NEW RHEOLOGIC MODELS OF THE FRACTIONAL TYPE

Abstract

This work presents seven novel fractional-type complex rheological models, each defined by specific structural formulas and fractional-order constitutive relations. These models incorporate fractional differential operators to describe the behavior of ideal materials. Two fundamental models are highlighted, with graphical representations of their structural configurations and corresponding fractional-order constitutive equations for normal stress and axial dilation.
The study also introduces the concepts of the compensated subsequential elasticity surface and the stress relaxation surface, both expressed as functions of time and the fractional differentiation exponent. A comprehensive overview of the models is provided, including their Laplace-transformed solutions, which characterize the evolution of normal stress or axial deformation in response to external stimuli.
These seven models offer a unified framework for describing the mechanical behavior of idealized fractional materials, encompassing both elasto-viscous solids and viscoelastic fluids.