Fractional modeling of cyclic loading behavior of polymeric materials

This paper introduces a fractional-order model integrated with a damage variable to effectively characterize the stress or strain responses under strain- or stress-controlled cyclic loading. We derive a relationship among mean stress, ratcheting strain, and cyclic number from the established fractional constitutive relationship. Experimental validation with polymeric data demonstrates the validity of our model, indicating how fractional order captures the effects of various loading conditions—including mean stress, temperature, and loading rate—on ratcheting strain responses. Additionally, our model offers a simpler mathematical framework than the existing models, without compromising accuracy.