Different ways are proposed to find the expression of the material inhomogeneity forces (so-called configuration forces) in the nonlinear elasticity of electromagnetic solids. This expression involves both the Eshelby material stress tensor and the pseudomomentum of which the interest has been shown by Peierls. It distinguishes automatically the essentially material quantities from those attached to pure fields. In the case of brittle fracture, it yields the electromagnetoelastic generalization of the J-integral (e.g., in piezoelectric ceramics or in magnetostrictive ferromagnets)
Get full access to this article
View all access options for this article.
References
1.
PakY.E. and HerrmannG., Conservation laws and the material momentum tensor for the elastic dielectric, Int. J. Engng. Sci.24 (1986) 1365–1374.
2.
PakY.E. and HerrmannG., Crack extension forces in a dielectric medium, Int. J. Engng. Sci.24 (1986) 1375–1388.
3.
PakY.E., Crack extension force in a piezoelectric material, ASME J. Appl. Mech.57 (1990) 647–653.
4.
PartonV.G. and KudryavtsevB.A., Electromagnetoelasticity (Gordon and Breach, New York, 1988)
5.
McMeekingR.M.A. J-integral for the analysis of electrically-induced mechanical stress at cracks in elastic dielectrics, Int. J. Engng. Sci. 28 (1990) 605–613.
6.
EpsteinM. and MauginG.A., Inhomogeneities, Eshelby's tensor and J-integral in electroelasticity, in: Mechanical Modelling of New Electromagnetic Materials, ed. HsiehR.K.T. (Elsevier, Amsterdam, 1990) pp. 253–258.
7.
MauginG.A. and EpsteinM., The electroelastic energy-momentum tensor, Proc. Roy. Soc. Lond.A433 (1991) 299–312.
8.
PeierlsR., Momentum and pseudomomentum of light and sound, in: Highlights of Condensed Matter Physics, Corso LXXXIX (Soc. Ital. Fisica, Bologna, 1985) pp. 237–255.
9.
NelsonD.F., Resolution of the problem of Minkowski and Abraham, in: Mechanical Modelling of New Electromagnetic Materials, ed. HsiehR.K.T. (Elsevier, Amsterdam, 1990) pp. 171–177.
10.
MauginG.A., Sur la conservation de la pseudo-quantité de mouvement en mécanique et électrodynamique des milieux continus, C.R. Acad. Sci. Paris, II-311 (1990) 763–768.
11.
MauginG.A. and TrimarcoC., Pseudo-quantité de mouvement et milieux élastiques inhomogènes, C.R. Acad. Sci. Paris, II-313 (1991).
12.
G.MauginA. and TrimarcoC., Pseudomomentum and material forces in nonlinear elasticity: Variational formulations and application to brittle fracture, Acta Mechanica (in press).
13.
TruesdellC.A. and ToupinR.A., The Classical theory of fields, in: Handbuch der-Physik, Bd. HI/1, ed. S. Flugge (Springer-Verlag, Berlin, 1960).
14.
NelsonD.F., Electric, Optic and Acoustic Interactions in Dielectrics (J. Wiley-Interscience, New York, 1979).
15.
MauginG.A., Continuum Mechanics of Electromagnetics Solids (North-Holland, Amsterdam, 1988).
16.
EringenA.C. and MauginG.A., Electrodynamics of Continua, Vol. I: Foundation and Solid Media (Springer-Verlag, New York, 1990).
17.
ColletB. and MauginG.A., Sur L'électrodynamique des milieux continus avec interactions, C.R. Acad. Sci. Paris, B279 (1974) 379–382, 439–442.
18.
MauginG.A. and EringenA.C., On the equations of the electrodynamics of deformable bodies of finite extent, J. Mecanique16 (1977) 101–147.
19.
MauginG.A., The principle of virtual power in continuum mechanics: Application to coupled fields, Acta Mechanica35 (1980) 1–70.
20.
AniW. and MauginG.A., Basic equations for shocks in nonlinear electroelastic materials, J. Acoust. Soc. Amer.85 (1989) 599–610.
21.
WalkerJ.B., PipkinA.C. and RivlinR.C., Maxwell's equations in a deformed body, Accad. Naz. Lincei, Ser.8, 38 (1965) 674–676.
22.
McCarthyM.F., Wave propagation in nonlinear magneto-thermoelasticity, Proc. Vibr. Probl. (Warsaw)9 (1968) 367–381.
23.
LaxM. and NelsonD.F., Maxwell's equations in material form, Phys. Rev., B13 (1976) 1777–1784.
24.
EischenJ.W. and HerrmannG., Energy-release rates and related balance laws in linear defect mechanics, ASME J. Appl. Mech.54 (1987) 388–392.
25.
EpsteinM. and MauginG.A., The energy-momentum tensor and material uniformity in finite elasticity, Acta Mechanica83 (1990) 127–133.
26.
MauginG.A. and TrimarcoC., Note on a mixed variational principle in finite elasticity, Rend. Mat. Accad. Lincei (Roma), in press.
27.
BatraR.C., The force on a lattice defect in an elastic body, J. Elasticity17 (1987) 3–8.
28.
StumpfH. and LeK.Ch., Variational principles of nonlinear fracture mechanics, Acta Mechanica83 (1990) 25–37.
29.
CasalP., Interpretation of the Rice integral in continuum mechanics, Lett. Appl. Engng. Sci.16 (1978) 335–347.
30.
MauginG.A., Thermomechanics of Plasticity and Fracture (Cambridge University Press, CambridgeU.K., 1991).
