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 quantiti es. A one-parameter family of free energies is constructed, ranging continu ously from the maximum to the minimum free energies, The simplest case of single component stress and strain tensors and a singl e viscoelastic function is considered in this paper. Explicit formulae are given for the particular case of a discrete spectrum model material respons e.