Phase transitions in two-phase media with the same moduli of elasticity

DOI10.1007/s10958-020-05124-1zbMath1453.74071OpenAlexW3104345581MaRDI QIDQ2214349

Viktor G. Osmolovskii

Publication date: 8 December 2020

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

Full work available at URL: https://doi.org/10.1007/s10958-020-05124-1

zbMATH Keywords

existenceenergy functionalequilibrium energyphase transition temperature

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Thermal effects in solid mechanics (74F05) Energy minimization in equilibrium problems in solid mechanics (74G65) Phase transformations in solids (74N99) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (3)

Phase transition temperatures for variational problem on equilibrium of a two-phase medium with constraints ⋮ Equilibrium energies of layered composite and two-phase media under periodic and zero boundary conditions on displacement fields ⋮ Model variational phase transition problem in continuum mechanics

Cites Work

• Existence of minimizers for non-quasiconvex functionals arising in optimal design
• Boundary value problems with free surfaces in the theory of phase transitions
• Independence of temperatures of phase transitions of the domain occupied by a two-phase elastic medium
• 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
• A variational problem of phase transitions for a two-phase elastic medium with zero coefficient of surface tension
• 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
• Optimal lower bounds on the elastic energy of a composite made from two non-well-ordered isotropic materials
• Direct methods in the calculus of variations
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