Fractional description of time-dependent mechanical property evolution in materials with strain softening behavior

On the basis of using the variable fractional order to characterize the time-dependent mechanical property, a variable order fractional viscoelastic model is presented to represent the time-dependent evolution of mechanical property including strain softening behaviors. The developed model is applied to analyze the constant strain rate tension and compression tests in ductile metals and soils. It is shown that the model can reasonably characterize the hardening and softening stages of constant strain rate tests and describe the evolution of mechanical property. The time-dependent mechanical property evolution can be split into three parts: in the first stage, the mechanical property is almost invariable, the second phase is a mutation stage, and in the third stage it changes slowly and linearly with strain. The simulated results reveal that the evolution from strain hardening to strain softening is a continuous linear change of mechanical property. Furthermore, it is known that the order obtained through fitting some test data can be greater than 1, which corresponds to strain softening response, while for a long time the order was always assumed to be between 0 and 1.