Browsing by Author "Rajapakse, R. K. N. D"

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Embargo
Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity
(ASME Digital Collection, 2007-05-01) Rajapakse, R. K. N. D; Tian, Lian
Two-dimensional elastic field of a nanoscale circular hole/inhomogeneity in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated. The Gurtin–Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects. A closed-form analytical solution is obtained by using the complex potential function method of Muskhelishvili. Selected numerical results are presented to investigate the size dependency of the elastic field and the effects of surface elastic moduli and residual surface stress. Stress state is found to depend on the radius of the inhomogeneity/hole, surface elastic constants, surface residual stress, and magnitude of far-field loading.
Embargo
Analytical solutions for a surface-loaded isotropic elastic layer with surface energy effects
(Pergamon, 2009-11-01) Rajapakse, R. K. N. D; Zhao, XJ
Consideration of surface (interface) energy effects on the elastic field of a solid material has applications in several modern problems in solid mechanics. The Gurtin–Murdoch continuum model [M.E. Gurtin, A.I. Murdoch, Arch. Ration. Mech. Anal. 57 (1975) 291–323; M.E. Gurtin, J. Weissmuller, F. Larché, Philos. Mag. A 78 (1998) 1093–1109] accounting for surface energy effects is applied to analyze the elastic field of an isotropic elastic layer bonded to a rigid base. The surface properties are characterized by the residual surface tension and surface Lame constants. The general solutions of the bulk medium expressed in terms of Fourier integral transforms and Hankel integral transforms are used to formulate the two-dimensional and axisymmetric three-dimensional problems, respectively. The generalized Young–Laplace equation for a surface yields a set of non-classical boundary conditions for the current class of problems. An explicit analytical solution is presented for the elastic field of a layer. The layer solution is specialized to obtain closed-form solutions for semi-infinite domains. Selected numerical results are presented to show the influence of surface elastic constants and layer thickness on stresses and displacements.
Open Access
Atomic-scale finite element modelling of mechanical behaviour of graphene nanoribbons
(Springer Netherlands, 2019-03) Damasceno, D. A; Mesquita, E; Rajapakse, R. K. N. D; Pavanello, R
Experimental characterization of Graphene NanoRibbons (GNRs) is still an expensive task and computational simulations are therefore seen as a practical option to study the properties and mechanical response of GNRs. Design of GNR elements 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. Graphene 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 size-dependency 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.
Embargo
Atomistic and continuum modelling of stress field at an inhomogeneity in graphene
(Elsevier, 2018-12-15) Dewapriya, M. A. N; Rajapakse, R. K. N. D
The influence of an atomic inhomogeneity on the resulting stress field of a nanoscopic matrix material can be remarkably different from the corresponding continuum descriptions due to the significance of surface energy and the discrete nature of matter at the nanoscale. In this work, we conducted a comprehensive molecular dynamics study to investigate the stress field at an atomic inhomogeneity, in the form of an elliptical hole or a circular hexagonal boron-nitride inclusion, in graphene. The results show that stress concentration factor at an inhomogeneity is higher than the corresponding classical continuum solution. We estimated the surface elastic constants for a modified continuum framework using the molecular dynamics results. Comparison between the atomic simulations and the modified continuum model reveals the limitations of such continuum-based models for the two-dimensional materials. Molecular dynamics results imply that the underlying atomic structure softens the effect of inhomogeneity compared to a continuum description thus causing an amplification of the stress filed. The molecular dynamics and modified continuum solutions for stress concentration are presented in simplified forms and design charts to facilitate preliminary design of graphene-based hybrid materials.
Embargo
Atomistic and continuum modelling of temperature-dependent fracture of graphene
(springer, 2014-06-01) Dewapriya, M. A. N; Rajapakse, R. K. N. D; Phani, A.S
This paper presents a comprehensive molecular dynamics study on the effects of nanocracks (a row of vacancies) on the fracture strength of graphene sheets at various temperatures. Comparison of the strength given by molecular dynamics simulations with Griffith’s criterion and quantized fracture mechanics theory demonstrates that quantized fracture mechanics is more accurate compared to Griffith’s criterion. A numerical model based on kinetic analysis and quantized fracture mechanics theory is proposed. The model is computationally very efficient and it quite accurately predicts the fracture strength of graphene with defects at various temperatures. Critical stress intensity factors in mode I fracture reduce as temperature increases. Molecular dynamics simulations are used to calculate the critical values of J integral (JIC) of armchair graphene at various crack lengths. Results show that JIC depends on the crack length. This length dependency of JIC can be used to explain the deviation of the strength from Griffith’s criterion. The paper provides an in-depth understanding of fracture of graphene, and the findings are important in the design of graphene based nanomechanical systems and composite materials
Embargo
Atomistic modelling of crack-inclusion interaction in graphene
(Pergamon, 2018-05-15) Dewapriya, M. A. N; Meguid, S. A; Rajapakse, R. K. N. D
In continuum fracture mechanics, it is well established that the presence of crack near an inclusion leads to a significant change in the crack-tip stress field. However, it is unclear how atomistic crack-inclusion interaction manifests itself at the nanoscale where the continuum description of matter breaks down. In this work, we conducted molecular dynamics simulations to investigate the interactions of an atomic-scale boron nitride inclusion with an edge crack in a graphene sheet. Numerical simulations of nanoscale tensile tests were obtained for graphene samples containing an edge crack and a circular inclusion. Stress analysis of the samples show the complex nature of the stress state at the crack-tip due to the crack-inclusion interaction. Results reveal that the inclusion results in an increase (amplification) or a decrease (shielding) of the crack-tip stress field depending on the location of the inclusion relative to the crack-tip. Our numerical experiments unveil that inclusions of specific locations could lead to a reduction in the fracture resistance of graphene. Results of the crack-inclusion interaction study were compared with the corresponding results of crack-hole interaction problem. The study also provides an insight into the applicability of well-established continuum crack-microdefect interaction models for the corresponding atomic scale problems.
Open Access
Atomistic modelling of size-dependent mechanical properties and fracture of pristine and defective cove-edged graphene nanoribbons
(Multidisciplinary Digital Publishing Institute, 2020-07) Damasceno, D. A; Rajapakse, R. K. N. D; Mesquita, E
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.
Open Access
Atomistic simulation of tensile strength properties of graphene with complex vacancy and topological defects
(Springer Vienna, 2020-08) Damasceno, D. A; Rajapakse, R. K. N. D; Mesquita, E; Pavanello, R
Defects including topological and vacancy defects have been observed in graphene during fabrication. Defects are also introduced to break the lattice symmetry of graphene and thereby obtain enhanced optoelectronic and other properties. It is important that gains in certain properties due to the presence defects are not at the expense of mechanical strength which is important in handling graphene and device fabrication. This paper presents a comprehensive study of the tensile strength and fracture strain of monolayer graphene with commonly observed topological defects and nanopores. Both molecular dynamics and the atomic-scale finite element method (AFEM) are used in this study, and the accuracy of AFEM in simulating complex topological and vacancy defects including line defects is established. It is found that the tensile strength properties have a complex dependency on the defect shape, size, and chirality. Certain defect geometries are found to be mechanically superior to other defect geometries thereby supporting the concept of topological design of graphene to optimize properties. The study also establishes AFEM as an efficient and potential tool for topological optimization of the mechanical behaviour of graphene.
Embargo
Characterizing fracture stress of defective graphene samples using shallow and deep artificial neural networks
(Pergamon, 2020-08-15) Dewapriya, M. A. N; Rajapakse, R. K. N. D; Dias, W. P. S
Advanced machine learning methods could be useful to obtain novel insights into some challenging nanomechanical problems. In this work, we employed artificial neural networks to predict the fracture stress of defective graphene samples. First, shallow neural networks were used to predict the fracture stress, which depends on the temperature, vacancy concentration, strain rate, and loading direction. A part of the data required to model the shallow networks was obtained by developing an analytical solution based on the Bailey durability criterion and the Arrhenius equation. Molecular dynamics (MD) simulations were also used to obtain some data. Sensitivity analysis was performed to explore the features learnt by the neural network, and their behaviour under extrapolation was also investigated. Subsequently, deep convolutional neural networks (CNNs) were developed to predict the fracture stress of graphene samples containing random distributions of vacancy defects. Data required to model CNNs was obtained from MD simulations. Our results reveal that the neural networks have a strong ability to predict the fracture stress of defective graphene under various processing conditions. In addition, this work highlights some advantages as well as limitations and challenges in using neural networks to solve complex problems in the domain of computational materials design.
Unknown
Continuum models incorporating surface energy for static and dynamic response of nanoscale beams
(IEEE, 2009-10-09) Liu, Chang; Rajapakse, R. K. N. D
Nanoscale beams are commonly found in nanomechanical and nanoelectromechanical systems (NEMS) and other nanotechnology-based devices. Surface energy has a significant effect on nanoscale structures and is associated with their size-dependent behavior. In this paper, a general mechanistic model based on the Gurtin-Murdoch continuum theory accounting for surface energy effects is presented to analyze thick and thin nanoscale beams with an arbitrary cross section. The main contributions of this paper are a set of closed-form analytical solutions for the static response of thin and thick beams under different loading (point and uniformly distributed) and boundary conditions (simply-supported, cantilevered, and clamped ends), as well as the solution of the free vibration characteristics of such beams. Selected numerical results are presented for aluminum and silicon beams to demonstrate their salient response features. It is shown that classical beam theory is not accurate in situations where the surface residual stress and/or surface elastic constants are relatively large. An intrinsic length scale for beams is identified that depends on beam surface properties and cross-sectional shape. The present work provides a convenient set of analytical tools for researchers working on NEMS design and fabrication to understand the static and dynamic behavior of nanoscale beams including their size-dependent behavior and the effects of common boundary conditions.
Unknown
A coupled thermoporoelastic model with thermo-osmosis and thermal-filtration
(Pergamon, 1998-12-01) Rajapakse, R. K. N. D; Zhou, Y; Graham, J
A coupled thermoporoelastic model accounting for compressibility and thermal expansion of constituents, convective heat flow and changing porosity and related properties of a saturated soil is presented. The model also considers thermodynamically coupled water and heat flow (thermal-filtration and thermo-osmosis that are analogous to Sorêt and Dufour effects in solutions) . These coupling effects are reported to be significant in the case of semi-impermeable clay barriers used in waste repositories. The governing equations derived in terms of displacements, temperature and pore water pressure are non-linear. A mixed finite element formulation is presented to obtain numerical solutions. An exact analytical solution for a 1-D soil column is presented for a simplified linear case that includes thermodynamic coupling. Selected numerical solutions for soil columns and radially symmetric plane strain problems are presented to demonstrate the principle features of the coupled model and the significance of thermodynamic coupling.
Unknown
Damping, tensile, and impact properties of superelastic shape memory alloy (SMA) fiber-reinforced polymer composites
(Elsevier, 2010-04-01) Raghavan, J; Bartkiewicz, Trevor; Boyko, Shawna; Shawna, Mike; Rajapakse, R. K. N. D
The potential of superelastic shape memory alloy (SMA) fibers to enhance the damping capacity and toughness of a thermoset polymer matrix was evaluated. A single-fiber winder was designed and built to manufacture a pre-form consisting of 102 μm diameter SMA fibers aligned parallel to each other. This pre-form was loaded to varying amounts of pre-strain and impregnated with vinyl ester to manufacture SMA fiber composites with 20% fiber volume fraction. The composites were tested using a Differential Scanning Calorimeter (DSC) and a Dynamic Mechanical Analysis (DMA), to evaluate the improvement in damping capacity of the polymer matrix due to the SMA fibers. Tensile and instrumented impact testing were carried out to evaluate improvements in mechanical properties and toughness of the composites. Appreciable improvement was observed in damping, tensile, and impact properties of the polymer matrix due to reinforcement with superelastic SMA fibers, highlighting the advantages of their use in polymer composites.
Unknown
Decay in Mechanical Properties of Catalyst Coated Membranes Subjected to Combined Chemical and Mechanical Membrane Degradation
(Wily, 2014-11-28) Rajapakse, R. K. N. D; Wang, G. G; Lauritzen, M; Kjeang, E; Lim, C; Ghataurah, J; Khorasany, R. M. H; Goulet, M. A; Alavijeh, A. S
The mechanical stability of catalyst coated membranes (CCMs) is an important factor for the overall durability and lifetime of polymer electrolyte fuel cells. In this article, the evolution of the mechanical properties of degraded CCMs is comprehensively assessed. A combined chemical and mechanical accelerated stress test (AST) was applied to simulate field operation and rapidly generate partially degraded CCM samples for tensile and expansion experiments under both room and fuel cell conditions. The tensile results indicated significant reductions in ultimate tensile strength, toughness, and fracture strain as a function of AST cycles, accompanied by a mild increase in elastic modulus. The increased brittleness and reduced fracture toughness of the CCM, caused primarily by chemical membrane degradation, is expected to play an important role in the ultimate failure of the fuel cell. The expansion tests revealed a linear decay in hygrothermal expansion, similar in magnitude to the loss of mechanical strength. The decline in CCM sensitivity to environmental changes leads to non-uniform swelling and contraction that may exacerbate local degradation. Interestingly, the hygrothermal expansion in the late stages of degradation coincided with the fracture strain, which correlates to in situ development of fractures in chemically weakened membranes.
Unknown
Development of a homogenous nonlinear spring model characterizing the interfacial adhesion properties of graphene with surface defects
(Elsevier, 2016-08-01) Dewapriya, M. A. N; Rajapakse, R. K. N. D
In graphene-based systems, the interface between graphene and other materials creates a mechanically weak region. Therefore, understanding the mechanical behaviour of graphene interfaces is critically important in designing reliable graphene-based systems. On the other hand, defects such as surface impurities are unavoidable during the fabrication of nanoscale systems. We developed a nonlinear spring model to characterize the influence of surface defects on the adhesion properties of graphene interfaces. The model was extensively validated using molecular dynamics simulations for graphene–silicon dioxide interface, and the computed cohesive energy is also in agreement with the recently measured energies. Our results indicate that low concentrations of hydrogen adatoms highly degrade the interfacial strength, whereas vacancies have a negligible effect on the interfacial strength. We also compared the influence of hydrogen adatoms on the properties of several commonly encountered graphene interfaces. In addition, we developed a novel analytical framework to compute the required graphene-substrate interfacial area to withstand an applied force during the indentation test. These findings are useful in designing graphene-based nanoelectromechanical systems and composite materials. More importantly, the developed spring model can be parameterized to investigate the mechanical behaviour of any material interface, which is vitally important in designing reliable nanodevices and nanocomposites.
Open Access
Dynamic axial load transfer from elastic bar to poroelastic medium
(American Society of Civil Engineers, 1999-09) Rajapakse, R. K. N. D; Zeng, X.I.
The time-harmonic response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a vertical load is considered. The bar is modeled using 1D elastic theory valid for long bars in the low-frequency range, and the porous medium using Biot's 3D elastodynamic theory. The bar is bonded to the surrounding medium along the contact surface. The problem is formulated by decomposing the bar/porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the distribution of axial force in the fictitious bar. The integral equation involves kernels that are displacement and strain influence functions of a poroelastic half-space subjected to a buried, uniform vertical patch load. The governing integral equation is solved by applying numerical quadrature. The solutions for axial displacement and axial force of the bar, and the pore pressure are also derived. Selected numerical results for vertical impedance, axial force, and pore pressure profiles are presented to portray the influence of bar stiffness and length/radius ratio, frequency of excitation, and poroelastic properties.
Embargo
Dynamic Green's functions of homogeneous poroelastic half-plane
(American Society of Civil Engineers, 1994-11) Rajapakse, R. K. N. D; Senjuntichai, T
This paper presents a comprehensive analytical and numerical treatment of two‐dimensional dynamic response of a dissipative poroelastic half‐plane under time‐harmonic internal loads and fluid sources. General solutions for poroelastodynamic equations corresponding to Biot's theory are obtained by using Fourier integral transforms in the x‐direction. These general solutions are used to solve boundary‐value problems corresponding to vertical and horizontal loads, and fluid sources applied at a finite depth below the surface of a poroelastic half‐plane. Explicit analytical solutions corresponding to above‐boundary‐value problems are presented. The solutions for poroelastic fields of a half‐plane subjected to internal excitations are expressed in terms of semiinfinite Fourier type integrals that can only be evaluated by numerical quadrature. The integration path is free from any singularities due to the dissipative nature of the elastic waves propagating in a poroelastic medium, and the Fourier integrals are evaluated by using an adaptive version of the trapezoidal rule. The accuracy of present numerical solutions are confirmed by comparison with existing solutions for ideal elasticity and poroelasticity. Selected numerical results are presented to portray the influence of the frequency of excitation, poroelastic material properties and types of loadings on the dynamic response of a poroelastic half‐plane. Green's functions presented in this paper can be used to solve a variety of elastodynamic boundary‐value problems and as the kernel functions in the boundary integral equation method.
Embargo
Dynamic response of a multi‐layered poroelastic medium
(John Wiley & Sons, Ltd, 1995-05) Rajapakse, R. K. N. D; Senjuntichai, T
An exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half-plane or a rigid base. Fourier integral transform is used with respect to the x-co-ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half-plane are derived explicitly in the Fourier-frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed.
Embargo
Dynamic response of a pile in a multi-layered soil to transient torsional and axial loading
(Thomas Telford Ltd, 1999-02-01) Rajapakse, R. K. N. D; Militano, G.
The dynamic response of an elastic pile subjected to transient torsional and axial loading is considered. The pile is embedded in a multi-layered elastic soil. The stress field in a soil is simplified by following the existing solutions for a pile subjected to static torsional and axial loading. The dynamic equilibrium equation of soil is solved in the Laplace domain by using analytical techniques. The soil resistance is coupled into a one-dimensional governing equation of a pile segment and an analytical solution is presented. An impedance matrix can then be derived for a pile segment relating end stress resultants to the displacements. Non-homogeneous initial conditions of the pile are considered. The impedance matrices of pile segments are assembled by following the concepts of finite element method to analyse a pile embedded in a multi-layered soil. The treatment of soil base response is also discussed. Time domain solutions are obtained by using a numerical Laplace inversion procedure. The extension of the analysis to linear viscoelastic soils using the correspondence principle in the theory of viscoelasticity is discussed. Selected numerical solutions for a pile embedded in a homogeneous soil and a &squo;Gibson’ soil are presented to portray the influence of pile moduli and slenderness ratios, loading history and soil non-homogeneity on the dynamic response of an elastic pile. Nous étudions la réponse dynamique d’un pilot élastique soumis à une charge de torsion et axiale transitoire. Le pilot est enfoui dans un sol élastique constittué de plusieurs couches. Nous simplifions le champ de contrainte dans un sol en appliquant les solutions existantes pour un pilot soumis à une charge de torsion et axiale statique. L’équation de 1’équilibre dynamique du sol est résolue dans le domaine de Laplace en utilisant des techniques analytiques. Nous couplons la résistance du sol en une équation standard unidimensionnelle pour un segment de pilot et nous présentons une solution analytique. Une matrice d’impédance pent alors être dérivée pour un segment de pilot en liant les résultantes de contrainte en bout aux déplacements. Nous examinons les conditions initiales non homogènes du pilot. Pour analyser un pilot enfoui dans un sol constitué de plusieurs couches, nous assemblons les matrices d’impédance des segments de pilot en suivant les concepts de la méthode d’éléments finis. Nous discutons aussi du traitement de la réponse de base du sol. Les solutions du domaine de temporisation sont obtenues en utilisant une procédure d’inversion numérique de Laplace. Nous discutons de l’extension de l’analyse aux sols à viscoèlasticit´e;aire en utilisant le principe de correspondance dans la théorie de viscoélasdcité. Nous présentons de solutions numériques choisies pour un pilot enfoui dans un sol homogène et un sol &squo;Gibson’ pour décrire l’influence des modules de pilot et des coefficients de gracilité, des comportements aux charges et de la non homégénéité du sol sur la réponse dynamique d’un pilot élastique.
Open Access
Effect of electric boundary conditions on crack propagation in ferroelectric ceramics
(The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences, 2014-04) Rajapakse, R. K. N. D; Li, F-X; Sun, Y
In this paper, the effect of electric boundary conditions on Mode I crack propagation in ferroelectric ceramics is studied by using both linear and nonlinear piezoelectric fracture mechanics. In linear analysis, impermeable cracks under open circuit and short circuit are analyzed using the Stroh formalism and a rescaling method. It is shown that the energy release rate in short circuit is larger than that in open circuit. In nonlinear analysis, permeable crack conditions are used and the nonlinear effect of domain switching near a crack tip is considered using an energy-based switching criterion proposed by Hwang et al. (Acta Metal. Mater., 1995). In open circuit, a large depolarization field induced by domain switching makes switching much more difficult than that in short circuit. Analysis shows that the energy release rate in short circuit is still larger than that in open circuit, and is also larger than the linear result. Consequently, whether using linear or nonlinear fracture analysis, a crack is found easier to propagate in short circuit than in open circuit, which is consistent with the experimental observations of Kounga Njiwa et al. (Eng. Fract. Mech., 2006).
Embargo
Effects of free edges and vacancy defects on the mechanical properties of graphene
(IEEE, 2014-08-18) Dewapriya, M. A. N; Rajapakse, R. K. N. D
Defects are unavoidable during synthesizing and fabrication of graphene based nanoelecromechanical systems. This paper presents a comprehensive molecular dynamics simulation study on the mechanical properties of finite graphene with vacancy defects. We characterize the strength and stiffness of graphene using the concept of surface stress in three-dimensional crystals. Temperature and strain rate dependent atomistic model is also presented to evaluate the strength of defective graphene. Free edges have a significant impact on the stiffness; the strength, however, is less affected. The vacancies exceedingly degrade the strength and the stiffness of graphene. These findings provide a remarkable insight into the strength and the stiffness of defective graphene, which is critical in designing experimental and instrumental applications.