Evaluating bounds and estimators for constants of random polycrystals composed of orthotropic elastic materials
Tài liệu tham khảo
Bass, J. D. (1995). Elasticity of Minerals, Glasses, and Melts. In: A. J. Ahrens(Ed.), Mineral Physics and Crystallography, American Geophysical Union, Washington, D.C. (pp. 45–63).
Berryman, 1980, Long-wavelength propagation in composite elastic media, Journal of the Acoustical Society of America, 68, 1820, 10.1121/1.385172
Berryman, 2005, Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries, Journal of the Mechanics and Physics of Solids, 53, 2141, 10.1016/j.jmps.2005.05.004
Berryman, 2011, Bounds and self-consistent estimates for elastic constants of polycrystals composed of orthorhombics or crystals with higher symmetries, Physical Review E, 83, 046130, 10.1103/PhysRevE.83.046130
Carmichael, 1989
Eshelby, 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London A, 241, 376, 10.1098/rspa.1957.0133
Gubernatis, 1975, Macroscopic engineering properties of polycrystalline materials: Elastic properties, Journal of Applied Physics, 46, 1875, 10.1063/1.321884
Hashin, 1962, A variational approach to the theory of elastic behaviour of polycrystals, Journal of the Mechanics and Physics of Solids, 10, 343, 10.1016/0022-5096(62)90005-4
Hill, R., (1952). The elastic behaviour of crystalline aggregate. In: Proceedings of the Physical Society of London A65 (pp. 349–354).
Hill, 1965, Theory of mechanical properties of fiber-strengthened materials. III. Self-consistent method, Journal of the Mechanics and Physics of Solids, 13, 189, 10.1016/0022-5096(65)90008-6
Kanaun, 2008
Kanaun, 2008
Kröner, 1977, Bounds for effective elastic moduli of disordered materials, Journal of the Mechanics and Physics of Solids, 25, 137, 10.1016/0022-5096(77)90009-6
Middya, 1986, Self-consistent T-matrix solution for the effective elastic properties of noncubic polycrystals, Journal of Applied Physics, 59, 2368, 10.1063/1.336336
Musgrave, M. J. P. (2003). Crystal acoustics: Introduction to the study of elastic waves and vibrations in crystals, Acoustical Society of America, New York, (pp. 278–281).
Olson, 1992, Effective dielectric and elastic constants of piezoelectric polycrystals, Journal of Applied Physics, 71, 4455, 10.1063/1.350788
Peselnick, 1965, Variational method of determining effective moduli of polycrystals: (A) Hexagonal symmetry and (B) trigonal symmetry, Journal of Applied Physics, 36, 2879, 10.1063/1.1714598
Pham, D. C. (2006). New estimates for macroscopic elastic moduli of random polycrystalline aggregates. Philosophical Magazine 86, (pp. 205–226).
Pham, D. C. (2011). On the scatter ranges for the elastic moduli of random aggregates of general anisotropic crystals. Philosophical Magazine 91, (pp. 609–627).
Ranganathan, 2008, Universal elastic anisotropy index, Physical Review Letters, 101, 055504, 10.1103/PhysRevLett.101.055504
Reuss, 1929, Berechung der Fliessgrenze von Mischkristallen, Zeitschrift fur Angewandte Mathematik und Mechanik, 9, 55
Simmons, 1971
Soven, 1967, Coherent-potential model of substitutional alloys, Physical Review, 156, 809, 10.1103/PhysRev.156.809
Taylor, 1967, Vibrational properties of imperfect crystals with large defect concentrations, Physical Review, 156, 1017, 10.1103/PhysRev.156.1017
Tsvankin, 2005
Voigt, 1928
Watt, 1979, Hashin–Shtrikman bounds on the effective elastic moduli of polycrystals with orthorhombic symmetry, Journal of Applied Physics, 50, 6290, 10.1063/1.325768
Watt, 1980, Clarification of the Hashin–Shtrikman bounds moduli of polycrystals with hexagonal, trigonal, and tetragonal symmetries, Journal of Applied Physics, 51, 1525, 10.1063/1.327804
Willis, 1981, Variational and related methods for the overall properties of composites, 1, 10.1016/S0065-2156(08)70330-2