Stability of a two-phase process involving a planar phase boundary in a thermoelastic solid
The phase transition in a cylindrical thermoelastic material of the generalized, non-elliptic neo-Hookean type under an antiplane shear motion is investigated. The phase transition manifests itself on a plane curve across which the displacement and the temperature are continuous. Field equations valid in both phases and jump conditions on the moving phase boundary are well-known in this particular case. First, a base process is studied in which the displacement field is a linear function of one of the space coordinates and time, and the temperature is uniform. Then the phase boundary is planar and moves with a constant velocity. The stability of this base process is investigated by superimposing a small antiplane motion and analyzing the linearized equations. It is shown that if the base process is stationary, then it is always stable while the moving interface loses its stability for perturbation of long wave lengths, but regains it for perturbation of short wave lengths. It is thus expected that the moving boundary favors a highly wrinkled shape.
scientific article; zbMATH DE number 124232