Advancing viscoelastic material modeling : Tackling time-dependent behavior with fractional calculus

Abstract

A combination of inherent unique stress-strain response features, Viscoelastic Materials (VM) provide an integral part in many different fields of engineering. Although practical, these materials’ highly complex time-dependent methods according to non-linear loading scenarios are impossible to model using conventional viscoelastic models such as Maxwell and Kelvin-Voigt. The present study introduces a framework that pushes over traditional Maxwell and Kelvin-Voigt approaches by employing fractional calculus in order to enhance the prediction of VM performance. The mathematical representation makes use of the Caputo fractional derivative for expressing an artificial viscoelastic polymer’s non-linear and time-dependent responses. Dynamic Mechanical Analysis (DMA) and Stress Relaxation Tests (SRT) proved the polymer possessed 1500 MPa fractional modulus and 0.65 fractional order, respectively. The resulting model involved more significant computing resources, but contrasting testing indicated that it accurately depicted stress relaxation and dynamic responses. As mentioned, the technique integrates mathematical and actual viscoelasticity for industrial uses while offering a precise basis for advanced material analysis.