Abstract
The field-equations in statics of polycrystalline materials constitued, for example, of martensitic and austenitic grains are described by use of Green’s functions taking into account inelastic and elastic heterogeneities. Now, question arises when looking at the evolution of inelasticity (phase transformation,…) induced by external loading. The main feature is that we observe experimentally movements of interfaces with velocities which are different than the particles, a natural concept is bringing out: the usual static field-equations are derived in time with respect to the proper velocities of the interfaces instead of the particles velocities. This technique gives us explicitly a simultaneous evolution of inelasticity with associated moving-boundaries.
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References
Sabar H., Berveiller M., Buisson M. “Probleme d’inclusion a frontiere mobile”, Comptes Rendus de l’Academie des Sciences, Serie II, (1990) t.310, pp. 477–452, Paris.
Sabar H., Buisson M., Berveiller M. The Inhomogeneous and Plastic Inclusion Problem with Moving boundariy, in press in Inter.J. of Plasticity.
Buisson M., Patoor E., Berveiller M. Comportement global associe aux mouvements d’interafces entre variantes de martensites, submit. in C.R.Acad.Sci.II.
Lifshits I.M., Rosentsveig L.N. Construction of the Green’s tensor for the basic equation of the theory of elasticity for the case of an infinite elastic-anisotropic medium, (1947) ZhETF, v. 17, N 9.
Indenbom V.L., Orlov S.S. Construciton of the Green’s functions in terms of Green’s function of lower dimension. (1968) J. Appl. Math. and Mech. v. 32, N 3, pp.414–420.
Berveiller M, Zaoui A. Journal de Mechanique (1980).
Mura T. Micromechanics of defects in Solids, Martinus Nijhoff Publishers, Dordreht. (1987)
Levin B.M. Contraintes thermoelasticues dans les milieux composites. Prikl. Mat. Meh., (1982) v. 46, N 3, pp.502–506.
Berveiller M., Fassi-Fehri O., Hihi A. Multiply Site Self Consistent Scheme, Int.J.Engng.Sci. (1897) 25, 681.
Buisson M., Molinari A., Berveiller M. On a constitutive relation for heterogeneous thermoelastic media. Arch.of Mech., v. 42–2 (1990), Warszawa.
Germain P., “Mecanique,” Ellipses, Ecole Polytechnique, (1986), Paris, 1.
Eshelby J.D., Inelastic Behaviour od Solids.ed. M.F. Kanninen, W.F. Adler, A.R. Rosenfield, R.I. Joffee, (1970) p. 77, Mac Crag Hill, New York.
Hill R. Energy-Momentum Tensors in Elastostatics: some reflections on the general theory. J.Mech.Phys.Solids, v. 34, N 3, (1986) pp. 305–317.
Berveiller M., Sabar H. Cont. Mod. and Discret Systems, Dijon II,ed Maugin, (1989).
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Sabar, H., Buisson, M., Berveiller, M. (1992). The Modelization of Transformation Phase Via the Resolution of an Inclusion Problem with Moving Boundary. In: Antontsev, S.N., Khludnev, A.M., Hoffmann, KH. (eds) Free Boundary Problems in Continuum Mechanics. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8627-7_31
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DOI: https://doi.org/10.1007/978-3-0348-8627-7_31
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