Source: http://www.proceedings.blucher.com.br/article-details/a-molecular-dynamics-derived-finite-element-method-for-structural-simulations-and-failure-of-graphene-nanocomposites-9226
Timestamp: 2019-04-22 01:00:55+00:00

Document:
The recent rise of 2D materials, such as graphene, has expanded the interest in nano-electromechanical systems (NEMS). The increasing ability of synthesizing more exotic NEMS architectures, creates a growing need for a cost-effective, yet accurate nano-scale simulation method. Established methodologies like Molecular Dynamics (MD) trail behind synthesis capabilities because the computational effort scales quadratically. The equilibrium equations of MD are equivalent with those of the computationally more favourable Finite Element Method (FEM). However, current implementations exploiting this equivalence re- main limited due to the FEM iterative solvers requiring a large number of lengthy force field derivatives and specifically tailored element topologies. This paper proposes a formal deriva- tion of the merged Molecular Dynamic Finite Element Method (MDFEM) which establishes an uncoupling of the force field potentials from the element topologies. An implementation approach, which does not require manual derivations, is presented. Different non-linear MD force field potentials are implemented exactly within the FEM, at reduced computational costs. The proposed multi-scale and multi-physics compatible MDFEM is equivalent to to the MD as demonstrated by an example of brittle fracture in Carbon Nanotubes (CNT).
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Wilmes, A. A. R.; Pinho, S. T.; "A Molecular Dynamics derived Finite Element Method for Structural Simulations and Failure of Graphene Nanocomposites", p. 3174-3193 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
Wilmes , A. A. R.
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Ernst, “Development of a 4-node finite element for the computation of nano-structured materials,” Computational Materials Science, 33, 443 – 458, 2005. M. Meo and M. Rossi, “Prediction of young’s modulus of single wall carbon nanotubes by molecular-mechanics based finite element modelling,” Composites Science and Tech- nology, 66, 1597 – 1605, 2006. K. Tserpes, P. Papanikos, and S. Tsirkas, “A progressive fracture model for carbon nan- otubes,” Composites Part B: Engineering, 37, 662 – 669, 2006. J. Xiao, J. Staniszewski, and J. G. Jr., “Fracture and progressive failure of defective graphene sheets and carbon nanotubes,” Composite Structures, 88, 602 – 609, 2009. M. Rossi and M. Meo, “On the estimation of mechanical properties of single-walled car- bon nanotubes by using a molecular-mechanics based fe approach,” Composites Science and Technology, 69, 1394 – 1398, 2009. T. C. Theodosiou and D. A. 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Tomnek, “Structural rigidity and low frequency vibra- tional modes of long carbon tubules,” Zeitschrift für Physik D Atoms, Molecules and Clusters, 27, 93–96, 1993. S. Govindjee and J. L. Sackman, “On the use of continuum mechanics to estimate the properties of nanotubes,” Solid State Communications, 110, 227 – 230, 1999. D. Qian, G. J. Wagner, W. K. Liu, M.-F. Yu, and R. S. Ruoff, “Mechanics of carbon nanotubes,” Applied Mechanics Reviews, 55, 495–533, 2002. L. Nasdala, A. Kempe, and R. Rolfes, “Are finite elements appropriate for use in molec- ular dynamic simulations?,” Composites Science and Technology, 2012. J. Wackerfuß, “Molecular mechanics in the context of the finite element method,” Inter- national Journal for Numerical Methods in Engineering, 77, 969–997, 2009. F. Scarpa, S. Adhikari, and A. S. Phani, “Effective elastic mechanical properties of single layer graphene sheets,” Nanotechnology, 20, 065709, 2009. S. Sihn, V. Varshney, A. K. Roy, and B. L. Farmer, “Prediction of 3d elastic moduli and poissons ratios of pillared graphene nanostructures,” Carbon, 50, 603 – 611, 2012. T. Belytschko, S. P. Xiao, G. C. Schatz, and R. S. Ruoff, “Atomistic simulations of nanotube fracture,” Phys. Rev. B, 65, 235430, Jun 2002. C. Lobo and J. L. Martins, “Valence force field model for graphene and fullerenes,” Zeitschrift fr Physik D Atoms, Molecules and Clusters, 159–164, 1997. 10.1007/s004600050123. A. Rapp´e and C. Casewit, Molecular Mechanics Across Chemistry. University Science Books, 1997. MathWorks, MATLAB R2011b. The MathWorks Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, USA, 2011. Simulia, ABAQUS 6.10-1. Dassault Systemes Simulia Corp, Rising Sun Mills, 166 Val- ley Street, Providence, RI 02909-2499, USA, 2010. M. Dresselhaus, G. Dresselhaus, and R. Saito, “Physics of carbon nanotubes,” Carbon, 33, 883 – 891, 1995. H. Terrones and A. Mackay, “The geometry of hypothetical curved graphite structures,” Carbon, 30, 1251 – 1260, 1992. D. Baowan, B. J. Cox, and J. M. Hill, “Junctions between a boron nitride nanotube and a boron nitride sheet,” Nanotechnology, 19, 075704, 2008. B. J. Cox and J. M. Hill, “A variational approach to the perpendicular joining of nan- otubes to plane sheets,” Journal of Physics A: Mathematical and Theoretical, 41, 125203, 2008. D. Baowan, B. Cox, and J. Hill, “Joining a carbon nanotube and a graphene sheet,” in Nanoscience and Nanotechnology, 2008. ICONN 2008. International Conference on, 5 –8, feb. 2008. D. Baowan, B. J. Cox, and J. M. Hill, “Two least squares analyses of bond lengths and bond angles for the joining of carbon nanotubes to graphenes,” Carbon, 45, 2972 – 2980, 2007. H. Terrones, “Curved graphite and its mathematical transformations,” Journal of Math- ematical Chemistry, 15, 143–156, 1994. A. L. Mackay, H. Terrones, and P. W. Fowler, “Hypothetical graphite structures with negative gaussian curvature[and discussion],” Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 343, 113–127, 1993.

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