Modelisation numerique des couplages en thermomecanique des solides
Keywords:
thermodynamics, thermomechanics, couplings, homogenization, temperature, heat, localization, polymers, shape memory alloys, composites, interface, residual stressesAbstract
In a first part the thermodynamic framework used to introduced the behavioral constitutive equations of solid materials is reminded. Using illustrative examples, the different terms of the energy balance are introduced, specially those due to thennomechanical coupling mechanisms. In a second part the main concepts on multiscale approach are introduced, focussing on coupling aspects, and the way of embedding coupled constitutive equations in a finite element code is discussed. We finally present four applications to illustrate the abovementioned approaches.
Downloads
References
[ASH 89] AsHBEE K., Fiber reinforced composites, Technomic pub. co. inc., 1989.
[BOC 76] BoccARA N., Les principes de Ia Thermodynamique Classique, PUF, 1976.
[BRA 89) BRAHIM-0rSMANE B., FRANCFORT G.A., "Homogenization in thermoelasticity",
Proceedings of Composite Materials and Random Media, Leesburg, Virginia, dec. 7-10,
, ed. by R.V. KoHN, G.W. MILTON, SIAM, Philadelphia, 1989, pp 13-45.
[CAL 85] CALLEN H., Thermodynamics and an introduction to thermostatistics, John Wiley &
sons, 1985.
[CAR 59] CARSLAW H.S., JAEGER J.C., Conduction of heat in solids, second edition, Oxford,
[CHR 79] CHRISTENSEN R.M., Mechanics of Composite Materials, John Wiley & sons, 1979.
[CHR 85] CHRYSOCHoos A., Bilan Energetique en Elastoplasticite Grandes Deformations,
J.M.T.A., Vol. 4, n° 5, 1985, p.589-614.
[CHR 92a] CHRYSOCHOOS A., DUPRE J.C., An infrared setup for continuum thermomechanics,
Quantitative Infra-Red Thermography, July 7-9, ECP, Proceedings of the Eurotherm
Seminar no 27, Ed. Euro. Thermique et Industrie, p.129-134, 1992.
[CHR 92b] CHRYSOCHOOS A., BELMAIUOUB F., Thermographic Analysis of Thermo-mechanical
Couplings, Archives of Mechanics, 44, 1992, pp.55-68.
[CHR 95] CHRYSOCHOOS A., Analyse du comportement thermomecanique des materiaux par
thermographie infrarouge, Photomecanique 95, Ed. Eyroles, 1995, p.l-9.
[CHR 96] CHRYSOCHOOS A., PHAM H., MAISONNEUVE 0., Energy balance of thermoelastic
martensite transformation under stress, Nuclear lngineering and Design, 162, pp. 1-12,
[CHR 96] CHRYSOCHOOS A., Vers une reformulation des transitions de phase du premier ordre,
(accepte), Revue Roumaine des Sciences Techniques, Mecanique Appliquee, Academie
Roumaine des Sciences, 1996.
[DUM 96] DUMONT S., Ondelettes, homogeneisation periodique et elasticite, These de
Doctorat, Universite Montpellier II, 1996.
[ESH 57] EsHELBY J.D., The determination of the elastic field of an ellipsoidal inclusion and
related problems, Proc. Roy. Soc., A241, 1957, pp. 376-396.
[FRA 84] FRANCFORT G.A., Homogenization and fast oscillations in linear thermoelasticity,
Numerical method for transient and coupled problems, Eels. R. LEWIS, E. HINTON, P.
BETERS, B. SCHREFFER, Pineridge, Swansea, 1984, pp. 382-393.
[FRA 91] FRANt;OIS D., PINEAU A., ZAOUil A., Comportement mecanique des materiaux,
Vol. I et 2, Editions Hermes, 1991.
[FRE 87] FREMOND M., Materiaux a memo ire de forme, c. R. A cad. Sci. Paris, II, n°7' 1987'
pp. 239-245.
[GAY 89] GAY D.: Materiaux composites, 2e edition, Editions Hermes, 1989.
[GER 73] GERMAIN P., Cours de Mecanique des Milieux Continus, T1, theorie generale,
Masson et Cie, 1973.
[GER 83] GERMAIN P., NGUYEN Q.S., SUQUET P., Continuum thermodynamics, Journal of
Applied Mechanics, Vol. 105, Ed. Transactions of the ASME, 1983
[GER 86] GERMAIN P., Mecanique, Tomes 1 et 2, Ellipses, Ecole Polytechnique, 1986.
[HAL 75] Halphen B., NGUYEN Q.S., Surles materiaux standards generalises, Journal de
Mecanique, Vol. 14, 1, 1975.
[HAS 62] HASHIN Z., SHTRIKMAN S., A variationnal approach to the theory of the elastic
behaviour of polycrystals, J. Mech. Phys. Solids, Vol. 10, 1962, pp. 343-352.
[HAS 83] HASHIN Z., Analysis of composite materials: a survey, J. of Appl. Mech., Vol. 50,
, pp. 481-505.
[HIL 65] HILL R., A Self-Consistent mechanics of composite materials, J. Mech. Phys. Solids,
Vol. 13, 1965, pp. 213-222.
[IOU 93] Iou D., CASAS-VASQUEZ I., LEBON G., Extended Thennodynamics, Springer-Verlag,
[LEM 85] LEMAITRE L., CHABOCHE I.-L., Mecanique des Materiaux Solides, Dunod, Paris,
[LOB 95] LOBEL M., Caracterisation thermomecanique d'alliages a memoire de forme de type
NiTI et CuZnAI. Domaine de transition et cinetique de changement de phase, These de
l'Universite Montpellier II, 1995.
[LUB 90] LUBLINER J., Plasticity Theory, Macmillan Publishing Co., 1990.
[MAU 92] MAUGIN G., The thermomechanics of plasticity and fracture, Cambridge University
Press, 1992.
[MEC 93] MECAMAT 93, Proceedings of International Seminar on Micromechnics of
Materials, Moret-sur-Loing, France, 6-9 juillet 1993, Collection de la Direction des Etudes
et Recherches d'Electricite de France, Ed. Eyrolles, 1993.
[MEC 95] Ecole d'ete MECAMAT-GFP, Introduction ala mecanique des polymeres, Ed. C.
G'SELL et J.M. HAUDIN, 1995.
[MEl 96] ME!SSONNIER F., PEYROUX R., CHRYSOCHOOS A., Finite element analysis of strain
localization induced by thermomechanical couplings in a Kelvin-Voigt model, ESDA' 96,
-4 juillet 1996, Montpellier, France.
[MEl 97] MErssoNN!ER F., Couplages thermomecaniques et Homogeneisation, These de
l'Universite Montpellier II, 1996
[MOR 73] MoRl T., TANAKA K., Average stress in matrix and average elastic energy of
materials with rnisfitting inclusions, Acta Metallurgica, 1973, Vol. 21, pp. 571-574.
[MUR 82] MURAT T., Micromechanics of defects in solids, Martinus Nijhoff Publishers, La
Hague, Boston, London, 1982.
[MUS 93] MuscHIK W., Non-equilibrium thermodynamics with applications to solids, CISM
courses and lectures n° 336, Springer Verlag, 1993.
[PEY 90] PEYROUX R., Caracteristiques thermoelastiques de materiaux composites a fibres
courtes, These de Doctorat, Universite Montpellier II, 1990.
[PEY 95] PEYROUX R., CHRYSOCHOOS A., LICHT C., LOBEL M., Phenomenological constitutive
equations for numerical simulations of SMA structures. Effects of thermomechanical
couplings, Mecamat 95, International Seminar, May 16-19, France, Les editions de
Physique, 1995.
[PEY 97] PEYROUX R., CHRYSOCHOOS A., LICHT C., LOBEL M., Thermomechanical couplings
and pseudoelasticity of shape memory alloys, Int. J. of Eng. Sci., a paraitre en 1997.
[REU 29] REuss A., Berechnug des Flessgrense von Mischkritallen auf Grund der
Plastizitatsbedingung ftlr Einkristalle, Zeitschrift fur Angewandte Mathematik und
Mechanik, Vol. 9, 1929, pp. 49-58.
[SID 82] SIDOROFF F., Les grandes Deformations, Greco 47 GDE, rapport n°5l, 1982.
[SUQ 82] SuQUET P., Plasticit6 et Homogeneisation, These d'Etat, Universit6 Pierre et Marie
Curie, Paris, 1982.
[SUQ 85] SUQUET P., in Homogenization techniques for composite media, Ed. E. SANCHEZPALENCIA
ETA. ZAOUI, Berlin, Springer Verlag, 1985.
[SUQ 94] SUQUET P., MouuNEc H., A fast numerical method for computing the linear and non
linear mechanical properties of composites, C. R. Acad. Sci. Paris, vol. 318, 1994, pp.
-1423.
[SUQ 96] SUQUET P. (Coord.), Continuum Micromechanics, Advanced School, CMSIM,
Udine, 2-6 septembre 1996.
[VOl 89] VOIGT W., Uber die Beziehung zwischen den heiden Elastizitlitskonstanten isotroper
Korper, Wied. Ann, 38, 1889, p. 573.
