Mathematical Problems in Mechanics
Non-existence of one-dimensional stress problems in solid–solid phase transitions and uniqueness conditions for incompressible phase-transforming materials
Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 981-984.

We show that for solid–solid phase transitions one-dimensional stress problems do not exist. The lack of uniqueness of solutions in modeling dynamical phase transitions was an unsolved issue. For a slender circular cylinder composed of an incompressible phase-transforming material we establish the proper model equation. From our model equation we establish three relations for three unknowns across the phase boundary, which provide the uniqueness conditions for solutions. Our results seem to resolve the long outstanding issue of nonuniqueness of solutions in modeling dynamical problems of phase-transforming materials.

Nous montrons que pour les changements de phases solide–solide, il n'existe pas de modèles de contraintes uni-dimensionnel. La non-unicité des solutions des modèles dynamiques de changement de phases était un problème non résolu. Nous obtenons la bonne équation qui modélise un cylindre circulaire mince constitué d'un matériau incompressible à changement de phases. A partir de notre modèle, nous établissons trois relations pour trois inconnues le long de la frontière de phase, qui permettent d'obtenir l'unicité de la solution. Nos résultats semblent résoudre une question restée ouverte pendant longtemps à propos de la non-unicité des solutions des modèles dynamiques de matériaux à changement de phase.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.03.036
Dai, Hui-Hui 1

1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
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Dai, Hui-Hui. Non-existence of one-dimensional stress problems in solid–solid phase transitions and uniqueness conditions for incompressible phase-transforming materials. Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 981-984. doi : 10.1016/j.crma.2004.03.036. http://www.numdam.org/articles/10.1016/j.crma.2004.03.036/

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