Speaker
Description
Viscoelastic materials appear in a wide range of fields: engineering, biology, geophysics, etc., such as synthetic polymers, biological tissues and concrete. In this talk we discuss a mathematical model of nonlinear fractional viscoelastic materials within the context of infinitesimal strain theory under quasi-static situation. Constitutive relations of such a generalized fractional viscoelastic models (shortly GFV models) are given by Volterra hereditary integrals with creep functions described by Prony series replaced with a Mittag-Leffler function. For a boundary value problem of the GFV model, we show the existence of a solution. Moreover, we also perform a numerical simulation for one-dimensional creep test under isotropic expansion, analyzing the effects of the fractional derivative order and non-linearity on material behavior in each of three stages: loading, maintaining, and release stages of the creep test.
