ABSTRACT
The viscoelastic models are represented by structural schemes (Sobotka 1981) with letters (H), (N) representing Hook elastic matter and Newton viscous matter respectively; and signs:| parallel connection-serial connection. By using these shortening tools we can construct the two and three element models as follows:
− (H)|(N) = {V} Voigt model, Figure 1c − (H)–(N) = {M}Maxwell model, Figure 1d − (H)–[(H)|(N)] = {PT} Poynting-Thompson model, Figure 1e − H)|[(H)–(N)] = {Z} Zener model, Figure 1f − (N)–[(H)|(N)] = {mPT} modified Poynting-Thompson model, Figure 1 g − (N)|[(H)–(N)] = {mZ} modified Zener model, Figure 1h
Considering the Constitutive Equations (CE) of basic matters ( ) : ( ) :N σ ηε CE of two and three element models can be derived from these CE heuristically. However heuristics is too cumbersome and in the case of four or more element models’ CE
derivation the conditional stiffness concept is used. Due to the presence of time derivative, the conditional stiffness in CE of a complex model will take of the form of a differential operator E(D) with D denoting time derivative of the operand, (Rabotnov 1966, Minárová & Sumec, 2016). Accordingly, E(D) will involve time derivatives of the certain order D d dtr r/ as well.
