A new and efficient constitutive model based on fractional time derivatives for transient analyses of viscoelastic systems

Abstract

In the open literature, many authors have used the fractional calculus in conjunction with the finite element method to model certain viscoelastic systems. The so-named fractional derivative model may be a better option for transient analyses of systems containing viscoelastic materials due to its causal behavior and its capability to fit accurately the viscoelastic damping properties and to represent properly their fading memory. However, depending on the situation, it leads to costly computations due to the integration of the non-local viscoelastic displacement and stress fields, especially for long time intervals. In this contribution, it is proposed a new and efficient general three-dimensional fractional constitutive formulation based on the use of a recurrence term to give a simplest and low-cost constitutive law to describe the frequency- and temperature-dependent behavior of viscoelastic materials, especially for complex systems. To demonstrate the efficiency and accuracy of the proposed formulation compared with those available in the literature, an academic example formed by a thin three-layer sandwich plate is performed and the main features and capabilities of the proposed methodology are highlighted.