Cauchy's theorem on manifolds

Journal of Elasticity

Volumn 56, Issue 2, 1999, Pages 129-144

  Segev, R ^a   Rodnay, G ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; MATHEMATICAL MODELS; STRESS ANALYSIS; VECTORS;

CAUCHY'S THEOREM; RIEMANNIAN MANIFOLDS;

ELASTICITY;

EID: 0033299015     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007651917362     Document Type: Article

References (18)

1. R. Abraham, J.E. Marsden and R. Ratiu, Manifolds, Tensor Analysis, and Applications. Springer, New York (1988).
2. G. Capriz, Continua with Microstructure. Springer, New York (1989).
3. G. Capriz and E. Virga, Interactions in general continua with microstructure. Arch. Rational Mech. Anal. 109 (1990) 323-342.
4. M. Epstein and R. Segev, Differentiable manifolds and the principle of virtual work in continuum mechanics. J. Math. Phys. 21 (1980) 1243-1245.
5. R. Fosdick and E. Virga, A variational proof of the stress theorem of Cauchy. Arch. Rational Mech. Anal. 105 (1989) 95-103.
6. M. Gurtin, An Introduction to Continuum Mechanics. Academic Press, Orlando (1981).
7. M.E. Gurtin and L.C. Martins, Cauchy's theorem in classical physics. Arch. Rational Mech. Anal. 60 (1976) 305-324.
8. M.E. Gurtin and W.O. Williams, An axiomatic foundation for continuum thermodynamics. Arch. Rational Mech. Anal. 26 (1967) 83-117.
9. J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs, NJ, 1983.
10. N.D. Mermin, The topological theory of defects in ordered media. Rev. Modern Phys. 51 (1979) 591-648.
11. W. Noll, The foundations of classical mechanics in light of recent advances in continuum mechanics. In: The Axiomatic Method, with Special Reference to Geometry and Physics, Symposium at Berkeley (1957). North-Holland, Amsterdam (1959) pp. 266-281.
12. W. Noll, Materially uniform simple bodies with inhomogeneities. Arch. Rational Mech. Anal. 27 (1967) 1-32.
13. W. Noll, A new mathematical theory of simple materials. Arch. Rational Mech. Anal. 48 (1972) 1-50.
14. J.A. Schouten and W.v.d. Kulk, Pfaff's Problem and its Generalizations. Chelsea, New York (1969).
15. R. Segev, Forces and the existence of stresses in invariant continuum mechanics. J. Math. Phys. 27 (1986) 163-170.
16. R. Segev, On the geometry of Cauchy's theory for balance of scalar valued properties. Arch. Rational Mech. Anal., to appear.
17. R. Segev and G. de Botton, On the consistency conditions for force systems. Internat. J. Nonlinear Mech. 26 (1991) 47-59.
18. R. Segev and G. Rodnay, Interactions on manifolds and the construction of material structure. Int. J. Solids Struct., to appear.