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Rheological constitutive equation of solids: a link between models based on irreversible thermodynamics and on fractional order derivative equations

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Abstract

In this paper we focus on the rheological problem of defining a constitutive equation for viscoelastic materials. In this simple case, we show that writing the dissipative component of the observable response to a given excitation as the result of multiple internal processes working for equilibrium recovery (flux of internal hidden variables), can yield a recursive series in time. This can be obtained when use is made of the theorem of created entropy equipartition as a model for fluctuation regression. A distribution (spectrum) for relaxation times naturally follows. The model thus obtained reflects the concept of a hierarchically constrained dynamic behavior. The conclusion is that the operator of non-integer differentiation in time applied to field variables can also be recovered from pure thermodynamic considerations.

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  1. LEMTA-UMR CNRS 7563, avenue de la forêt de Haye, 2, 54504, Vandoeuvre Lès Nancy, France

    Stéphane André, Yves Meshaka & Christian Cunat

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  1. Stéphane André
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  2. Yves Meshaka
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  3. Christian Cunat
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Correspondence to Stéphane André.

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André, S., Meshaka, Y. & Cunat, C. Rheological constitutive equation of solids: a link between models based on irreversible thermodynamics and on fractional order derivative equations. Rheol Acta 42, 500–515 (2003). https://doi.org/10.1007/s00397-003-0305-z

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