Elastic phase transitions: A new model

DOI10.1016/S0167-2789(97)00058-4zbMath0963.74547OpenAlexW2068352495MaRDI QIDQ1963253

James M. Greenberg

Publication date: 24 January 2000

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(97)00058-4

zbMATH Keywords

hyperbolic systemslong-term behaviorelastic phase transitionsmicrostructural equilibrium solutionsslow-moving under-compressive shocksviscosity-capillarity theories

Mathematics Subject Classification ID

Micromechanics of solids (74M25) Dynamics of phase boundaries in solids (74N20) Theory of constitutive functions in solid mechanics (74A20)

Related Items (5)

Uniqueness and stability of an inverse problem for a phase field model using data from one component ⋮ Time harmonic solutions to a model of ferroelectric materials ⋮ A phase-field model based on a three-phase-lag heat conduction ⋮ Convergence to equilibrium for a parabolic-hyperbolic phase-field system with dynamical boundary condition ⋮ On the long-time behavior of ferroelectric systems

Cites Work

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• The viscosity-capillarity criterion for shocks and phase transitions
• A limiting ``viscosity approach to the Riemann problem for materials exhibiting change of phase
• An analysis of a phase field model of a free boundary
• Dynamic solid-solid transitions with phase characterized by an order parameter
• Admissibility criteria for propagating phase boundaries in a van der Waals fluid
• Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)

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