Application of variable-order fractional calculus in solid mechanics

This chapter discusses the adoption of fractional derivative operators in modeling viscoelastic materials and their creep behavior. The damper elements in three conventional rheological models are replaced by fractional-order dashpots that include fixed- and variable-order fractional derivative operators. It is shown that the creep response of the presented fractional rheological models can be realistic if and only if they have monotonically decreasing variable-order functions. Finally, the presented rheological models are used to model the creep behavior of an epoxy by using experimental isothermal creep tests