Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation

International Journal of Engineering Science

Volumn 41, Issue 1, 2003, Pages 61-83

  Chen, Youping ^a   Lee, James D ^a   Eskandarian, Azim ^a  

^a George Washington University   (United States)

Author keywords

Couple stress; Dynamics of atoms; Micromorphic; Micropolar; Microstructure; Nonlocal; Phonon dispersion relation

Indexed keywords

CRYSTAL MICROSTRUCTURE; ELASTIC WAVES; PHONONS; PIEZOELECTRICITY; POLARIZATION; STRESS ANALYSIS;

MICROMORPHIC THEORY;

CONTINUUM MECHANICS;

EID: 0037211732     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7225(02)00141-6     Document Type: Article

References (59)

1. Aifantis E.C. On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mater. Technol. 106:1984;326-330.
2. Aifantis E.C. Gradient deformation models at nano, micro, and macro scales. J. Eng. Materials Technol. 121:1999;189-202.
3. Askar A. Lattice Dynamics Foundations of Continuum Theories. 1985;World Scientific Publishing.
4. Baldereschi A., Resta R. Dielectric properties and lattice dynamics of semiconductors. Devreese, Van Doren, Van Camp AB Initio Calculation of Phonon Spectra. 1981;Plenum Press, New York.
5. Bertoni C.M., Bisi O., Calandra C., Nizzoli F. J. Phys. F. 5:1975;419.
6. Born M., von Karman Th. Phys. Zeit. 13:1912;297.
7. Born M., Hung K. Dynamical Theory of Crystal Lattice. 1954;Oxford University Press.
8. Brockhouse B.W., Iyengar P.K. Phys. Rev. 111:1958;747.
9. Brockhouse B.N. Neutron scattering by phonons. Stevenson R.W.H. Phonons in Perfect Lattice and in Lattice with Point Imperfections. 1966;110-152 Plenum Press, New York.
10. Bruesch P. Phonons: Theory and Experiments I - Lattice Dynamics and Models of Interatomic Forces. 1982;Springer-Verlag, New York.
11. Y. Chen, J.D. Lee, A. Eskandarian, Determination of material constants in micromorphic elasticity through phonon dispersion relation, Int. J. of Eng. Sci., submitted for publication.
12. Cochran W. Theory of phonon dispersion curves. Stevenson R.W.H. Phonons in Perfect Lattice and in Lattice with Point Imperfections. 1966;53-72 Plenum Press, New York.
13. Cochran W. The dynamics of atoms in crystals. 1973;Edward Arnold Ltd. London.
14. Cosserat E.F. Theorie des corps deformable. 1909;Hermann, Paris.
15. De Borst R., Pamin J., Sluys L.J. Computational Issues in Gradient Plasticity. Muhlhaus H.-B. Continuum Models for Materials with Microstructure. 1995;John Wiley.
16. Dick B.G., Overhauser A.W. Theory of the dielectric constant of alkali halide crystal. Phys. Rev. 112:1958;90-103.
17. Dolling G., Waugh J.L.T. Normal vibrations in Gallium Arsenide. Wallis R.F. Lattice Dynamics. 1965;19-32 Pergamon Press.
18. Dorner B., Grimm H., Rzany H. Phonon dispersion branches in. α -quartz J. Phys. C: Solid State Phys. 13:1980;6607-6612.
19. 10 -anthracene at 12 K J. Phys. C: Solid State Phys. 15:1982;2353-2365.
20. Dove M. Introduction to Lattice Dynamics. 1993;Cambridge University Press.
21. Eringen A.C., Suhubi E.S. Nonlinear theory of simple micro-elastic solids-I. Int. J. Eng. Sci. 2:1964;189-203.
22. Eringen A.C. On bridging the gap between macroscopic and microscopic physics. Recent Adv. Eng. Sci. 6:1973;1-18.
23. Eringen A.C. Continuum Physics. 1976;Academic Press, New York.
24. Eringen A.C. Vistas of nonlocal continuum physics. Int. J. Eng. Sci. 30(10):1992;1551-1565.
25. Eringen A.C. Microcontinuum Field Theories I: Foundations and Solids. 1999;Springer Verlag, New York.
26. Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W. Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42:1994;475-487.
27. Fleck N.A., Hutchinson J.W. Strain Gradient Plasticity. Adv. Appl. Mech. 13:1997;295-361.
28. Fujii Y., Lurie N.A., Pynn R., Shirane G. Inelastic neutron scattering from solid. Phys. Rev. B. 10:1974;3647-3659.
29. E.S.R. Gopal, Statistical Mechanics and Properties of Matter, Theory and Applications, Ellis Horwood, John Wiley, New York, 1974.
30. Giddy A.P., Dove M.T., Pawley G.S., Heine V. Acta Crystallogr. A. 49:1993;697.
31. Grimvall G. Lattice vibrations in simple metals. Devreeseet al. Ab Initio Calculation of Phonon Spectra. 1982;Plenum Press, New York.
32. Harrison W.A. Phonon in metals. Stevenson R.W.H. Phonons in Perfect Lattice and in Lattice with Point Imperfections. 1966;53-72 Plenum Press, New York.
33. Harrison W.A. Pseudopotentials in the Theory of Metals. 1966;W.A. Benjamin, New York.
34. Kittel C. Introduction to Solid State Physics. 1967;John Wiley.
35. Kogure Y., Kouchi O., Doyama M. Elastic and lattice dynamics properties of Metals studied by. n -body potential Mater. Res. Soc. Symp. Proc. 367:1995;385-390.
36. Kress W. Phys. Status Solid B. 49:1972;239.
37. Kramer G.J., Farragher N.P., van Beest B.W., van Santen R.A. Interatomic force filed for silicates, aluminophosphates, and zeolites: derivation based on ab initio calculations. Phys. Rev. B. 43:1991;5068-5079.
38. Lasaga A.C., Gibbs G.V. Application of quantum mechanical potential surfaces to mineral physics calculations. Phys. Chem. Min. 16:1988;29-41.
39. Lehman G.W., Wolfram T., Dewames R.E. Study in lattice dynamics of metals using the A-S model. Wallis R.F. Lattice Dynamics. 1965;101-107 Pergamon Press.
40. Maliszewski E., Rosolowski J., Sledziewski D., Czachor A. Lattice dynamics of zinc. Wallis R.F. Lattice Dynamics. 1965;33-37 Pergamon Press.
41. Mindlin R.D. Microstructure in linear elasticity. Arch. Rat. Mech. Anal. 16:1964;51-78.
42. Mindlin R.D., Tiersten H.F. Effects of couple stresses in linear elasticity. Arch. Rat. Mech. Anal. 11:1962;415-448.
43. Nata R., Catlow C.R.A., Dovesi R., Pisani C. An ab initio Hartree-Fock study of. α -quartz and stishovite Phys. Chem. Min. 17:1990;353-362.
44. Parlinski K., Lazewski J., Kawazoe Y. Ab inito studies in MgO by the direct method including LO mode. J. Phys. Chem. Solid. 61:2000;87-90.
45. Peckham G. Phonon dispersion relations in magnesium oxide. Wallis R.F. Lattice Dynamics. 1965;49-52 Pergamon Press.
46. Pope N.K. The force constants of Germanium. Wallis R.F. Lattice Dynamics. 1965;147-157 Pergamon Press.
47. Rustagi K.C., Weber W. Solid State Commun. 18:1976;673.
48. Shaw R.W., Pynn R. J. Phys. C. 2:1969;2071.
49. 2. J. Chem. Soc. Chmm. 1984;1271-1273.
50. Schroder U. Solid State Commun. 4:1966;347.
51. Schutt O., Pavone P., Windl W., Karch K., Srtrauch D. Ab inito lattice dynamics and charge fluctuations in alkaline-earth oxides. Phys. Rev. B. 50:1995;3746-3753.
52. Sollich P., Heine V., Dove M.T. The Ginzburg interval in soft-mode phase transitions: consequence of rigid unit mode picture. J. Phys. Condens. Matter. 6:1994;3171-3196.
53. Taylor R., MacDonald A.H. J. Phys. F. 10:1980;2387.
54. Toupin R.A. Elastic materials with couple-stresses. Arch. Rat. Mech. Anal. 11:1962;385-414.
55. Waugh J.L.T., Dolling G. Phys. Rev. 132:1963;2410.
56. Weber W. Phys. Rev. Lett. 33:1974;371.
57. Van Camp P.E., Van Doren V.E., Devreese J.T. Ab-initio calculation of the lattice dynamics of silicon: dielectric screening theory. Devreese J.T., Van Doren V.E., Van Camp P.E. Ab Initio Calculation of Phonon Spectra. 1983;Plenum Press.
58. Venkadaraman G., Sahni C. Rev. Mod. Phys. 42:1970;409.
59. S. Yip, 1985. Round-table: perspective in material science, in: G. Ciccotti, W.G. Hoover (Eds.), Proceedings of the International School of Physics, Molecular Dynamics Simulation of Statistical Mechanical Systems, North-Holland, Amsterdam, p. 565.