Energy-Momentum Tensor and J -Integral in Electrodeformable Bodies *

Abstract

An energy-momentum tensor of the Eshelby type is constructed in the exact theory of nonlinear electrodeformable dielectrics. This tensor does not involve the Maxwell stress of free electric fields. In the quasi-linear approximation the material force defined from this tensor leads to the notion of a path-independent J-integral useful in the study of cracks in electrodeformable ceramics.

Get full access to this article

View all access options for this article.

References

Maugin

G.A.

, Continuum Mechanics of Electromagnetic Solids (North-Holland, Amsterdam, 1988).

Parton

V.Z.

and Kudryavstev

B.A.

, Electromag-netoelasticity, (Gordon and Breach, New York, 1988).

Golubiewska-Herrmann

, On conservation laws of continuum mechanics, Int. J. Solids Struct. 17 (1981) 1–9.

Bui

H.D.

, Mecanique de la Rupture Fragile (Masson, Paris, 1977).

Toupin

R.A.

, Stress tensors in elastic dielectrics, Arch. Ration. Mech. Anal. 5 (1960) 440–452.

Maugin

G.A

, Quasi-electrostatics of electrically polariz-able continua, Lett. Appl. Eng. Sci. 2 (1974) 293–306.

Maugin

G.A.

and Eringen

A.C.

, On the equations of the electrodynamics of continua of finite extent, J. Mec. 16 (1977) 101–147.

Epstein

and Maugin

G.A.

, Sur le tenseur de moment matériel d'Eshelby en élasticité non linéaire, C.R. Acad. Sci. II-310 (1990), 675–678.

Epstein

and Maugin

G.A.

, The energy-momentum tensor and material uniformity in finite elasticity, Acta Mech. 83 (1990) 127–133.

10.

Eshelby

J.D.

, The force of an elastic singularity, Philos. Trans. R. Soc. London A244 (1951) 87–112.

11.

Maugin

G.A.

and Epstein

, The electroelastic energy-momentum tensor Proc. R. Soc. London A433 (1991) 299–312.

12.

Pak

Y.E.

and Hermann

, Conservation laws and the material momentum tensor for the elastic dielectric, Int. J. Ent. Sci. 24 (1986) 1365–1374.