Constraints, constitutive limits, and instability in finite thermoelasticity

Journal of Elasticity

Volumn 74, Issue 2, 2004, Pages 109-133

  Rooney, Francis J ^a   Bechtel, Stephen E ^b  

^a Bishop O'Dowd   (United States)

^b Ohio State University   (United States)

Author keywords

Constitutive limits; Constraints; Entropy; Legendre Hadamard condition; Stability; Thermoelasticity

Indexed keywords

DEFORMATION; ENTHALPY; ENTROPY; GIBBS FREE ENERGY; POTENTIAL ENERGY; STRESS ANALYSIS; THERMAL EFFECTS;

CONSTITUTIVE LIMITS; CONSTRAINTS; LEGENDRE-HADAMARD CONDITION;

THERMOELASTICITY;

EID: 3142769313     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000033864.58356.38     Document Type: Article

References (26)

1. S.E. Bechtel, D. Cao and H. Hsiao, Geometry and heat loss in channel flow of a fluid with temperature-dependent density. Amer. Inst. Chemical Engrg. J. 42 (1996) 2453-2466.
2. S.E. Bechtel, M.G. Forest, F.J. Rooney and Q. Wang, Thermal expansion models of viscous fluids based on limits of free energy. Phys. Fluids (2003) submitted.
3. S.E. Bechtel, F.J. Rooney and M.G. Forest, Internal constraint theories for the thermal expansion of viscous fluids. Internat. J. Engrg. Sci. (2003) submitted.
4. H.B. Callen, Thermodynamics and an Introduction to Thermostatics. Wiley, New York (1985).
5. D. Cao, S.E. Bechtel and M.G. Forest, Thermomechanical equations governing a material with prescribed temperature-dependent density with application to nonisothermal plane Poiseuille flow. ASME J. Appl. Mech. 63 (1996) 1011-1018.
6. D.E. Carbon and D.A. Tortorelli, On hyperelasticity with internal constraints. J. Elasticity 42 (1996) 91-98.
7. J. Casey, A treatment of internally constrained materials. ASME J. Appl. Mech. 62 (1995) 542-544.
8. J. Casey, Strain-temperature and strain-entropy constraints in finite thermoelasticity. Finite Thermoelasticity 236 (1999) 45-66.
9. J. Casey and S. Krishnaswamy, A characterization of internally constrained thermoelastic materials. Math. Mech. Solids 3 (1998) 71-79.
10. P. Chadwick and N.H. Scott, Linear dynamical stability in constrained thermoelasticity I. Deformation-temperature constraints. Quart. J. Mech. Appl. Math. 45 (1992) 641-650.
11. J. Dunwoody and R.W. Ogden, On the thermodynamic stability of elastic heat-conducting solids subject to a deformation temperature constraint. Math. Mech. Solids 7 (2002) 285-306.
12. J.W. Gibbs, A method of geometrical representation of the thermodynamic properties of substances by means of surfaces. In: Transactions of the Connecticut Academy II 1873, Collected Works (1873) pp. 33-54.
13. J.W. Gibbs, On the equilibrium of heterogeneous substances. In: Transactions of the Connecticut Academy III 1873, Collected Works (1875-1878) pp. 55-354.
14. A.E. Green and P.M. Naghdi, A note on thermodynamics of constrained materials. ASME J. Appl. Mech. 44 (1977) 787.
15. A.E. Green, P.M. Naghdi and J.A. Trapp, Thermodynamics of a continuum with internal constraints. Internat. J. Engrg. Sci. 8 (1970) 891-908.
16. J.D. Humphrey and K.R. Rajagopal, Finite thermoelasticity of constrained elastomers subject to biaxial loading. J. Elasticity 49 (1998) 189-200.
17. R.J. Knops and E.W. Wilkes, Theory of Elastic Stability, Mechanics of Solids III. Springer, Berlin (1984) pp. 125-302.
18. J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Proc. Roy. Soc. London 454 (1998) 2617-2654.
19. T. Manacorda, Onde elementari nella termoelastica di solidi incomprimibili. Atti dell' Academia delle Scienze Torino 101 (1967) 503-509.
20. R.S. Rivlin, Reflections on certain aspects of thermomechanics. In: Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e loro Applicazioni, Rome, No. 76: Finite Thermoelasticity (1986) 11-43.
21. F.J. Rooney and S.E. Bechtel, Modeling of thermal expansion. Finite Thermoelasticity 236 (1999) 77-86.
22. N.H. Scott, Linear dynamical stability in constrained thermoelasticity II. Deformation-entropy constraints. Quart. J. Mech. Appl. Math. 45 (1992) 641-650.
23. N.H. Scott, Connections between deformation-temperature and deformation-entropy constraints and near constraints in thermoelasticity. Internat. J. Engrg. Sci. 34 (1996) 1689-1704.
24. N.H. Scott, Thermoelasticity with thermomechanical constraints. Internat. J. Non-Linear Mech. 36 (2001) 549-564.
25. M. Silhavy, The Mechanics and Thermodynamics of Continuous Media. Springer, Berlin (1997).
26. C. A. Truesdell and W. Noll, The Nonlinear Field Theories of Mechanics, Handbuch der Physik, Vol. III/3. Springer, Berlin (1965).