Viscoelastic Stress-Strain via CFD Fractional Conformable Derivatives

Abstract

The Conformable Fractional Calculus revolutionized mathematical modeling by extending the scope of differentiation and integration to include the ordering of non-integers in the broadest sense. This paper aims to incorporate the Conformable Fractional Derivative (CFD) on the viscoelastic model by proving and analyzing its element analysis. Furthermore, it highlights the challenges facing viscoelastic materials, including polymers and biomaterials, exhibit anomalous damping characterized by power-law relaxation and frequency-dependent dissipation through relation between the viscoelastic and stress-strain. Subsequently, the application of the CFD overcomes all the numerical and physical inconsistencies present in traditional fractional calculus models (e.g., Caputo derivatives) that rely on singular kernels. Finally, applying the CFD to the Oscillatory Strain Response through the elastic modulus results in no stress relaxation over a period of time.