The relaxation function in viscoelasticity : classical and non-classical thermodynamically admissible examples

The model of a viscoelastic body is considered focussing the attention on the the kernel of the integro- differential model equation. It represents the relaxation modulus which characterises the response of the material with memory to deformation. An overview on the classical viscoelasticity model is followed by different generalisations. Two different cases of relaxation functions, whose physical admissibility is guarantied by appropriate assumptions, are listed. The first one concerns a relaxation modulus at the initial time t = 0. The second one, a relaxation modulus whose regularity is the weakest possible to guarantee the admissibility of the model. One-dimensional evolution problems are considered, but, when present, references to results in the corresponding three-dimensional ones are provided.