Rheological Behaviour Modelling of Viscoelastic Materials by Using Fractional Model

We supposed in the work of the research fractional model with one mechanism, which simplifies to study the behavior of viscoelastic materials. The original method used in this work is the Laplace transforms technique and the fractional derivatives theory of the order α (0 ≤α ≤ 1). Two cases were studied: deformation (displacement) imposed, and stresses (forces) imposed. In these two cases all analytical formulas were calculated by solving the model equations using Laplace transform technique. To verify the model we studied three applications: 1) Response to constant loads, 2) Response to loads with Rampe function, 3) Response to periodic loads. This modelisation allowed obtaining the modulus of relaxation and the modulus of the greep compliance, then the study of deformations and stresses as a function of time in short and longing ranges and plotting the suitable curves of these charges.The good concordance between the theoretical results which we obtained from our model and experiences results for many researchers in this field (domain) of studies, show dearly clearly that our model in this research is applicable for studding the behavior of viscoelastic materials accurately.