Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2025, Volume 12, Issue 1, Pages 18–36
DOI: https://doi.org/10.21638/spbu01.2025.102
(Mi vspua337)
 

MATHEMATICS

The set of all equilibrium states of a two-phase thermoelastic medium. Part 2: Dependence of the set of all equilibrium states of a two-phase thermoelastic medium on the temperature

E. A. Efimovab

a St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
b Institute of Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoi pr. V.O., St. Petersburg, 199178, Russian Federation
References:
DOI: https://doi.org/10.21638/spbu01.2025.102
Abstract: This article is the second part of the work devoted to the study of the set of all equilibrium states of a two-phase thermoelastic medium. The equilibrium state of a twophase elastic medium is understood as an ordered pair: a displacement field and a spatial phase distribution which provide the free energy functional with a global minimum. For thermoelastic media, the free energy densities are obtained by adding to the strain energy densities the terms associated with the temperature stresses of each phase and the terms associated with the energies of each phase in the unstressed state at zero stres-temperature tensors. Under zero Dirichlet boundary conditions on the displacement field and certain restrictions on the elasticity tensors, the strain tensors providing each phase with the unstressed state at the initial temperature, the stres-temperature tensors and the terms in the definition of the free energy densities associated with the energies of each phase in the unstressed state at zero stres-temperature tensors the dependence of the set of all equilibrium states of a two-phase thermoelastic medium on the temperature is found and studied.
Keywords: two-phase thermoelastic medium, free energy functional, free energy density, spatial phase distribution, equilibrium state.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 124041500009-8
The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme no. 124041500009-8).
Received: 20.05.2024
Revised: 06.06.2024
Accepted: 29.08.2024
Document Type: Article
UDC: 51-72+531.64+539.311+539.87
MSC: 74G65, 74N99, 74P99
Language: Russian
Citation: E. A. Efimov, “The set of all equilibrium states of a two-phase thermoelastic medium. Part 2: Dependence of the set of all equilibrium states of a two-phase thermoelastic medium on the temperature”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 12:1 (2025), 18–36
Citation in format AMSBIB
\Bibitem{Efi25}
\by E.~A.~Efimov
\paper The set of all equilibrium states of a two-phase thermoelastic medium. Part 2: Dependence of the set of all equilibrium states of a two-phase thermoelastic medium on the temperature
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2025
\vol 12
\issue 1
\pages 18--36
\mathnet{http://mi.mathnet.ru/vspua337}
Linking options:
  • https://www.mathnet.ru/eng/vspua337
  • https://www.mathnet.ru/eng/vspua/v12/i1/p18
    Cycle of papers
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025