Non-existence of one-dimensional stress problems in solid–solid phase transitions and uniqueness conditions for incompressible phase-transforming materials

Abstract

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. To cite this article: H.-H. Dai, C. R. Acad. Sci. Paris, Ser. I 338 (2004).