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The minimum free energy for incompressible viscoelastic fluids. (English) Zbl 1104.76032

Summary: A general closed expression is given in the frequency domain for the isothermal minimum free energy of an incompressible viscoelastic fluid, whose constitutive equation is expressed by a linear functional of the history of strain. Another equivalent form of the minimum free energy is also derived and used to study the particular case of a discrete model material response.

MSC:

76A10 Viscoelastic fluids
74A15 Thermodynamics in solid mechanics
76M30 Variational methods applied to problems in fluid mechanics
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[1] Fabrizio, Advances in Differential Equations 7 pp 319– (2002)
[2] Golden, Quarterly of Applied Mathematics pp 127– (2000)
[3] Gentili, Quarterly of Applied Mathematics pp 153– (2002)
[4] , . On the minimal free energy and the Saint-Venant principle in linear viscoelasticity. In Mathematical Models and Methods for Smart Materials, , (eds). World Scientific: Singapore, 2002; 73–88. · Zbl 1103.74028 · doi:10.1142/9789812776273_0008
[5] Fabrizio, Archive for Rational Mechanics and Analysis 125 pp 341– (1994)
[6] Fabrizio, Quarterly of Applied Mathematics pp 341– (2002)
[7] . Mathematical Problems in Linear Viscoelasticity. SIAM: Philadelphia, 1992. · doi:10.1137/1.9781611970807
[8] Breuer, Zeitschrift fur Angewandte Mathematik und Physik 15 pp 13– (1981)
[9] Day, Quarterly Journal of Mechanics and Applied Mathematics 23 pp 1– (1970)
[10] Fabrizio, Differential and Integral Equations 6 pp 491– (1993)
[11] Joseph, Archive for Rational Mechanics and Analysis 56 pp 99– (1974)
[12] Fluid Dynamics of Viscoelastic Liquids. Springer: New York, 1990. · Zbl 0698.76002 · doi:10.1007/978-1-4612-4462-2
[13] Slemrod, Archive for Rational Mechanics and Analysis 62 pp 303– (1976)
[14] Slemrod, Archive for Rational Mechanics and Analysis 68 pp 1– (1978)
[15] Coleman, Reviews of Modern Physics 33 pp 239– (1961)
[16] . The nonlinear field theories of mechanics. Handbuch der Physik III/3. Springer: Berlin, New York, 1965.
[17] Truesdell, Annual Review of Fluid Mechanics 6 pp 111– (1974)
[18] Coleman, Archive for Rational Mechanics and Analysis 54 pp 1– (1974)
[19] Noll, Archive for Rational Mechanics and Analysis 48 pp 1– (1972)
[20] Fabrizio, Boll. U.M.I. 5-B pp 441– (1986)
[21] An outline on thermodynamical structure. In Article in New Perspective in Thermodynamics, (ed.). Springer: Berlin, 1986. · Zbl 0612.73002 · doi:10.1007/978-3-642-70803-9
[22] Fabrizio, Journal of Non-equilibrium Thermodynamics 16 pp 1– (1991)
[23] Deseri, Archive for Rational Mechanics and Analysis 181 pp 43– (2006)
[24] Singular Integral Equations. Noordhoff: Groningen, 1953.
[25] Amendola, Applicable Analysis 84 pp 67– (2005)
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