On the appearance of fractional operators in non-linear stress-strain relation of metals

Here we present a non linear stress-strain relation based on fractional operators. The proposed constitutive law is based on integral formulation, and takes into account the viscoelastic behavior of the material and the inelastic phenomenon that appears when the stress reaches a particular yielding value. A specific case of the proposed constitutive law for imposed strain history is used to fit experimental data obtained from tensile tests on two kind of metal alloys. A best-fitting procedure demonstrates the accuracy of the proposed stress-strain relation and its results are compared to those obtained with some classical models. We conclude that the proposed model provides the best results in predicting the mechanical behavior for low and high values of stress/strain.