Nonlinear elasticity in nanostructured materials

Reports on Progress in Physics

Volumn 74, Issue 11, 2011, Pages

  Colombo, Luciano ^a   Giordano, Stefano ^b  

^a UNIVERSITY OF CAGLIARI   (Italy)

^b INSTITUT D ELECTRONIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80055095258     PISSN: 00344885     EISSN: None     Source Type: Journal    
DOI: 10.1088/0034-4885/74/11/116501     Document Type: Review

References (107)

1. Moriarty P 2001 Nanostructured materials Rep. Prog. Phys. 64 297-381 (Pubitemid 32248012)
2. Gleiter H 2000 Nanostructured materials: basic concepts and microstructure Acta Mater. 48 1-29 (Pubitemid 30558393)
3. Konstantatos G and Sargent E H 2010 Nanostructured materials for photon detection Nature Nanotechnol. 5 391-400
4. Aricò A S, Bruce P, Scrosati B, Tarascon J M and Van Schalkwijk W 2005 Nanostructured materials for advanced energy conversion and storage devices Nature Mater. 4 366-77 (Pubitemid 40557887)
5. Sahimi M 2003 Heterogeneous Materials I, Linear Transport and Optical Properties (New York: Springer)
6. Sahimi M 2003 Heterogeneous Materials II, Nonlinear and Breakdown Properties and Atomistic Modeling (New York: Springer)
7. Atkin R J and Fox N 1980 An Introduction to the Theory of Elasticity (New York: Dover)
8. Novozhilov V V 1999 Foundations of the Nonlinear Theory of Elasticity (New York: Dover)
9. Gurtin M E 1981 An Introduction to Continuum Mechanics (New York: Academic)
10. Gurtin M E 1983 Topics in Finite Elasticity (Philadelphia: SIAM)
11. Love A E H 2002 A Treatise on the Mathematical Theory of Elasticity (New York: Dover)
12. Graff K F 1991 Wave Motion in Elastic Solids (New York: Dover)
13. Broberg K B 1999 Cracks and Fracture (London: Academic)
14. Hirth J P and Lothe J 1991 Theory of Dislocations (Malabar, FL: Krieger)
15. Mura T 1987 Micromechanics of Defects in Solids (Dordrecht: Kluwer)
16. Asaro R J and Lubarda V A 2006 Mechanics of Solids and Materials (Cambridge: Cambridge University Press)
17. Landau L D and Lifschitz E M 1986 Theory of Elasticity (Oxford: Butterworth Heinemann)
18. Amenzade Y A 1979 Theory of Elasticity (Moscow: MIR)
19. Den Hartog J P 1987 Advanced Strength of Materials (New York: Dover)
20. Lubliner J 1998 Plasticity Theory (New York: Macmillan)
21. Frenkel D and Smit B 2002 Understanding Molecular Simulation (London: Academic)
22. Finnis M 2003 Interatomic Forces in Condensed Matter (Oxford: Oxford University Press)
23. Eshelby J D 1957 The determination of the elastic field of an ellipsoidal inclusion and related problems Proc. R. Soc. Lond. A 241 376-96
24. Eshelby J D 1959 The elastic field outside an ellipsoidal inclusion Proc. R. Soc. Lond. A 252 561-9
25. Eshelby J D 1961 Elastic inclusions and inhomogeneities Progress in Solid Mechanics vol 2 ed I N Sneddon and R Hill (Amsterdam: North-Holland) pp 89-140
26. Xiao S and Belytschko T 2004 A bridging domain method for coupling continua with molecular dynamics Comput. Methods Appl. Mech. Eng. 193 1645-69 (Pubitemid 38462116)
27. Li X and W. E 2005 Multiscale modeling of the dynamics of solids at finite temperature J. Mech. Phys. Solids 53 1650-85 (Pubitemid 40654370)
28. Ghoniem N M, Busso E P, Kioussis N and Huang H 2003 Multiscale modeling of nano and micro-mechanics: an overview Phil. Mag. 83 3475-528
29. Miller R E and Tadmor E B 2002 The quasicontinuum method: overview, applications and current directions J. Comput.-Aided Mater. Des. 9 203-39
30. Sharma P and Ganti S 2002 Interfacial elasticity corrections to the elastic state of quantum dots Phys. Status Solidi b 234 R10
31. Yang M, Sturm J C and Prevost J 1997 Calculation of band alignments and quantum confinement effects in zero- and one-dimensional pseudomorphic structures Phys. Rev. B 56 1973-80
32. Zhang X and Sharma P 2005 Size dependency of strain in arbitrary shaped, anisotropic embedded quantum dots due to nonlocal dispersive effects Phys. Rev. B 72 195345
33. Sharma P and Ganti S 2004 Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies J. Appl. Mech. 71 663-71 (Pubitemid 40122560)
34. Sharma P, Ganti S and Bhate N 2003 The effect of surfaces on the size-dependent elastic state of (nano) inhomogeneities Appl. Phys. Lett. 82 535-7
35. Suresh S 2001 Graded materials for resistance to contact deformation and damage Science 292 2447-51 (Pubitemid 32601650)
36. Lin D S, Wu J L, Pan S Y and Chiang T C 2003 Atomistics of Ge deposition on Si(1 0 0) by atomic layer epitaxy Phys. Rev. Lett. 90 046102
37. Hwang H Y 2006 Tuning interface states Science 313 1895-6 (Pubitemid 44497984)
38. Erdélyi Z, Sladecek M, Stadler L M, Zizak I, Langer G A, Kis-Varga M, Beke D L and Sepiol B 2004 Transient interface sharpening in miscible alloys Science 306 1913-5 (Pubitemid 39627850)
39. Bertoldi K, Bigoni D and Drugan W J 2007 Structural interfaces in linear elasticity: I. Nonlocality and gradient approximations J. Mech. Phys. Solids 55 1-34 (Pubitemid 44827118)
40. Bertoldi K, Bigoni D and Drugan W J 2007 Structural interfaces in linear elasticity: II. Effective properties and neutrality J. Mech. Phys. Solids 55 35-63 (Pubitemid 44827119)
41. Christensen R M 2005 Mechanics of Composite Materials (New York: Dover)
42. Ajayan P M, Schadler L S and Braun P V 2003 Nanocomposite Science and Technology (Weinheim: Wiley-VCH)
43. Giordano S 2003 Differential schemes for the elastic characterization of dispersions of randomly oriented ellipsoids Eur. J. Mech. A/Solids 22 885-902
44. Lee C, Wei X, Kysar J W and Hone J 2008 Measurement of the elastic properties and intrinsic strength of monolayer graphene Science 321 385-8 (Pubitemid 352029970)
45. Cocco G, Cadelano E and Colombo L 2010 Gap opening in graphene by shear strain Phys. Rev. B 81 241412(R)
46. Cadelano E, Giordano S and Colombo L 2010 Interplay between bending and stretching in carbon nanoribbons Phys. Rev. B 81 144105
47. Elias D C et al 2009 Control of graphene's properties by reversible hydrogenation: evidence for graphane Science 323 610-13
48. Marsden J E and Thomas J R 1983 Mathematical Foundations of Elasticity (New York: Dover)
49. Goldstein H 1959 Classical Mechanics (London: Addison-Wesley)
50. Polizzotto C 2001 Nonlocal elasticity and related variational principles Int. J. Solids Struct. 38 7359-80 (Pubitemid 32889985)
51. Triantafyllidis N and Bardenhagen S 1996 The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models J. Mech. Phys. Solids 44 1891-928 (Pubitemid 126374485)
52. Lam D C C, Yang F, Chong A C M, Wang J and Tong P 2003 Experiments and theory in strain gradient elasticity J. Mech. Phys. Solids 51 1477-508
53. Ciarletta M and Iesan D 1993 Non-Classical Elastic Solids (Harlow: Longman Scientific and Technical)
54. Giordano S, Palla P L and Colombo L 2008 Nonlinear elastic Landau coefficients in heterogeneous materials Eur. Phys. Lett. 83 66003
55. Giordano S, Palla P L and Colombo L 2009 Nonlinear elasticity of composite materials Eur. Phys. J. B 68 89-101
56. Nye J F 1985 Physical Properties of Crystals (Oxford: Oxford University Press)
57. Huntington H B 1958 The Elastic Constants of Crystals (New York: Academic)
58. Giordano S, Mattoni A and Colombo L 2011 Brittle fracture: from elasticity theory to atomistic simulations Rev. Comput. Chem. 27 1-83
59. Palla P L, Giordano S and Colombo L 2010 Lattice model describing scale effects in nonlinear elasticity of nanoinhomogeneities Phys. Rev. B 81 214113
60. Palla P L, Giordano S and Colombo L 2008 Interfacial elastic properties of a-Si and c-Si Phys. Rev. B 78 012105
61. Palla P L, Giordano S and Colombo L 2009 The role of interface elasticity in nanostructured silicon Phys. Rev. B 80 054105
62. Schnabel T, Vrabec J and Hasse H 2007 Unlike Lennard-Jones parameters for vapor-liquid equilibria J. Mol. Liq. 135 170-8 (Pubitemid 46671648)
63. Duan H L, Wang J, Huang Z P and Karihaloo B L 2005 Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress J. Mech. Phys. Solids 53 1574-96 (Pubitemid 40644971)
64. Duan H L, Wang J, Huang Z P and Luo Z Y 2005 Stress concentration tensors of inhomogeneities with interface effects Mech. Mater. 37 723-36 (Pubitemid 40357036)
65. Duan H L, Yi X, Huang Z P and Wang J 2007 A unified scheme for prediction of effective moduli of multiphase composites with interface effects: I. Theoretical framework Mech. Mater. 39 81-93 (Pubitemid 44374776)
66. Duan H L, Yi X, Huang Z P and Wang J 2007 A unified scheme for prediction of effective moduli of multiphase composites with interface effects: II. Application and scaling laws Mech. Mater. 39 94-103 (Pubitemid 44374777)
67. Duan H L, Wang J, Huang Z P and Karihaloo B L 2005 Eshelby formalism for nano-inhomogeneities Proc. R. Soc. Lond. A 461 3335-53
68. Duan H L, Wang J and Karihaloo B L 2009 Theory of elasticity at the nano-scale Adv. Appl. Mech. 42 1-68
69. Duan H L, Karihaloo B L, Wang J and Yi X 2006 Strain distributions in nano-onions with uniform and non-uniform compositions Nanotechnology 17 3380-7 (Pubitemid 43996722)
70. Duan H L, Karihaloo B L, Wang J and Yi X 2006 Compatible composition profiles and critical sizes of alloyed quantum dots Phys. Rev. B 74 195328
71. Gurtin M E and Murdoch A I 1975 A continuum theory of elastic material surfaces Arch. Ration. Mech. Anal. 57 291-323
72. Gurtin M E and Murdoch A I 1978 Surface stress in solids Int. J. Solids Struct. 14 431-440
73. Eringen A C 2002 Non-Local Continuum Field Theories (New York: Springer)
74. Wang J, Duan H L, Huang Z P and Karihaloo B L 2006 A scaling law for properties of nano-structured materials Proc. R. Soc. Lond. A 462 1355-63 (Pubitemid 44922093)
75. Giordano S 2005 Disordered lattice networks: general theory and simulations Int. J. Circ. Theor. Appl. 33 519-40 (Pubitemid 41807914)
76. Giordano S 2007 Two-dimensional disordered lattice networks with substrate Physica A 375 726-40 (Pubitemid 44894772)
77. Giordano S 2007 Relation between microscopic and macroscopic mechanical properties in random mixtures of elastic media J. Eng. Mater. Technol. 129 453-61 (Pubitemid 47240858)
78. Hughes D S and Kelly J L 1953 Second-order elastic deformation of solids Phys. Rev. 92 1145-9
79. Bateman T, Mason W P and McSkimin H J 1961 Third-order elastic moduli of germanium J. Appl. Phys. 32 928-36
80. Cain T and Ray J R 1988 Third-order elastic constants from molecular dynamics: theory and an example calculation Phys. Rev. B 38 7940-6
81. Zhao J, Winey J M and Gupta Y M 2007 First-principles calculations of second- and third-order elastic constants for single crystals of arbitrary symmetry Phys. Rev. B 75 094105
82. Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V and Geim A K 2005 Two-dimensional atomic crystals Proc. Natl. Acad. Sci. USA 102 10451-3 (Pubitemid 41061574)
83. Sahin H, Cahangirov S, Topsakal M,Bekaroglu E, Akturk E, Senger R T and Ciraci S 2009 Monolayer honeycomb structures of group-IV elements and III-V binary compounds: first-principles calculations Phys. Rev. B 80 155453
84. Zhi C, Bando Y, Tang C, Kuwahara H and Golberg D 2009 Large-scale fabrication of boron nitride nanosheets and their utilization in polymeric composites with improved thermal and mechanical properties Adv. Mater 21 2889-93
85. Lee C, Li Q, Kalb W, Liu X-L, Berger H, Carpick R W and Hone J 2010 Frictional characteristics of atomically thin sheets Science 328 76-80
86. March N H and Rubio A 2011 Structural and electronic properties of low-dimensional C-nanoassemblies and possible analogues for Si (and Ge) J. Nanomater. 2011 932350
87. Coleman J N et al 2011 Two-dimensional nanosheets produced by liquid exfoliation of layered materials Science 331 568-71
88. Dimiev A, Kosynkin D V, Sinitskii A, Slesarev A, Sun Z and Tour J M 2011 Layer-by-layer removal of graphene for device patterning Science 331 1168-72
89. Kotakoski J, Krasheninnikov A V, Kaiser U and Meyer J C 2011 From point defects in graphene to two-dimensional amorphous carbon Phys. Rev. Lett. 106 105505
90. Wu Y H, Yu T and Shen Z X 2010 Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications J. Appl. Phys. 108 071301
91. Gómez-Navarro C, Burghard M and Kern K 2008 Elastic properties of chemically derived single graphene sheets Nano Lett. 8 2045-9
92. Cadelano E, Palla P L, Giordano S and Colombo L 2009 Nonlinear elasticity of monolayer graphene Phys. Rev. Lett. 102 235502
93. Colombo L 2005 Tight-binding molecular dynamics: a primer Riv. Nuovo Cimento 28 1-59 (Pubitemid 44540115)
94. Xu C H, Wang C Z, Chan C T and Ho K M 1992 A transferable tight-binding potential for carbon J. Phys.: Condens. Matter 4 6047-54
95. Wei X, Fragneaud B, Marianetti C A and Kysar J W 2009 Nonlinear elastic behavior of graphene: ab initio calculations to continuum description Phys. Rev. B 80 205407
96. Michel K H and Verberck B 2008 Theory of the elastic constants of graphite and graphene Phys. Status. Solidi. b 245 2177-80
97. 2F, BN, and C nanoshell elasticity from ab initio computations Phys. Rev. B 64 235406
98. Liu F, Ming P and Li J 2007 Ab initio calculation of ideal strength and phonon instability of graphene under tension Phys. Rev. B 76 064120
99. Gui G, Li J and Zhong J 2008 Band structure engineering of graphene by strain: first-principles calculations Phys. Rev. B 78 075435
100. Senchez-Portal D, Artacho E, Soler J M, Rubio A and Ordejen P 1999 Ab initio structural, elastic and vibrational properties of carbon nanotubes Phys. Rev. B 59 12678
101. Zhou G, Duan W and Gu B 2001 First-principles study on morphology and mechanical properties of single-walled carbon nanotube Chem. Phys. Lett. 333 344-9 (Pubitemid 33642258)
102. Al-Jishi R and Dresselhaus G 1982 Lattice-dynamical model for graphite Phys. Rev. B 26 4514-22
103. Peng B, Locascio M, Zapol P, Li S, Mielke S L, Schatz G C and Espinosa H D 2008 Measurements of near-ultimate strength for multiwalled carbon nanotubes and irradiation-induced crosslinking improvements Nature Nanotechnol. 3 626-31
104. Sofo J O, Chaudhari A S and Barber G D 2007 Graphane: a two-dimensional hydrocarbon Phys. Rev. B 75 153401
105. Boukhvalov D W, Katsnelson M I and Lichtenstein A I 2008 Hydrogen on graphene: electronic structure, total energy, structural distortions and magnetism from first-principles calculations Phys. Rev. B 77 035427
106. Cadelano E, Palla P L, Giordano S and Colombo L 2010 Elastic properties of hydrogenated graphene Phys. Rev. B 82 235414
107. Giannozzi P et al 2009 Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials J. Phys.: Condens. Matter 21 395502