Referential Doyle-Ericksen formulae for the Eshelby tensor in non-linear elasticity

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 54, Issue 6, 2003, Pages 964-976

  Lu, Jia ^a   Papadopoulos, Panayiotis ^b  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Covariance; Doyle Ericksen formula; Elasticity; Eshelby tensor

Indexed keywords

EID: 0344063377     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-1117-9     Document Type: Article

References (24)

1. M. F. Beatty, Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues - with examples. ASME Appl. Mech. Rev. 40 (1987), 1699-1734.
2. P. Chadwick, Applications of an energy momentum tensor in non-linear elastostatics. J. Elast. 5 (1975), 249-258.
3. H. Cohen and M. Epstein, Remarks on uniformity in hyperelastic materials. Int. J. Sol. Struct. 20 (1984), 233-243.
4. T. C. Doyle and J. L. Ericksen, Non-linear elasticity. Adv. Appl. Mech. 4 (1956), 53-115.
5. M. Epstein and G. A. Maugin, The energy-momentum tensor and material uniformity in finite elasticity. Acta Mech. 83 (1990), 127-133.
6. J. D. Eshelby, The force on an elastic singularity. Phil. Trans. Royal Soc. London 244 (1951), 87-112.
7. J. D. Eshelby, The Continuum Theory of Lattice Defects, volume III of Solid State Physics, pages 79-144. Academic Press, 1956.
8. J. D. Eshelby, The elastic energy-momentum tensor. J. Elast. 5 (1975), 321-335.
9. T. Frankel, The Geometry of Physics: An Introduction. Cambridge University Press, New York, 1997.
10. A. Golebiewska-Herrmann, On conservation laws of continuum mechanics. Int. J. Sol. Struct. 17 (1981), 1-9.
11. A. E. Green and R. S. Rivlin, On Cauchy's equations of motion. J. Appl. Math. Phys. 15 (1964), 290-292.
12. J. K. Knowles and E. Sternberg, On a class of conservation laws in linearized and finite elasticity. Arch. Rat. Mech. Anal. 44 (1972), 187-211.
13. T. Lehmann, On large elastic-plastic deformations. In Proceedings of the International Symposium on Foundations of Plasticity, A. Sawczyk, editor, pages 571-585, Noordhoff, Leyden, 1973.
14. J. Lu and P. Papadopoulos, A covariant constitutive description of anisotropic non-linear elasticity. Z. Angew. Math. Phys. 51 (2000), 204-217.
15. J. E. Marsden and T. J. R. Hughes, Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs, 1983.
16. G. A. Maugin, Material Inhomogeneities in Elasticity. Chapman & Hall, London, 1993.
17. C. Miehe, A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric. Int. J. Sol. Struct. 35 (1998), 3859-3897.
18. W. Noll, Materially uniform simple bodies with inhomogeneities. Arch. Rat. Mech. Anal. 27 (1967), 1-32.
19. R. W. Ogden, Dual reciprocal states in finite elasticity. J. Elast. 5 (1975), 149-153.
20. C. Sansour, On the spatial description in elasticity and the Doyle-Ericksen formula. Gomp. Meth. Appl. Mech. Engr. 107 (1993), 239-249.
21. R.T. Shield. Inverse deformation results in finite elasticity. Z. Angew. Math. Phys. 18 (1967), 490-500.
22. J.C. Simo and J.E. Marsden. On the rotated stress tensor and the material version of the Doyle-Ericksen formula. Arch. Rat. Mech. Anal. 86 (1984), 213-231.
23. H. Stumpf and U. Hoppe, The application of tensor algebra on manifolds to nonlinear continuum mechanics - Invited survey article. Z. Angew. Mat. Mech. 77 (1997), 327-339.
24. C. C. Wang, On the geometric structure of simple bodies, a mathematical foundation for the theory of continuous distribution of displations. Arch. Rat. Mech. Anal. 27 (1967), 33-94.