Comptes Rendus
A time-integration scheme for thermomechanical evolutions of shape-memory alloys
Comptes Rendus. Mécanique, Volume 334 (2006) no. 4, pp. 266-271.

This Note presents a time-integration strategy for computing the evolution of structures embedding shape-memory alloys in a thermomechanical setting. A variational formulation is associated with the scheme proposed, which allows one to study the existence and unicity of solutions depending on the material model considered. A numerical example is presented to illustrate the method and discuss the influence of the thermomechanical coupling.

Cette Note présente un algorithme d'intégration en temps pour l'évolution thermomécanique des structures formées d'alliages à mémoire de forme. On donne une formulation variationnelle du problème discrétisé en temps, ce qui permet d'étudier l'existence et l'unicité de solutions en fonction de la loi de comportement utilisée. Un exemple numérique est présenté afin d'illustrer la méthode et d'étudier l'influence du couplage thermomécanique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2006.02.006
Keywords: Solids and structures, Shape-memory alloys, Phase transformation, Thermomechanical coupling, Numerical algorithms
Mot clés : Solides et structures, Alliages à mémoire de forme, Transformation de phase, Couplage thermomécanique, Algorithmes numériques

Michaël Peigney 1

1 Laboratoire central des ponts et chaussées, 58 boulevard Lefebvre, 75732 Paris cedex 15, France
@article{CRMECA_2006__334_4_266_0,
     author = {Micha\"el Peigney},
     title = {A time-integration scheme for thermomechanical evolutions of shape-memory alloys},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {266--271},
     publisher = {Elsevier},
     volume = {334},
     number = {4},
     year = {2006},
     doi = {10.1016/j.crme.2006.02.006},
     language = {en},
}
TY  - JOUR
AU  - Michaël Peigney
TI  - A time-integration scheme for thermomechanical evolutions of shape-memory alloys
JO  - Comptes Rendus. Mécanique
PY  - 2006
SP  - 266
EP  - 271
VL  - 334
IS  - 4
PB  - Elsevier
DO  - 10.1016/j.crme.2006.02.006
LA  - en
ID  - CRMECA_2006__334_4_266_0
ER  - 
%0 Journal Article
%A Michaël Peigney
%T A time-integration scheme for thermomechanical evolutions of shape-memory alloys
%J Comptes Rendus. Mécanique
%D 2006
%P 266-271
%V 334
%N 4
%I Elsevier
%R 10.1016/j.crme.2006.02.006
%G en
%F CRMECA_2006__334_4_266_0
Michaël Peigney. A time-integration scheme for thermomechanical evolutions of shape-memory alloys. Comptes Rendus. Mécanique, Volume 334 (2006) no. 4, pp. 266-271. doi : 10.1016/j.crme.2006.02.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.02.006/

[1] S. Pagano; P. Alart Solid–solid phase transition modelling: relaxation procedures, configurational energies and thermomechanical behaviour, Int. J. Eng. Sci., Volume 37 (1999), pp. 1821-1840

[2] M. Frémond Non-Smooth Thermomechanics, Springer-Verlag, Berlin/New York, 2002

[3] H. Brezis Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1972

[4] L. Anand; M.E. Gurtin Thermal effects in the superelasticity of crystalline shape-memory alloys, J. Mech. Phys. Solids, Volume 51 (2003), pp. 1015-1058

[5] A. Chrysochoos; C. Licht; R. Peyroux A one-dimensional thermomechanical modeling of phase change front propagation in a SMA polycrystal, C. R. Mecanique, Volume 331 (2003), pp. 25-32

[6] F. Auricchio; L. Petrini A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems, Int. J. Num. Meth. Eng., Volume 61 (2004), pp. 807-836

[7] C. Miehe; J. Schotte; M. Lambrecht Homogenization of inelastic solid materials at finite strains based on incremental variational principles: Application to the texture analysis of polycrystals, J. Mech. Phys. Solids, Volume 50 (2002), pp. 2123-2167

Cited by Sources:

Comments - Policy