Stability of a two-phase process involving a planar phase boundary in a thermoelastic solid
type: Item
instance of: scholarly article
title: Stability of a two-phase process involving a planar phase boundary in a thermoelastic solid
zbMATH Open document ID: 0772.73004
DOI: 10.1007/BF01126387
published in: Continuum Mechanics and Thermodynamics
publication date: 1993-02-18T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74G99
Mathematics Subject Classification ID: 74H99
zbMATH DE Number: 124232
zbMATH Keywords: field equations
zbMATH Keywords: phase transition
zbMATH Keywords: non-elliptic neo-Hookean
zbMATH Keywords: antiplane shear motion
zbMATH Keywords: jump conditions
zbMATH Keywords: linearized equations
zbMATH Keywords: long wave
zbMATH Keywords: short wave
author: Eliot Fried
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
cites work: Linear stability of planar solidification fronts
cites work: On the modeling of thermo-mechanical phase transformations in solids
cites work: On finite anti-plane shear for imcompressible elastic materials
cites work: Ellipticity and deformations with discontinuous gradients in finite elastostatics
cites work: A class of compressible elastic materials capable of sustaining finite anti-plane shear
cites work: Transverse deformations associated with rectilinear shear in elastic solids
cites work: Rectilinear steady flow of simple fluids
cites work: On the driving traction acting on a surface of strain discontinuity in a continuum
cites work: Implications of Viscosity and Strain-Gradient Effects for the Kinetics of Propagating Phase Boundaries in Solids
cites work: Kinetic relations and the propagation of phase boundaries in solids
cites work: On the propagation of maximally dissipative phase boundaries in solids
cites work: Multiphase thermomechanics with interfacial structure. III: Evolving phase boundaries in the presence of bulk deformation
description: scientific article; zbMATH DE number 124232