Thermodynamic Properties of Fractional Differ-Integro Type Constitutive Relations

Using the asymptotic properties of Riemann-Liouville form, the intrinsic rate-based first and second laws of thermodynamics properties of fractional differintegro operator type constitutive representations are investigated by illustrating how the conservative and nonconservalive features of the response behavior interact under spectrally rich inputs. Due to the generality of the development, fractional operator representations of any order are considered. This includes the determination of the underlying features giving rise to frequency dependencies in the phasing and amplitude behavior and in this context the irreversible energy release rate process associated with fractional viscoelastic simulations.