Alternative calculation of the retardation and relaxation spectra for the viscoelastic response of the solid phase materials

It is a well-known fact that rheology operates within the material science. Viscoelastic models represent various materials' mechanical behavior as building materials, polymers, tissues. The constitutive relation of the model can be used for the prediction of the materials behavior. As each viscoelastic model consists of several Hookean elastic (H) and Newton viscous (N) matters, interconnected serially or in parallel, for constitutive equation deriving of the resulting model, the coupling of the elementary constitutive equations of (H) and (N) is performed with regard to configuration of the entire model. Within the creep and relaxation tests, the spectra of the retardation and relaxation are yielded. These spectra are important in hereditary integrals and Prony's series for materials that perform the hysteresis. As the mathematical tool the theory of ordinary differential equations systems is used. (C) 2017 The Authors. Published by Elsevier Ltd.