A fractional Maxwell approach for the shock response of viscoelastic oscillator

Abstract

Viscoelastic damping structures under shock loading with variable amplitude and frequency are always in the multifactorial dynamic state, of which the shock response is obviously different from that under low strain rate. In order to accurately describe the impact mechanical properties of viscoelastic damped materials, a fractional order Maxwell model (FMM) is constructed. To verify the adopted model, the dynamic experiments for different strain rates (1800 s-1 , 2500 s-1 , 3500 s-1 and 4000 s-1) are performed by SHPB system. The experimental stress-strain curves should be divided into three stages: the linear stage, the strain-softening stage and the strain-hardening stage. As increase with the strain rate, the peak strain, the peak stress and the curvature of the curve in strain-softening stage increase, and the hardening effect in the strain-hardening stage tends to stronger, demonstrating a distinct strain rate effect in viscoelastic damped materials. The reason is that as increase of the strain rate, the action time of external loading gets closer to the relaxation time of the molecular chain segment, indicating the apparent strain rate-dependence of molecular slip and friction. The comparisons are made between the models of FMM, fractional Kelvin-Voight, ZWT and Ogden considering the strain rate-dependent. As a fractional-order model, FMM model has the minimum mean of RMSE 0.460 among the four models. The results indicate that FMM model could accurately describe the impact mechanical behavior characteristics of viscoelastic materials in a wider range of strain rate with comprehensive superiority of higher fitting precision, fewer parameters and clear physical meaning.