Fractional viscoelastic modeling of modified asphalt mastics using response surface method

Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

“…The two-parameter Mitteg-Leffler function E κ,µ (x) (6) is known to be differentiable and continuous with respect to real argument x and parameters κ and µ [36]. Therefore, by (13) and (14), the differentiability of the function G M (t, g) with respect to the positive relaxation time parameter τ r and parameters α and β directly results. To show that the condition (22) is satisfied, it is enough to prove that the partial derivatives of G M (t, g) with respect to the four model parameters are bounded uniformly on T × G 1 .…”

“…The applicability of such models to the description of different polymers is well known, for example, poly-isobutylene [4], polyurea and PET [6], shape memory polymers [7], amorphous polymers [8] and flax fiber-reinforced polymer [9]. Fractional viscoelastic models are also used for modeling laminated glass beams in the pre-crack state under explosive loads [10]; stress relaxation behavior of glassy polymers [11]; description of fiber-reinforced rubber concrete [12]; viscoelastic modeling of modified asphalt mastics [13]; and modeling rate-dependent nonlinear behaviors of rubber polymers [14]. The modeling and simulation of viscoelastic foods, for example, food gums [15], carrot root [16], fish burger baking [17], is another field of application of rheological fractional models.…”