A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials

Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. mainly characterized by three time-dependent mechanical properties such creep, stress relaxation hysteresis. Among them, is one of the most important features characterization viscoelastic materials. This phenomenon defined a decrease under constant strain. Due to inherent nonlinearity shown material response over certain range strain subjected external loads, nonlinear rheological models needed better describe experimental data. In this study, singlenonlinear differential constitutive equation derived froma model composed generalized Maxwell fluid parallel with spring obeying power law prediction behavior Under strain-history, analytically cases where positive exponent, α ˂ 1 ˃1. The Trust Region Method available MATLAB Optimization Toolbox identify parameters. Significant correlations found between data taken from literature exact analytical predictions. obtained results show that developed integer non-integer orders nonlinearities accurately describes some