Free energies in the frequency domain: The scalar case

A general closed expression is given for the isothermal minimum free energy of a linear viscoelastic material in terms of Fourier-transformed quantities. A one-parameter family of free energies is constructed, ranging continuously from the maximum to the minimum free energies, The simplest case of single component stress and strain tensors and a single viscoelastic function is considered in this paper. Explicit formulae are given for the particular case of a discrete spectrum model material response.