In this paper the authors discuss the free energy function of fractional hereditary materials. The evaluation of the free energy has been obtained from a mechanical model that represents, exactly, the power-law relaxation of the material. The mechanical model separates, exactly, the elastic and the viscous phases, yielding the stored energy of the material that corresponds to the Staverman-Schwarz stress based free energy. Some numerical approximations of the free energy function in terms of the discretized rheological model have been reported in the paper.
Burlon, A., Pinnola, F., Zingales, M. (2014). A numerical assessment of the free energy function for fractional-order relaxation. In 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014 [10.1109/ICFDA.2014.6967374].
A numerical assessment of the free energy function for fractional-order relaxation
PINNOLA, Francesco Paolo;ZINGALES, Massimiliano
2014-01-01
Abstract
In this paper the authors discuss the free energy function of fractional hereditary materials. The evaluation of the free energy has been obtained from a mechanical model that represents, exactly, the power-law relaxation of the material. The mechanical model separates, exactly, the elastic and the viscous phases, yielding the stored energy of the material that corresponds to the Staverman-Schwarz stress based free energy. Some numerical approximations of the free energy function in terms of the discretized rheological model have been reported in the paper.
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