Fractional Integral Formulation of Constitutive Equations of Viscoelasticity

Abstract

A fractional integral viscoelasticity model is discussed. The model has the same constitutive advantages as the fractional derivative viscoelasticity model. Both models need few parameters to model the weak frequency dependence of many engineering materials. Also, both models represent a causal relation between excitation and response. The fractional integral model, however, gives a unique relation between excitation and response, whereas the fractional derivative model needs initial conditions to give a unique relation. The fractional integral model is incorporated into structural equations of motion. A time-discretization scheme for the solution of these equations is outlined, and some examples are given.