Prog. Theor. Phys. Vol. 68 No. 2 (1982) pp. 349-362

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Coninuum Approximation of the Self-Consistent Einstein Model under an External Force

— Basic Equations for Thermo-Elasticity and Lattice Vibration —

Masaru Sugiyama

Department of Engineering Sciences, Nagoya Institute of Technology, Nagoya 466

(Received October 19, 1981)

Abstract:

The following are studied in this paper: (1) The continuum approximation of the self-consistent Einstein model subjected to an external force is proposed with the aid of the finite deformation theory. (2) The field equations and the boundary condition which describe consistently both deformations and vibrations of lattices are derived by using the coutinuum approximation. (3) The linearized basic equations are explicitly derived. These equations can be regarded as an extension of the phenomenological elastic theory and of the lattice vibration theory with no deformation. A simple illustrative example is also investigated in order to show characteristic features of the basic equations.

URL : http://ptp.ipap.jp/link?PTP/68/349/
DOI : 10.1143/PTP.68.349

References:

T. Matsubara and K. Kamiya, Prog. Theor. Phys. 58 (1977), 767[PTP].
T. Hama and T. Matsubara, Prog. Theor. Phys. 59 (1978), 1407[PTP].
T. Matsubara, J. Phys. Soc. Jpn. 40 (1976), 603[JPSJ].
See for example,
Dynamic Properties of Solids, edited by G. K. Horton and A. A. Maradudin (North-Holland, Amsterdam, American Elsevier, New York, 1974), vol. 1.
A. Nakanishi and T. Matsubara, J. Phys. Soc. Jpn. 39 (1975), 1415[JPSJ].
T. Matsubara, Y. Iwase and A. Momokita, Prog. Theor. Phys. 58 (1977), 1102[PTP].
E. Matsushita and T. Matsubara, Prog. Theor. Phys. 59 (1978), 15[PTP].
M. Sugiyama and H. Okamoto, Prog. Theor. Phys. 64 (1980), 1945[PTP].
For general refereces, see, for example,
C. Truesdell and R. Toupin, The Classical Field Theories, Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, Göttingen, Heidelberg, 1960), vol. III/ 1.
C. Truesdell and W. Noll, The Nonlinear Field Theories of Mechanics, Encyclopedia of Physics, edited by S. Flügge (Springer-Verleg, Berlin, Heidelberg, New York, 1965), vol. III/ 3.
R. A. Toupin, J. Rat. Mech. Anal. 5 (1956), 849.
C.-C. Wang, Arch. Rat. Mech. Anal. 36 (1970), 166; ibid. 36 (1970), 198.
See, for example,
R. R. Birss, Rep. Prog. Phys. 26 (1963), 307[CrossRef].

Citing Article(s) :

Journal of the Physical Society of Japan 61 (1992) pp. 2260-2268 :
A Unified Approach to Nonequilibrium Phenomena in a Crystalline Lattice. I. Formulation

Masaru Sugiyama
Journal of the Physical Society of Japan 72 (2003) pp. 1989-1994 :
Statistical-Thermodynamic Study of Nonequilibrium Phenomena in Three-Dimensional Anharmonic Crystal Lattices: II. Continuum Approximation of the Basic Equations

Masaru Sugiyama