On dual configurational forces

Journal of Elasticity

Volumn 84, Issue 1, 2006, Pages 13-31

  Li, Shaofan ^a   Gupta, Anurag ^a  

^a Berkeley   (United States)

Author keywords

Complementary variational principles; Configuration force; Conservation laws; Energy momentum tensor

Indexed keywords

CONTINUUM MECHANICS; DEFECTS; ELASTICITY; TENSORS; THERMODYNAMICS;

COMPLEMENTARY VARIATIONAL PRINCIPLES; CONFIGURATION FORCE; CONSERVATION LAWS; ENERGY-MOMENTUM TENSORS;

FORCE CONTROL;

EID: 33745728257     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-005-9047-8     Document Type: Article

References (34)

1. H.D. Bui, Dual path independent integrals in the boundary-value problems of cracks. Eng. Fract. Mech. 6 (1974) 287-296.
2. B.D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13 (1963) 167-178.
3. J.D. Eshelby, The force on an elastic singularity. Philos. Trans. R. Soc. 244(877) (1951) 87-111.
4. J.D. Eshelby, The continuum theory of lattice defects. In: F. Seitz and D. Turnbull (eds.), Solid State Physics, Vol. 3. Academic, New York (1956) pp. 79-144.
5. D.Y. Gao, Duality Principles in Nonconvex Systems. Kluwer (2000).
6. D.Y. Gao, General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics. Meccanica 34 (1999) 169-198.
7. D.Y. Gao, Perfect duality theory and complete solutions to a class of global optimization. Optimization 52 (2003) 467-493.
8. Z.H. Guo, The unified theory of variational principles in nonlinear elasticity. Arch. Mech. 32 (1980) 577-596.
9. M.E. Gurtin, The nature of conflgurational forces. Arch. Ration. Mech. Anal. 131 (1995) 67-100.
10. M.E. Gurtin, Configurational Forces as Basic Concepts of Continuum Mechanics. Springer, Berlin Heidelberg New York (1999).
11. R. Kienzler and G. Herrmann, Mechanics in Material Space. Springer, Berlin Heidelberg New York (2001).
12. J.K. Knowles and E. Sternberg, On a class of conservation laws in linear and finite elastostatics. Arch. Ration. Mech. Anal. 44 (1972) 187-211.
13. M. Levinson, Complementary energy theorem in finite elasticity. J. Appl. Mech. 32(4) (1965) 826-828.
14. S. Li, On dual conservation laws in linear elasticity: Stress function formalism. Nonlinear Dyn. 36 (2004) 77-96.
15. S. Li, A. Gupta and X. Markenskoff, Conservation laws of linear elasticity in stress formulations. Proc. R. Soc. Lond, A 461 (2005) 99-116.
16. X. Li, Dual conservation laws in elastostatics. Eng. Fract. Mech. 29(2) (1988) 233-241.
17. J.D. Logan, Invariant Variational Principles, Vol. 138, Mathematics in Science and Engineering. Academic, New York (1977).
18. G.A. Maugin, Material Inhomogeneties in Elasticity. Springer, Chapman and Hall, London (1993).
19. G.A. Maugin, Material forces: Concepts and applications. Appl. Mech. Rev. 48(5) (1995) 247-285.
20. B. Moran and C.F. Shih, Crack tip and associated domain integrals from momentum and engergy balance. Eng. Fract. Mech. 27 (1987) 615-642.
21. B. Moran and C.F. Shih, A general treatment of crack tip contour integrals. Int. J. Fract. 35 (1987) 295-310.
22. E. Noether, Invariante Variationsprobleme. Göttinger Nachrichten, (Mathematisch-physikalische Klasse) 2 (1918) 235-257.
23. (Transl. Transport Theory and Statistical Physics 1 (1971) 186-207.)
24. R.W. Ogden, A note on variational theorems in non-linear elastostatics. Math. Proc. Camb. Philos. Soc. 77 (1975) 609-615.
25. R.W. Ogden, Non-linear Elastic Deformations. Dover (1997).
26. P.J. Olver, Conservation laws in elasticity. I. General results. Arch. Ration. Mech. Anal. 85 (1984) 119-129.
27. P.J. Olver, Conservation laws in elasticity. II. Linear homogeneous elastostatics. Arch. Ration. Mech. Anal. 85 (1984) 131-160.
28. P.J. Olver, Applications of Lie Group to Differential Equations. Springer, Berlin Heidelberg New York (1986).
29. E. Reissner, On a variational theorem for finite elastic deformations. J. Math. Phys. 32(2-3) (1953) 129-135.
30. J.R. Rice, A path-independent integral and the approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech. 35 (1968) 379-386.
31. S.X. Sun, Dual conservation laws in elastostatics. Int. J. Eng. Sci. 23 (1985) 1179-1186.
32. C. Trimarco and G.A. Maugin, Bui's path-independent integral in finite elasticity. Meccanica 30 (1995) 139-145.
33. B.F. Veubeke, A new variational principle for finite elastic displacements. Int. J. Eng. Sci. 10 (1972) 745-763.
34. K. Washizu, Variational Methods in Elasticity and Plasticity, Vol. II. Oxford University Press (1975).