Comparison of a rapidely converging phase field model for interfaces in solids with the Allen-Cahn model

DOI10.1007/s10659-012-9398-xzbMath1272.35031OpenAlexW2050907304MaRDI QIDQ359569

Peicheng Zhu, Hans-Dieter Alber

Publication date: 12 August 2013

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-012-9398-x

zbMATH Keywords

phase transformationasymptotic solutionnumerical efficiencydriving force without curvature termdynamics of sharp interfacesinterfaces with nonlinear kinetic relation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Dynamics of phase boundaries in solids (74N20) Asymptotic expansions of solutions to PDEs (35C20) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (8)

Viscosity solutions to a model for solid-solid phase transitions driven by material forces ⋮ Stability and errors analysis of two iterative schemes of fractional steps type associated to a nonlinear reaction-diffusion equation ⋮ Asymptotics and numerical efficiency of the Allen-Cahn model for phase interfaces with low energy in solids ⋮ Structure preserving discretization of Allen-Cahn type problems modeling the motion of phase boundaries ⋮ New Phase-Field Models with Applications to Materials Genome Initiative ⋮ Regularity of solutions to a model for solid-solid phase transitions driven by configurational forces ⋮ Viscosity solutions to a new phase-field model with Neumann boundary condition for solid-solid phase transitions ⋮ Weak solutions and simulations to a new phase-field model with periodic boundary

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