On separation of energies in viscoelasticity

Separation of the storaged and dissipated energies in viscoelastic deformation is considered. This is a key problem for the construction of viscoelastic minimum rinciples and for the micromechanics of heterogeneous materials with memory. The notion of the viscoelastic free energy functional is discussed, thermodynamic admissibility conditions are established. An engineering analysis is realized through the method of harmonic strain regimes, influence of the loss and the storage moduli on the dissipation rate is studied. For the Volterra-Frechet integral expansion approach, necessary conditions on the general form of a free energy viscoelastic functional are formulated. The obtained results are used to examine the thermodynamic validity of certain classic viscoelastic models, like that of Staverman-Schwarzl. Through the spectral method, this energy representation is shown to correspond to a generalized Maxwell model.