of the stress boundary value problems, it is possible to show that from every surface stress discontinuity three wave fronts are generated. (continued on next The displacement velocity of these wave fronts can be associated to compression, shear and Rayleigh waves. It is shown that the half-space transient displacement solutions present abrupt jumps or oscillations which can be correlated to the arrival of these wave fronts at the observation point. Such a detailed analysis connecting half-space transient responses to the wave propagation fronts in viscoelastic half-spaces have not been reported in the reviewed literature.

SUMMARYIn this article a numerical solution for a three-dimensional isotropic, viscoelastic half-space subjected to concentrated surface stress loadings is synthesized with the aid of the Radon and Fourier integral transforms. Dynamic displacement and stress fields are computed for points at the surface and inside the domain. The analysis is performed in the frequency domain. Viscoelastic effects are incorporated by means of the elastic-viscoelastic correspondence principle. The equations of motion are solved in the Radon-Fourier transformed domain. Inverse transformations to the physical domain are accomplished numerically. The scheme used to perform the numerical inverse transformations is addressed. The solution is validated by comparison with results available in the literature. A set of original dynamic displacement and stress solutions for points within the half-space is presented.

Cove-edged graphene nanoribbons (CGNR) are a class of nanoribbons with asymmetric edges composed of alternating hexagons and have remarkable electronic properties. Although CGNRs have attractive size-dependent electronic properties their mechanical properties have not been well understood. In practical applications, the mechanical properties such as tensile strength, ductility and fracture toughness play an important role, especially during device fabrication and operation. This work aims to fill a gap in the understanding of the mechanical behaviour of CGNRs by studying the edge and size effects on the mechanical response by using molecular dynamic simulations. Pristine graphene structures are rarely found in applications. Therefore, this study also examines the effects of topological defects on the mechanical behaviour of CGNR. Ductility and fracture patterns of CGNR with divacancy and topological defects are studied. The results reveal that the CGNR become stronger and slightly more ductile as the width increases in contrast to normal zigzag GNR. Furthermore, the mechanical response of defective CGNRs show complex dependency on the defect configuration and distribution, while the direction of the fracture propagation has a complex dependency on the defect configuration and position. The results also confirm the possibility of topological design of graphene to tailor properties through the manipulation of defect types, orientation, and density and defect networks.

SUMMARYIn this article a numerical solution for a 3D isotropic, viscoelastic half-space subjected to vertical rectangular surface stress loading of constant amplitude is evaluated with the aid of the Radon and Fourier integral transforms. Dynamic displacement and stress fields are computed for the half-space surface as well as for points inside the domain. The analysis is performed in the frequency domain. Viscoelastic effects are incorporated by means of the elastic-viscoelastic correspondence principle. The equations of motion are solved in the Radon-Fourier transformed domain. Inverse transformations to the physical domain are accomplished numerically. The scheme used to perform the numerical inverse transformations is addressed. The solution is validated by comparison with results available in the literature. A sample of original dynamic results for displacement and stress fields for the 3D half-space is furnished.

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