Memory and non-locality effects in wave propagation modelling
Classical wave equation is generalized within the framework of fractional calculus in order to account for the memory and non-local effects that might be material features. Both effects are included in the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through distributed-order fractional constitutive equation that generalizes all linear models having differentiation orders up to order one. Microlocal approach in analyzing the singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.
Seminar with Dusan Zorica - The Serbian Academy of Arts and Sciences and University of Novi Sad.