Approximation of Linear Viscoelastic Model in the 3 Dimensional Case with Mechanical Analogues of Finite Size

A linear viscoelastic model having a continuous spectrum is difficult to implement in a finite element calculation. Then approximation of this model by a generalized Kelvin Voigt model or generalized Maxwell model is another option allowing calculation. A simple method allowing approximation of a linear viscoelastic model by a generalized Kelvin Voigt or generalized Maxwell model having “n” bodies is proposed. This method is applied to bituminous materials. The continuous spectrum 2S2P1D model developed at the “Ecole Nationale des Travaux Publics de l'Etat” (ENTPE) for bituminous materials is approximated by a generalized Kelvin Voigt and a generalized Maxwell Model having any chosen number (n) of bodies. The three-dimensional case is also considered and influence of the number of chosen bodies “n” is presented.