Application to linear viscoelasticity
Introduction to the fractional derivative

For a mechanical system such as a mass attached to a spring, the applied force (the stress in a continuous medium description) is proportional to the displacement. In addition, classical viscous dissipation is proportional to the time derivative of displacement.

The basic assumption made for linear viscoelastic materials is that the stress at the current time is a linear function of the entire deformation history. Two static tests are most often used to define the coefficients of long-time behavior laws: the creep test and the relaxation test. In the creep test, a constant stress is instantaneously imposed on a specimen and its deformation is monitored as a function of time. In the relaxation test, an instantaneous...