Microscopic discussions of macroscopic balance equations for solids based on atomic configurations

Archive of Applied Mechanics

Volumn 70, Issue 8-9, 2000, Pages 533-549

  Nakane, M ^a   Shizawa, K ^a   Takahashi, K ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Atom; Balance equation; Mesodomain; Micromorphic material; Stress

Indexed keywords

EID: 0007669093     PISSN: 09391533     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004190000092     Document Type: Article

References (18)

1. Askar, A.: Lattice dynamical foundations of continuum theories. Singapore: World Scientific 1985
2. Bardenhagen, S.; Triantafyllidis, N.: Derivation of higher order gradient continuum theories in 2,3-D non-linear elasticity from periodic lattice models. J Mech Phys Solids 42 (1994) 111-139
3. Oda, M.; Nemat-Nasser, S.; Mehrabadi, M.M.: A statistical study of fabric in a random assembly of spherical granules. Int J Numer Anal Methods Geomech 6 (1982) 77-94
4. Eringen, A.C.; Suhubi, E.S.: Nonlinear theory of simple micro-elastic solids-I. Int J Eng Sci 2 (1964) 189-203
5. Eringen, A.C.: Mechanics of micromorphic materials. Proc. 11th Int Congr Appl Mech 131-138. Berlin, Heidelberg, New York, Springer 1966
6. Eringen, A.C.: Mechanics of micromorphic continua. In: Kröner, E. (ed.) Mechanics of Generalized Continua, 18-35. Berlin, Heidelberg, New York, Springer 1968
7. Eringen, A.C.: Balance laws of micromorphic mechanics. Int J Eng Sci 8 (1970) 819-828
8. Eringen, A.C.: Continuum Physics IV, 33-71. New York, San Francisco, London: Academic Press 1976
9. Green, A.E.; Rivlin, R.S.: Multipolar continuum mechanics. Arch Rational Mech Anal 17 (1964) 113-147
10. Irving, J.H.; Kirkwood, J.G.: The statistical mechanical theory of transport process. J Chem Phys 18 (1950) 817-829
11. Kröner, E. (ed.): Mechanics of generalized continua. Berlin, Heidelberg, New York, Springer 1968
12. Kunin, I.A.: Elastic media with microstructure-I (One-Dimensional Models). Berlin, Heidelberg, New York, Springer 1982
13. Mindlin, R.D.; Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch Rational Mech Anal 11 (1962) 415-448
14. Mindlin, R.D.: Micro-structure in linear elasticity. Arch Rational Mech Anal 16 (1964) 51-78
15. Toupin, R.A.: Elastic materials with couple-stresses. Arch Rational Mech Anal 11 (1962) 385-414
16. Weiner, J.H.: Statistical mechanics of elasticity. New York, Chichiester, Brisbane, Toronto, Singapore: John Wiley & Sons 1983
17. Yasui, Y.; Shizawa, K.; Takahashi, K.: Equivalence between higher-order stress power and heat flux in energy equation based on lattice dynamics. Trnas ASME J Eng Mat Tech 121 (1999) 240-246
18. Yasui, Y.; Hoshino, Y.; Shizawa, K.; Takahashi, K.: Geometric indexes of atomic configurations and microscopic expressions for elastic constants of solids (in Japanese). Trnas JSME 66-641 (2000) 7-13