The thermoelastic material-momentum equation

Journal of Elasticity - Tập 39 Số 3 - Trang 201-212 - 1995
Cristian Dascalu1, Gérard A. Maugin1
1Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie, Paris Cedex 05, France

Tóm tắt

Từ khóa


Tài liệu tham khảo

R. Peieris, Momentum and pseudomomentum of light and sound, In: M. Tosi (ed.), Highlights of Condensed-matter Physics. Corso. LXXXIX. Soc. Ital. Fisica, Bologna (1979) pp. 237–255.

D.F. Nelson, Momentum, pseudomomentum and wave momentum: toward resolving the Minkowski-Abraham controversy. Phys. Rev. A 44 (1991) 3905–3916.

J.D. Eshelby, The force on an elastic singularity. Phil Trans. Roy. Soc. Lond. A 244 (1951) 87–112.

J.D. Eshelby, Energy relations and the energy-momentum tensor in continuum mechanics. In: M.F. Kanninen, W.F. Adler, A.R. Rosenfield and R.I. Jaffe (eds), Inelastic Behaviour of Solids. McGraw-Hill, New York (1970) pp. 77–114.

D. Rogula, Forces in material space. Arch. Mech. 29 (1977) 705–715.

G.A. Maugin, 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.

G.A. Maugin and C. Trimarco, Pseudomomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture. Acta Mechanica 94 (1992) 1–28.

C. Dascalu and G.A. Maugin, Forces matérielles et taux de restitution de l'énergie dans les corps élastiques homogènes avec défauts. C.R. Acad. Sci. Paris II-317 (1993) 1135–1140.

G.A. Maugin, Material Inhomogeneities in Elasticity. Chapman and Hall, London (1993).

J.R. Rice, A path-independent integral and the approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech. 35 (1968) 379–388.

G. Francfort and A. Golebiewska, Conservation laws and material momentum in thermoelasticity. J. Appl. Mech. 22 (1982) 710–714.

G. Francfort and A. Golebiewska, A contour integral and an energy release rate in thermoelasticity. Int. J. Solids Structures 22 (1986) 759–766.

M. Epstein, Eshelby-like tensors in thermoelasticity. In: W. Muschik and G.A. Maugin (eds), Non-linear Thermodynamical Processes in Continua. TUB-Dokumentation Kongresse und Tagungen, Heft 61, T.U.B. Berlin (1992) pp. 147–159.

M. Epstein and G.A. Maugin, Thermoelastic material; forces: definition and geometric aspects. C.R. Acad. Sci. Paris, II-320 (1995) 63–68.

Kostrov and Nikitin, Some general problems of mechanics of brittle fracture. Arch. Mech. Stos. 22 (1970) 749–776.

M. Gurtin, Thermodynamics and the Griffith criterion for brittle fracture. Int. J. Solids Structures 15 (1979) 553–560.

H.D. Bui, A Erlacher and Q.S. Nguyen, Propagation de fissure en thermoélasticité dynamique. J. Mécanique 19 (1980) 697–725.

A.E. Green and P.M. Naghdi, Thermoelasticity without energy dissipation. J. Elasticity 31 (1993) 189–208.

G.A. Maugin, Application of an energy-momentum tensor in nonlinear elastodynamics (pseudomomentum and Eshelby stress in solitonic systems). J. Mech. Phys. Solids 40 (1992) 1543–1558.

G.A. Maugin and C. Trimarco, On material and physical forces in liquid crystals. Int. J. Engng. Sci. 33 (1995) (to appear).

D.E. Carlson, Linear thermoelasticity. In: C. Truesdell (ed.), Handbuch der Physik. Vol. VI/2 Springer Verlag, Berlin (1972) pp. 297–345.

E.S. Suhubi, Thermoelastic solids. In: A.C. Eringen (ed.), Continuum Physics. Academic Press, New York (1975) pp. 174–265.

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

G.A. Maugin, Magnetized deformable media in general relativity. Ann. Inst. Henri Poincaré A 15 (1971) 275–302.

M. Von Laue, Relativitätstheorie, Vol.1. Vieweg, Braunschweig (1921).

D. Lhuillier, M. François and M. Karatchentzeff, Conjugate variables and a variational principle in superfluid helium. Phys. Rev. B 12 (1975) 2656–2666.

A.E. Green and P.M. Naghdi, On thermodynamics and the nature of the second law. Proc. Roy. Soc. Lond. A357 (1977) 253–270.

A.E. Green and P.M. Naghdi, A re-examination of the basic postulates of thermomechanics. Proc. Roy. Soc. Lond. A432 (1991) 171–194.

M. Gurtin, On the energy release rate in quasi-static elastic crack propagation. J. Elasticity 9 (1979) 187–195.

G.A. Maugin, The Thermomechanics of Plasticity and Fracture. Cambridge University Press, Cambridge, U.K. (1992).

H.D. Bui, Stress and crack-displacement intensity factors in elastodynamics. In: Proc 4th Conf. Fracture. Waterloo, 3 (1977) 91.