Lattice with vacancies: elastic fields and effective properties in frameworks of discrete and continuum models

References

• J.D. Eshelby , Distortion of a crystal by point imperfections , J. Appl. Phys. 25 (1954), pp. 255–261.
   Web of Science ®Google Scholar
• J.D. Eshelby , The continuum theory of lattice defects , Solid State Phys. 3 (1956), pp. 79–144.
   Web of Science ®Google Scholar
• J.D. Eshelby , The determination of the elastic field of an ellipsoidal inclusion, and related problems , Proc. R. Soc. A 241 (1957), pp. 376–396.
   Web of Science ®Google Scholar
• R. Bonnet and S. Neily , An anisotropic thin crystal deformed by an inclined dislocation , Philos. Mag. 95 (2015), pp. 2764–2776.
   Web of Science ®Google Scholar
• R.V. Goldstein and N.F. Morozov , Mechanics of deformation and fracture of nanomaterials and nanotechnology , Phys. Mesomech. 10 (2007), pp. 235–246.
   Web of Science ®Google Scholar
• L. Pizzagalli , S. Brochard , J. Godet , and C. Gérard , Mechanical Properties of Nanostructure , in Encyclopedia of Nanotechnology , B. Bhushan , ed., Springer, Dordrecht, 2015, pp. 1–11.
   Google Scholar
• A.M. Krivtsov and N.F. Morozov , On mechanical characteristics of nanocrystals , Phys. Solid State 44 (2002), pp. 2260–2265.
   Web of Science ®Google Scholar
• V.A. Eremeyev , On effective properties of materials at the nano-and microscales considering surface effects , Acta Mech. 227 (2016), pp. 29–42.
   Web of Science ®Google Scholar
• H. Kanzaki , Point defects in face-centred cubic lattice --- I distortion around defects , J. Phys. Chem. Solids 2 (1957), pp. 24–36.
   Web of Science ®Google Scholar
• J.W. Flocken , Modified lattice-statics approach to point-defect calculations , Phys. Rev. B 6 (1972), pp. 1176–1181.
   Web of Science ®Google Scholar
• J.R. Hardy , A theoretical study of point defects in the rocksalt structure substitutional K+ in NaCl , J. Phys. Chem. Solids 15 (1960), pp. 39–49.
   Web of Science ®Google Scholar
• J.R. Hardy and R. Bullough , Point defect interactions in harmonic cubic lattices , Philos. Mag. 15 (1967), pp. 237–246.
   Web of Science ®Google Scholar
• J.W. Flocken and J.R. Hardy , Application of the method of lattice statics to interstitial Cu atoms in Cu , Phys. Rev. 175 (1968), pp. 919–927.
   Web of Science ®Google Scholar
• J.W. Flocken and J.R. Hardy , Application of the method of lattice statics to vacancies in Na, K, Rb, and Cs , Phys. Rev. 177 (1969), pp. 1054–1062.
   Web of Science ®Google Scholar
• J.W. Flocken and J.R. Hardy , Asymptotic lattice displacements about point defects in cubic metals , Phys. Rev. B 1 (1970), pp. 2447–2456.
   Web of Science ®Google Scholar
• K.M. Miller and P.T. Heald , The lattice distortion around a vacancy in FCC metals , Phys. Status Solidi B 67 (1975), pp. 569–576.
   Google Scholar
• S.K. Rattan , P. Singh , S. Prakash , and J. Singh , Strain field due to point defects in metals , Phys. Rev. B 47 (1993), pp. 599–607.
   PubMed Web of Science ®Google Scholar
• A.J.E. Foreman , Elastic relaxation at a vacancy in solid argon , Philos. Mag. 8 (1963), pp. 1211–1217.
   Web of Science ®Google Scholar
• A. Yavari , M. Ortiz , and K. Bhattacharya , A theory of anharmonic lattice statics for analysis of defective crystals , J. Elast. 86 (2007), pp. 41–83.
   Web of Science ®Google Scholar
• S. Kavianpour and A. Yavari , Anharmonic analysis of defective crystals with many-body interactions using symmetry reduction , Comput. Mater. Sci. 44 (2009), pp. 1296–1306.
   Web of Science ®Google Scholar
• V.K. Tewary , Green-function method for lattice statics , Adv. Phys. 22 (1973), pp. 757–810.
   Web of Science ®Google Scholar
• R. Thomson and S.J. Zhou , Interfacial crack in a two-dimensional hexagonal lattice , Phys. Rev. B 49 (1994), pp. 44–54.
   PubMed Web of Science ®Google Scholar
• X. Liu and N. Liang , Effective elastic moduli of triangular lattice material with defects , J. Mech. Phys. Solids 60 (2012), pp. 1722–1739.
   Web of Science ®Google Scholar
• B. Yang and V.K. Tewary , Green’s function-based multiscale modeling of defects in a semi-infinite silicon substrate , Int. J. Solids Struct. 42 (2005), pp. 4722–4737.
   Web of Science ®Google Scholar
• B. Yang and V.K. Tewary , Multiscale Green’s function for the deflection of graphene lattice , Phys. Rev. B 77 (2008), pp. 245442-1–245442-5.
   Web of Science ®Google Scholar
• R. Migoni , C.N. Tome , N. Smetniansky-De Grande , and E.J. Savino , Lattice static Green function for an hcp lattice , Phys. Rev. B 22 (1980), pp. 2658–2664.
   Web of Science ®Google Scholar
• W. Lechner , E. Scholl-Paschinger , and C. Dellago , Displacement fields of point defects in two-dimensional colloidal crystals , J. Phys.-Condens. Matter 20 (2008), p. 404202 (7pp).
   Web of Science ®Google Scholar
• W. Lechner and C. Dellago , Point defects in two-dimensional colloidal crystals: simulation vs. elasticity theory , Soft Matter 5 (2009), pp. 646–659.
   Web of Science ®Google Scholar
• H. Cong , B. Yu , S. Wang , L. Qi , J. Wang , and Y. Ma , Preparation of iridescent colloidal crystal coatings with variable structural colors , Opt. Express 21 (2013), pp. 17831–17838.
   PubMed Web of Science ®Google Scholar
• B. van der Meer , W. Qi , J. Sprakel , L. Filion , and M. Dijkstra , Dynamical heterogeneities and defects in two-dimensional soft colloidal crystals , Soft Matter 11 (2015), pp. 9385–9392.
   PubMed Web of Science ®Google Scholar
• M. Shariyat , Z. Sarvi , and M. Asgari , A unit-cell-based three-dimensional molecular mechanics analysis for buckling load, effective elasticity and Poisson’s ratio determination of the nanosheets , Mol. Simulat. 42 (2016), pp. 353–369.
   Web of Science ®Google Scholar
• N.I. Muskhelishvili , Some Basic Problems of the Mathematical Theory of Elasticity , Groningen, Noordhoff, 1953.
   Google Scholar
• L. Filshtinskii and E. Grigoliuk , Perforated Plates and Shells , Nauka, Moscow, 1970. Russian.
   Google Scholar
• A.M. Linkov , Boundary Integral Equations in Elasticity Theory , Kluwer Academic Publishers, Dordrecht, 2002.
   Google Scholar
• B.L. Karihaloo and J. Wang , On the solution of doubly periodic array of cracks , Mech. Mater. 26 (1997), pp. 209–212.
   Web of Science ®Google Scholar
• A.A. Kelly and K.M. Knowles , Crystallography and Crystal Defects , 2nd ed., John Wiley and Sons Ltd, Chichester, 2012.
   Google Scholar
• R. Thomson , S.J. Zhou , A.E. Carlsson , and V.K. Tewary , Lattice imperfections studied by use of lattice Green’s functions , Phys. Rev. B 46 (1992), pp. 10613–10622.
   PubMed Web of Science ®Google Scholar
• R.P. Agarwal , Difference Equations and Inequalities , Marcel Dekker, New York, 2000.
   Google Scholar
• A. Metsue , A. Oudriss , and X. Feaugas , Displacement field induced by a vacancy in nickel and some implications for the solubility of hydrogen , Philos. Mag. 94 (2014), pp. 3978–3991.
   Web of Science ®Google Scholar
• W. Lechner , D. Polster , G. Maret , P. Keim , and C. Dellago , Self-organized defect strings in two-dimensional crystals , Phys. Rev. E 88 (2013), pp. 060402-1–060402-4.
   Web of Science ®Google Scholar
• L. Verlet , Computer "experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules , Phys. Rev. 159 (1967), pp. 98–103.
   Web of Science ®Google Scholar
• S.K. Kanaun and V. Levin , Self-consistent Methods for Composites , Static Problems Vol. 1, Netherlands, Springer, 2007.
   Google Scholar
• M. Kachanov , I. Tsukrov , and B. Shafiro , Effective moduli of solids with cavities of various shapes , Appl. Mech. Rev. 47 (1994), pp. S151–S174.
   Google Scholar
• T.C. Ekneligoda and R.W. Zimmerman , Compressibility of two-dimensional pores having n-fold axes of symmetry , Proc. R. Soc. A 462 (2006), pp. 1933–1947.
   Google Scholar
• T.C. Ekneligoda and R.W. Zimmerman , Shear compliance of two-dimensional pores possessing N-fold axis of rotational symmetry , Proc. R. Soc. A 464 (2008), pp. 759–775.
   Google Scholar
• A.M. Krivtsov and M. Wiercigroch , Molecular dynamics simulation of mechanical properties for polycrystal materials , Mater. Phys. Mech. 3 (2001), pp. 45–51.
   Google Scholar
• V.A. Kuzkin , A.M. Krivtsov , R.E. Jones , and J.A. Zimmerman , Material frame representation of equivalent stress tensor for discrete solids , Phys. Mesomech. 18 (2015), pp. 13–23.
   Web of Science ®Google Scholar
• V.A. Kuzkin , Interatomic force in systems with multibody interactions , Phys. Rev. E 82 (2010), pp. 016704-1–016704-6.
   Web of Science ®Google Scholar
• T.C. Ekneligoda and R.W. Zimmerman , Boundary perturbation solution for nearly circular holes and rigid inclusions in an infinite elastic medium , J. Appl. Mech. 75 (2008), p. 011015 (8pp).
   Web of Science ®Google Scholar