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Solutions to a phase‐field model for martensitic phase transformations driven by configurational forces
Author(s) -
Wu Fan,
Bian Xingzhi,
Zhao Lixian
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12365
Subject(s) - degenerate energy levels , shape memory alloy , elasticity (physics) , boundary value problem , martensite , phase (matter) , phase field models , phase boundary , field (mathematics) , mathematics , mathematical analysis , classical mechanics , field equation , physics , materials science , thermodynamics , pure mathematics , microstructure , quantum mechanics , metallurgy
We study the existence of weak solutions to an initial‐boundary value problem for a new phase‐field model, which consists of a degenerate parabolic equation coupled to linear elasticity equations. This model is used to describe the evolution of interfaces in elastically deformable solid materials which moves by configurational forces, such as martensitic phase transformations in shape memory alloys. The existence proof is valid only for one‐dimensional case.