Adequacy of a nonlinear theory of viscoelasticity

The specific properties of viscoelastic materials behavior carrying into the choice of nonlinear constitutive relations are discussed. The classification for these constitutive relations is given as well as the requirements that the practice produces to their adequacy are formulated. The nonlinear theory of viscoelasticity possessing all preferences in comparison with the theory where stresses are expressed in terms of strains by the integral operators of increasing multiplicity is proposed. An inverse structure of the operator constitutive relations is shown by a one-dimensional example.