Model variational phase transition problem in continuum mechanics

DOI10.1007/S10958-021-05386-3zbMath1464.74133OpenAlexW3161447210MaRDI QIDQ2027463

Viktor G. Osmolovskii

Publication date: 27 May 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-021-05386-3

zbMATH Keywords

uniquenesstwo-phase compositeminimizer existenceenergy fuctionalminimizer non-existence

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Phase transformations in solids (74N99) Random materials and composite materials (74A40) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

• Quasiconvex hull of energy densities in a homogeneous isotropic two-phase elastic medium and solutions of the original and relaxed problems
• Boundary value problems with free surfaces in the theory of phase transitions
• Minimizing sequences and equilibrium energy in the variational problem of elasticity in two-phase media
• Phase transitions in two-phase media with the same moduli of elasticity
• A criterion for the coincidence of the phase transition temperatures in the variational problem on the equilibrium of a two-phase elastic medium
• Sufficient conditions for absence of two-phase equilibrium states of elastic media with different phase transition temperatures
• The volume fraction of one of the phases in equilibrium two-phase elastic medium
• Bounds and extremal microstructures for two-component composites: a unified treatment based on the translation method
• Minimizers for a double-well problem with affine boundary conditions
• Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials
• Mathematical problems of the theory of phase transitions in continuum mechanics

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