Two approaches to aging and fatigue models in viscoelastic solids

The paper deals with viscoelastic solids subject to aging and fatigue effects. First a scheme is set up on the basis of physical insights, provided by the analysis of a rheological model, by letting the elastic moduli and the viscosity coefficients be functions of time. Hence the functional providing the stress in terms of the strain is established. The procedure has the advantage of showing how the dependence on the present value and that on the history of the strain are influenced by the rheological parameters. The three-dimensional version is then considered and the thermodynamic restrictions are determined. Next a second approach is set up by letting the stress be given by a constitutive equation involving a fractional derivative. The coefficient characterizing the kernel is assumed to obey an evolution equation that incorporates the fatigue effects. Compatibility with thermodynamics is shown to hold with an appropriate internal structural power.