1 Title, abstract and keywords
2 The main text
3 Bibliography
4 Acknowledgments
5 References
Back to Top
Document information
Published on 01/01/2004
DOI: 10.1002/nme.944
Licence: CC BY-NC-SA license
Web of Science Core Collection® Times cited: 108
Crossref Cited-by Times cited: 112
OpenCitations.net Times cited: 63
OpenCitations.net - Citing documents:
- W. E, ,Department of Mathematics, Princeton University, Princeton, N.J. 08544, J. Lu, ,Departments of Mathematics, Physics, and Chemistry, Duke University, Durham NC. Mathematical theory of solids: From quantum mechanics to continuum models. 34(12) DOI 10.3934/dcds.2014.34.5085
- K. Zhang, M. Arroyo. Adhesion and friction control localized folding in supported graphene. Journal of Applied Physics 113(19) DOI 10.1063/1.4804265
- Y. Sun, K. Liew. Multiscale Modeling of Carbon Nanotubes. (2009) DOI 10.1007/978-1-4020-9785-0_14
- S. Im, S. Kwon, J. Park. Quasicontinuum Simulations of Deformations of Carbon Nanotubes. (2009) DOI 10.1007/978-1-4020-9785-0_15
- S. Zhang, S. Mielke, R. Khare, D. Troya, R. Ruoff, G. Schatz, T. Belytschko. Mechanics of defects in carbon nanotubes: Atomistic and multiscale simulations. Phys. Rev. B 71(11) (2005) DOI 10.1103/physrevb.71.115403
- S. Kitipornchai, X. He, K. Liew. Continuum model for the vibration of multilayered graphene sheets. Phys. Rev. B 72(7) (2005) DOI 10.1103/physrevb.72.075443
- A. Sears, R. Batra. Buckling of multiwalled carbon nanotubes under axial compression. Phys. Rev. B 73(8) (2006) DOI 10.1103/physrevb.73.085410
- J. Yang, W. E. Generalized Cauchy-Born rules for elastic deformation of sheets, plates, and rods: Derivation of continuum models from atomistic models. Phys. Rev. B 74(18) (2006) DOI 10.1103/physrevb.74.184110
- R. Khare, S. Mielke, J. Paci, S. Zhang, R. Ballarini, G. Schatz, T. Belytschko. Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Phys. Rev. B 75(7) (2007) DOI 10.1103/physrevb.75.075412
- S. Zhang, T. Zhu, T. Belytschko. Atomistic and multiscale analyses of brittle fracture in crystal lattices. Phys. Rev. B 76(9) (2007) DOI 10.1103/physrevb.76.094114
- D. Golovaty, S. Talbott. Continuum model of polygonization of carbon nanotubes. Phys. Rev. B 77(8) (2008) DOI 10.1103/physrevb.77.081406
- K. Liew, Y. Sun. Elastic properties and pressure-induced structural transitions of single-walled carbon nanotubes. Phys. Rev. B 77(20) (2008) DOI 10.1103/physrevb.77.205437
- F. Hill, T. Havel, C. Livermore. Modeling mechanical energy storage in springs based on carbon nanotubes. Nanotechnology 20(25) (2009) DOI 10.1088/0957-4484/20/25/255704
- W. Sommanawat, W. Kanok-Nukulchai. Multiscale simulation based on kriging based finite element method. Interaction and multiscale mechanics 2(4) DOI 10.12989/imm.2009.2.4.353
- H. Teng, C. Lee, J. Chen. On the continuum formulation for modeling DNA loop formation. Interaction and multiscale mechanics 4(3) DOI 10.12989/imm.2011.4.3.219
- S. Hollerer. Buckling analysis of carbon nanotubes - a molecular statics investigation into the influence of non-bonded interactions. Int. J. Numer. Meth. Engng 91(4) (2012) DOI 10.1002/nme.4277
- D. Qian, Z. Zhou, Q. Zheng. Coarse-grained modeling and simulation of graphene sheets based on a discrete hyperelastic approach. Int. J. Numer. Meth. Engng 102(3-4) (2015) DOI 10.1002/nme.4872
- C. Findeisen, J. Wackerfuß. A general approximation of the exponential Cauchy-Born hypothesis to model arbitrarily shaped shell-like nanostructures within continuum mechanics. Int. J. Numer. Meth. Engng 105(10) (2015) DOI 10.1002/nme.4992
- L. Zhang, L. Berlyand, M. Fedorov, H. Owhadi. Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates. Multiscale Model. Simul. 8(5) DOI 10.1137/090781619
- P. Bělík, M. Luskin. Analysis of the Quasi-Nonlocal Approximation of Linear and Circular Chains in the Plane. Multiscale Model. Simul. 9(4) DOI 10.1137/100806242
- S. Mielke, T. Belytschko, G. Schatz. Nanoscale Fracture Mechanics. Annu. Rev. Phys. Chem. 58(1) DOI 10.1146/annurev.physchem.58.032806.104502
- P. Guidault, T. Belytschko. On theL2 and theH1 couplings for an overlapping domain decomposition method using Lagrange multipliers. Int. J. Numer. Meth. Engng 70(3) (2007) DOI 10.1002/nme.1882
- S. Zhang, R. Khare, Q. Lu, T. Belytschko. A bridging domain and strain computation method for coupled atomistic–continuum modelling of solids. Int. J. Numer. Meth. Engng 70(8) (2007) DOI 10.1002/nme.1895
- R. Sauer, S. Li. A contact mechanics model for quasi-continua. Int. J. Numer. Meth. Engng 71(8) (2007) DOI 10.1002/nme.1970
- Y. Sun, K. Liew. Application of the higher-order Cauchy-Born rule in mesh-free continuum and multiscale simulation of carbon nanotubes. Int. J. Numer. Meth. Engng 75(10) DOI 10.1002/nme.2299
- P. Guidault, T. Belytschko. Bridging domain methods for coupled atomistic-continuum models withL2orH1couplings. Int. J. Numer. Meth. Engng 77(11) DOI 10.1002/nme.2461
- R. Gracie, T. Belytschko. Concurrently coupled atomistic and XFEM models for dislocations and cracks. Int. J. Numer. Meth. Engng 78(3) DOI 10.1002/nme.2488
- M. Leamy, C. Lee. Dynamic response of intrinsic continua for use in biological and molecular modeling: Explicit finite element formulation. Int. J. Numer. Meth. Engng 80(9) DOI 10.1002/nme.2650
- M. Xu, R. Gracie, T. Belytschko. A continuum-to-atomistic bridging domain method for composite lattices. Int. J. Numer. Meth. Engng DOI 10.1002/nme.2745
- J. Zou, W. Liang, S. Zhang. Coarse-grained molecular dynamics modeling of DNA-carbon nanotube complexes. Int. J. Numer. Meth. Engng. 83(8-9) (2010) DOI 10.1002/nme.2819
- X. Huang, J. Zou, S. Zhang. Bilinear responses and rippling morphologies of multiwalled carbon nanotubes under torsion. Appl. Phys. Lett. 93(3) DOI 10.1063/1.2965800
- J. Mackerle. Bibliography (1994–2004) of nanomaterials/nanostructures and their properties. Modelling Simul. Mater. Sci. Eng. 13(1) (2004) DOI 10.1088/0965-0393/13/1/081
- Q. Lu, R. Huang. Mechanical Behavior of Monolayer Graphene by Continuum and Atomistic Modeling. (2012) DOI 10.1201/b11384-17
- N. Silvestre, D. Camotim. Stability of Compressed Carbon Nanotubes Using Shell Models. DOI 10.1007/978-3-642-00980-8_48
- E. Marenić, A. Ibrahimbegovic, J. Sorić, P. Guidault. Homogenized Elastic Properties of Graphene for Small Deformations. Materials 6(9) (2013) DOI 10.3390/ma6093764
- I. Arias, M. Arroyo. Size-Dependent Nonlinear Elastic Scaling of Multiwalled Carbon Nanotubes. Phys. Rev. Lett. 100(8) (2008) DOI 10.1103/physrevlett.100.085503
- B. Annin, S. Korobeynikov, A. Babichev. Computer simulation of a twisted nanotube buckling. J. Appl. Ind. Math. 3(3) (2009) DOI 10.1134/s1990478909030028
- G. Szefer, D. Jasińska. Modeling of strains and stresses of material nanostructures. 57(1) DOI 10.2478/v10175-010-0103-6
- X. He, S. Kitipornchai, C. Wang, Y. Xiang, Q. Zhou. A Nonlinear Van Der Waals Force Model for Multiwalled Carbon Nanotubes Modeled by a Nested System of Cylindrical Shells. 77(6) (2010) DOI 10.1115/1.4001859
- S. Singh. Exploring the Effect of Dihedral Energy on the Nonlinear Mechanics of the Carbon Nanotubes Using a Multiscale Modeling. 141(4) (2019) DOI 10.1115/1.4043242
- K. Cai. Mechanical Properties of Single-Walled Carbon Nanotubes under Large Axial Deformation. AMR 97-101 (2010) DOI 10.4028/www.scientific.net/amr.97-101.3910
- Y. Sun, J. Wang, K. Liew. A Multiscale Modeling Approach for Carbon Nanotubes. AMR 97-101 (2010) DOI 10.4028/www.scientific.net/amr.97-101.4201
- S. Zhang, T. Zhu. Atomic geometry and energetics of carbon nanotube necking. Philosophical Magazine Letters 87(8) (2007) DOI 10.1080/09500830701370799
- Y. Zhuk, I. Guz. Influence of prestress on the velocities of plane waves propagating normally to the layers of nanocomposites. Int Appl Mech 42(7) DOI 10.1007/s10778-006-0141-9
- Y. Zhuk, I. Guz. Features of plane wave propagation along the layers of a prestrained nanocomposite. Int Appl Mech 43(4) DOI 10.1007/s10778-007-0032-8
- A. Mourad, I. Zalzali. Discrete and homogenized mechanical models for single walled carbon nanotubes. Mathematics and Mechanics of Solids 21(7) (2014) DOI 10.1177/1081286514537011
- X. Huang, H. Yuan, K. Hsia, S. Zhang. Coordinated buckling of thick multi-walled carbon nanotubes under uniaxial compression. Nano Res. 3(1) (2010) DOI 10.1007/s12274-010-1005-5
- M. Arroyo, T. Belytschko. Continuum Mechanics Modeling and Simulation of Carbon Nanotubes. Meccanica 40(4-6) DOI 10.1007/s11012-005-2133-y
- Q. LU, R. HUANG. NONLINEAR MECHANICS OF SINGLE-ATOMIC-LAYER GRAPHENE SHEETS. Int. J. Appl. Mechanics 01(03) (2012) DOI 10.1142/s1758825109000228
- Y. Yang, W. Liou. A Reduced-Order General Continuum Method for Dynamic Simulations of Carbon Nanotube. (2012) DOI 10.2514/6.2010-2898
- X. He, X. Huang. On the use of cellular automata algorithm for the atomic-based simulation of carbon nanotubes. Proc. R. Soc. A 465(2101) (2008) DOI 10.1098/rspa.2008.0233
- M. Shubov, M. Rojas-Arenaza. Four-branch vibrational spectrum of double-walled carbon nanotube model. Proc. R. Soc. A 467(2125) (2010) DOI 10.1098/rspa.2010.0100
- S. Hollerer. Buckling Analysis of Carbon Nanotubes. Proc. Appl. Math. Mech. 10(1) (2010) DOI 10.1002/pamm.201010076
- S. Hollerer. Buckling Analysis of Carbon Nanotubes - a molecular mechanics approach using the finite element framework. Proc. Appl. Math. Mech. 11(1) (2011) DOI 10.1002/pamm.201110102
- C. Findeisen, J. Wackerfuß. A modified approximation of the exponential Cauchy-Born rule for arbitrary shell-like nanostructures. Proc. Appl. Math. Mech. 14(1) (2014) DOI 10.1002/pamm.201410270
- J. Chen, C. Lee, H. Teng, H. Wang. Atomistic to Continuum Modeling of DNA Molecules. DOI 10.1007/978-3-642-19373-6_1
- M. Arroyo, T. Belytschko. Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule. Phys. Rev. B 69(11) (2004) DOI 10.1103/physrevb.69.115415
- X. Wang, H. Qi, Z. Sun, X. Wang, X. Song, J. Wang, X. Guo. Quasi-continuum study of the buckling behavior of single-walled carbon nanocones subjected to bending under thermal loading. J. Mater. Res. 32(12) (2017) DOI 10.1557/jmr.2017.185
- B. Annin, V. Alekhin, A. Babichev, S. Korobeynikov. Computer simulation of nanotube contact. Mech. Solids 45(3) (2010) DOI 10.3103/s0025654410030064
- S. Hollerer, C. Celigoj. Buckling analysis of carbon nanotubes by a mixed atomistic and continuum model. Comput Mech 51(5) (2012) DOI 10.1007/s00466-012-0757-z
- M. Rahimi, K. Zhang, M. Arroyo. Computing the volume enclosed by a periodic surface and its variation to model a follower pressure. Comput Mech 55(3) (2015) DOI 10.1007/s00466-014-1119-9
- A. Memarnahavandi, F. Larsson, K. Runesson. A goal-oriented adaptive procedure for the quasi-continuum method with cluster approximation. Comput Mech 55(4) (2015) DOI 10.1007/s00466-015-1127-4
- X. Huang, W. Liang, S. Zhang. Radial Corrugations of Multi-Walled Carbon Nanotubes Driven by Inter-Wall Nonbonding Interactions. Nanoscale Res Lett (2010) DOI 10.1007/s11671-010-9801-0
Share this document
claim authorship
Are you one of the authors of this document?