Creep and Stress Relaxation in a Viscoelasticity Theory with Derivatives of Fractional Order

Dušan Zorica

We study stress relaxation, creep and forced oscillations of a viscoelastic rod. One end of a rod is fixed, while we prescribe displacement or stress on the other end of a rod. We assume a general form of distributed-order fractional constitutive equation. Then we specify it for the solid and fluid-like viscoelastic body and obtain the displacement and stress. Existence of the solution for displacement and stress is proved via the Laplace transform method. Numerical examples in cases of stress relaxation and creep are presented as well.