Conservation laws in non-homogeneous electro-magneto-elastic materials

European Journal of Mechanics, A/Solids

Volumn 22, Issue 2, 2003, Pages 217-230

  Weichen, Shi ^a   Kuang, Zhen Bang ^b  

^a SHANGHAI MARITIME UNIVERSITY   (China)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Conservation law; Electromagnetic enthalpy; Infinitesimal symmetry transformation; Invariant condition; Non homogeneous electro magneto elastic material

Indexed keywords

CRACKS; DIFFERENTIAL EQUATIONS; ENTHALPY; FRACTURE MECHANICS; MAGNETOELECTRIC EFFECTS; PIEZOELECTRIC MATERIALS; TENSORS;

CONSERVATION LAWS; ELECTROMAGNETIC ENTHALPY; ENERGY-MOMENTUM TENSORS; INVARIANT CONDITION;

ELASTICITY;

EID: 2942519994     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7538(03)00012-3     Document Type: Article

References (31)

1. Atkinson C., Aparicio N.D. Fracture detection problems: applications and limitations of the energy momentum tensor and related invariants. Int. J. Solids Structures. 36:1999;4889-4899.
2. Cherepanov G.P. Mechanics of Brittle Fracture. 1979;McGraw-Hill, New York.
3. Chien N., Honein T., Herrmann A.G. Dissipative systems, conservation laws and symmetries. Int. J. Solids Structures. 33:1996;2959-2968.
4. Delale F., Erdogan F. The crack problem for a nonhomogeneous plane. ASME J. Appl. Mech. 50:1983;609-614.
5. Eischen J.W., Herrmann G. Energy release rate and related balance laws in linear elastic defect mechanics. ASME J. Appl. Mech. 54:1987;388-392.
6. Erdogan F., Wu B.H. The surface crack problem for plate with functionally graded properties. ASME J. Appl. Mech. 64:1997;449-456.
7. Eshelby J.D. The continuum theory of lattice defects. Seitz F., Turnbull D. Solid State Physics. Adv. Res. Appl. III:1956;79-144 Academic Press, New York.
8. Eshelby J.D. Energy relations and the energy-momentum tensor in continuum mechanics. Kanninen M.F., Adler W.F., Rosenfield A.R., Jaffee R.I. Inelastic Behavior of Solids. 1970;77-113 McGraw-Hill, New York.
9. Eshelby J.D. The elastic energy-momentum tensor. J. Elasticity. 5:(3-4):1975;321-335.
10. Fletcher D.C. Conservation laws in linear elastodynamics. Arch. Rational Mech. Anal. 60:1975;330-353.
11. Gao X., Kuang Z.-B. Mode I fracture in two dissimilar functional nonhomogeneous plane. Eng. Fracture Mech. 42:1992;33-44.
12. Gu P., Dao M., Asaro R.J. A simplified method for calculating the crack-tip field of functionally graded materials using the domain integral. ASME J. Appl. Mech. 66:1999;101-108.
13. Gerasoulis A., Strivastav R.P. A Griffith crack problem for nonhomogenous medium. Int. J. Eng. Sci. 18:1980;239-247.
14. Herrmann A.G. On conservation laws of continuum mechanics. Int. J. Solids Structures. 17:1981;1-9.
15. Holt J., Koizumi M., Hirai T., Munir Z. Functionally Gradient Materials: Ceramic Transactions. 34:1992;American Ceramic Society, Westerville.
16. Honein T., Herrmann G. Conservation laws in nonhomogeneous plane elastostatics. J. Mech. Phys. Solids. 45:(5):1997;789-805.
17. Jackson J.D. Classical Electrodynamics. 1975;Wiley, New York.
18. Knowles J.K., Sternberg E. On a class of conservation laws in linearized and finite elastostatics. Arch. Rational Mech. Anal. 44:1972;187-211.
19. Landau L.D., Lifshitz E.M., Pitaevskii L.P. Electrodynamics of Continuous Media. 1984;Pergamon Press, Oxford.
20. Maugin G. Material Inhomogeneities in Elasticity. 1993;Chapman & Hall, New York.
21. Maugin G.A., Epstein M., Trimarco C. Pseudomomentum and material forces in inhomogeneous material. Int. J. Solids Structures. 29:(14/15):1992;1889-1900.
22. Maugin G.A., Epstein M., Trimarco C. Theory of elastic inhomogeneities in electromagnetic materials. Int. J. Eng. Sci. 30:(10):1992;1441-1449.
23. Noether E. Invariant variational problems. Klg-Ges. Wiss. Nach. Göttingen, Math. Phys., Kl. 2:1918;235-253. English translation: Noether, E., 1971. Transport Theory Statist. Phys. 1, 183-207.
24. Noether E. Invariant variational problems. Klg-Ges. Wiss. Nach. Göttingen, Math. Phys., Kl. 2:1918;235-253. English translation: Noether, E., 1971. Transport Theory Statist. Phys. 1, 183-207.
25. Olver P.J. Conservation laws in elasticity - I: General results. Arch. Rational Mech. Anal. 85:1984;119-129.
26. Olver P.J. Conservation laws in elasticity - II: Linear homogeneous isotropic elastostatics. Arch. Rational Mech. Anal. 85:1984;131-160.
27. Olver P.J. Applications of Lie Groups to Differential Equations. 1993;Springer-Verlag, New York.
28. Rice J.R. A path-independent integral and the approximate analysis of strain concentrations by notches and cracks. ASME J. Appl. Mech. 35:1968;379-388.
29. Rice J.R. Mathematical analysis in the mechanics of fracture. Liebowitz H. Fracture: An advanced Treatise. II:1968;191-310 Academic Press, New York.
30. Wang B.L., Noda N. Design of a smart functionally graded thermopiezoelectric composite structure. Smart Mater. Struct. 10:2001;189-193.
31. Wang B.L., Noda N. Thermally induced fracture of a smart functionally graded composite structure. Theoret. Appl. Fracture Mech. 35:2001;93-109.