Stability of interphase boundaries in solid elastic media

DOI10.1016/0021-8928(87)90089-XzbMath0667.73002MaRDI QIDQ1117734

Michael A. Grinfeld

Publication date: 1987

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

zbMATH Keywords

isothermal systemnecessary conditions for stabilitysufficient conditions for instabilityasymptotic of low intrinsic straincoherent transformationsequilibrium of heterogeneous thermodynamic systemsexplicit second-variation formulasisotropic elastic phaseslinear homogeneous system of partial differential equationsmartensitic typenon-negative-definitenessnon-negativity of spectral valuesphase transformation surfaces of the first kindsecond energy variationsolid single-component phasestransitions with slip

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Inhomogeneity in solid mechanics (74E05) Thermodynamics in solid mechanics (74A15) Phase transitions (general) in equilibrium statistical mechanics (82B26) Thermodynamics and heat transfer (80A99)

Related Items (4)

Legendre-Hadamard conditions for two-phase configurations ⋮ Stability of heterogeneous systems with coherent interphase boundaries ⋮ Normality condition in elasticity ⋮ The relaxation of a double-well energy

Cites Work

• Quasiconvexity at the boundary, positivity of the second variation and elastic stability
• Asymptotic form of small density differences in the problem of coherent phase transformations
• On heterogeneous equilibrium of nonlinear elastic phases and chemical potential tensors
• Stability of heterogeneous equilibrium in a system with liquid phases

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