Failure Analysis of Graphene Sheets with Multiple Stone-Thrower-Wales Defects Using Molecular-Mechanics Based Nonlinear Finite Element Models

Experimental studies show that Stone-Thrower-Wales STW defects generally exist in graphene sheets GSs and these defects considerably affect the fracture strength of GSs. Thus, prediction of failure modes of GSs with STW defects is useful for design of graphene based nanomaterials. In this paper, effects of multiple STW defects on fracture behavior of GSs are investigated by employing molecular mechanics based nonlinear finite element models. The modified Morse potential is used to define the non-linear characteristic of covalent bonds between carbon atoms and geometric nonlinearity effects are considered in models. Different tilting angles of STW defects are considered in simulations. The analysis results showed that the fracture strength of GSs strongly depends on tilting angle of multiple STW defects and the STW defects cause significant strength loss in GSs. The crack initiation and propagation are also studied and brittle failure characteristics are observed for all samples. The results obtained from this study provide some insights into design of GS based-structures with multiple STW defects

Numerical solution of two phase solidification problem using dynamic substructuring based on adaptive error estimation

N umerical solution of solidification of metals with a sharp front, in particular solidification of lead, is investigated. Considering the fact that the associated CPU time and memory requirement may be costly for large domains, alternatives are searched. It is observed that using a substructuring technique with a local mesh refinement is promising. Following, by the use of an adaptive error estimation algorithm to find the location of solidification front and mushy zone, dynamic substructuring technique is developed to decrease the computational cost and to increase the accuracy of results. Superconvergent patch recovery technique is used to obtain the heat fluxes to evaluate the error energy norm of elements at each analysis step. Solidification front, mushy zone and elements having errors above a threshold value are captured with the error estimator. Then, elements having errors above the threshold value are refined by creating a substructure which is independent from the original global mesh. Equations of the global coarse mesh are augmented with the equations of the substructure. Employing the equations of the original coarse mesh help reduce the computational cost. Numerical solutions are presented and it is shown that the proposed approach has advantages over the alternative methods and, by the virtue of the adaptive error estimation algorithm, significantly decreases the CPU time of numerical solutions while it increases the accuracy of solutions and locates precisely the solidification front and mushy zon

Nonreflecting boundary conditions for finite element methods based upon off-surface boundary integral equations.

In this work, an off-surface boundary integral method (OSBI) is presented as a mesh termination scheme for finite element formulations of acoustics and elasto-dynamics problems. By using finite element approximations for both the unknown Dirichlet boundary condition and the unknown Neumann boundary condition on the artificial boundary, the discretized boundary integral equation is used to solve for the discrete Neumann boundary condition term on the artificial boundary in terms of the unknown Dirichlet boundary condition term; this expression is then substituted into finite element formulations. As the observation points are placed off-surface, the difficulties are avoided in evaluating the singular boundary integral kernels. Of particular emphasis in this work is to show that new integral operators avoid singularity, the artificial boundary can be arbitrarily shaped, and no special operators need to be derived. It is easy to embed this method into a standard finite element code by supplying a library of fundamental solutions. Nonuniqueness can be suppressed either by choosing the observation points accordingly or by resorting to a Burton-Miller approach, which does not result in hyper-singular kernels owing to off-surface placement of observation points. For acoustics and elastodynamics equations, comparison is made of the new OSBI technique with the DtN method and several popular local nonreflecting boundary conditions (NRBC's). The OSBI approach is accurate, robust to parameter changes and has a uniform convergence, whereas local NRBC's are shown to be sensitive to parameter changes and may not have a uniform convergence. Notably, the OSBI method is competitive with the DtN method, and is not restricted to circular artificial boundaries. Even though acoustics and elastodynamics equations are considered, the approach developed here is general and can be extended to other time-dependent and time-harmonic problems.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104521/1/9527706.pdfDescription of 9527706.pdf : Restricted to UM users only

Large deformation object modeling using finite element method and proper orthogonal decomposition for haptic applications

Haptic Rendering has a wide range of application areas from entertainment to sur-gical simulations, from CAD/CAM to rehabilitation purposes. In each of these applications the main problem is the real-time performance of the overall system. The balance between realistic force reflecting object models and system performance is an important factor in hap-tic simulations. In general, two methods are used in haptic rendering: particle based and fi-nite element method based models. Although particle based methods are easier to implement and faster in computational manner, they have a limited capability to reflect the underlying mechanics. In order to obtain physically realistic models, finite element methods are widely used. Since finite element methods are computationally expensive further decomposition methods are applied to increase the real-time performance. In this work, two large deforma-tion object models are developed for force reflecting purposes and in order to increase the real-time performance, the proper orthogonal decomposition (POD) method is applied to the nonlinear models and performance increase in the overall system is investigated. By the use of finite element methods, proper orthogonal decomposition method is applied to the solutions of the large deflection problem of a beam. Even though the original structure behaves in a nonlinear manner, the POD method resulted in very accurate and fast solutions in real time. Experiments are carried out by using the haptic robot arm of Sensable Technologies. The numerical solutions and animations for haptic arm application will be presented