A numerical assessment of the free energy function for fractional-order relaxation

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.