A NONLINEAR STRAIN-DEPENDENT VARIABLE-ORDER FRACTIONAL MODEL WITH APPLICATIONS TO ALUMINUM FOAMS

In this paper, a power-law strain-dependent variable order is first incorporated into the fractional constitutive model and employed to describe mechanical behaviors of aluminum foams under quasi-static compression and tension. Comparative results illustrate that power-law strain-dependent variable order is capable of better describing stress–strain responses compared with the traditional linear one. The evolution of fractional order along with the porosities or relative densities can be well qualitatively interpreted by its physical meaning. Furthermore, the model is also extended to characterize the impact behaviors under large constant strain rates. It is observed that fractional model with sinusoidal variable order agrees well with the experimental data of aluminum foams with impact and non-impact surfaces.