On the microscopic interpretation of stress and couple stress

Journal of Elasticity

Volumn 71, Issue 1-3, 2003, Pages 105-131

  Murdoch, A Ian ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Couple stress; Microscopic interpretation; Stress; Weighting function

Indexed keywords

CONTINUUM MECHANICS; MICROSCOPIC EXAMINATION; STATISTICAL MECHANICS; STRESS ANALYSIS;

COUPLE STRESS; MICROSCOPIC INTERPRETATION; WEIGHTING FUNCTION;

ELASTICITY;

EID: 0345761824     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000005552.04968.08     Document Type: Article

References (22)

1. J.H. Irving and J.G. Kirkwood, The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18 (1950) 817-829.
2. W. Noll, Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik. J. Rational Mech. Anal. 4 (1955) 627-646.
3. M. Pitteri, Continuum equations of balance in classical statistical mechanics. Arch. Rational Mech. Anal. 94 (1986) 291-305.
4. M. Pitteri, On a statistical-kinetic model for generalized continua. Arch. Rational Mech. Anal. 111 (1990) 99-120.
5. A.I. Murdoch and D. Bedeaux, Continuum equations of balance via weighted averages of microscopic quantities. Proc. Roy. Soc. London A 445 (1994) 157-179.
6. D.L. Goodstein, States of Matter. Dover, New York (1985).
7. A.I. Murdoch, A corpuscular approach to continuum mechanics: basic considerations. Arch. Rational Mech. Anal. 88 (1985) 291-321.
8. A.I. Murdoch, Elements of the continuum modelling of material behaviour and its relation to the fundamentally-discrete nature of matter. In: Lecture Notes, Centre of Excellence for Advanced Materials and Structures, IPPT, Polish Academy of Sciences, Warsaw (2002).
9. S.G. Brush, The Kind of Motion We Call Heat. North-Holland, Amsterdam/New York (1986).
10. H.C. Ohanian, Physics, Vol. 1. Norton, New York/London (1985).
11. C. Truesdell and R.A. Toupin, The Classical Field Theories, S. Flügge (ed.), Handbuch der Physik. Springer, Berlin (1960).
12. R.M. Bowen, Theory of Mixtures, A.C. Eringen (ed.), Continuum Physics, Vol. III. Academic Press, New York, (1976).
13. M.E. Gurtin, M.L. Oliver, and W.O. Williams, On the balance of forces for mixtures. Quart Appl. Math. 30 (1973) 527-530.
14. A. Morro, and A.I. Murdoch, Stress, body force, and momentum balance in mixture theory. Mechanica 21 (1986) 184-190.
15. A.I. Murdoch and A. Morro, On the continuum theory of mixtures: Motivation from discrete considerations. Internat. J. Engrg. Sci. 25 (1987) 9-25.
16. C. Truesdell and W. Noll, The Non-linear Field Theories of Mechanics, Handbuch der Physik, S. Flügge (ed.), Vol. III/3. Springer, Berlin (1965).
17. C. Truesdell, Six Lectures on Modern Natural Philosophy. Springer, Berlin 1966.
18. C. Truesdell, A First Course in Rational Continuum Mechanics, Vol. 1. Academic Press, New York (1977).
19. A.C. Eringen, Mechanics of micromorphic continua. In: E. Kröner (ed.), Mechanics of Generalized Continua. Springer, Berlin (1968).
20. A.I. Murdoch, On time-dependent material systems. Internat. J. Engrg. Sci. 38 (2000) 429-452.
21. A.I. Murdoch and S.M. Hassanizadeh, Macroscale balance relations for bulk, interfacial and common line systems in multiphase flows through porous media on the basis of molecular considerations. Internat. J. Multiphase Flow 28 (2002) 1091-1123
22. A.I. Murdoch, On the relationship between balance relations for generalised continua and molecular behaviour. Internat. J. Engrg. Sci. 25 (1987) 883-914.