Fractional Order Kelvin-Voigt Constitutive Model and Dynamic Damping Characteristics of Viscoelastic Materials

Viscoelastic damping materials are often under complex service conditions. To precisely characterize its dynamic damping properties, based on fractional calculus and viscoelastic theory, considering the periodic characteristics of viscoelastic materials, the distributed fractional order Kelvin-Voigt constitutive model (DFKV) was constructed. The model accuracy was validated by quasi-static experiments. The dynamic modulus expressions were derived, and the model parametric feature analysis was carried out. Dynamic Mechanical Analysis (DMA) and Separate Hopkinson Pressure Bar (SHPB) experiments were performed with silicone rubber as the subject. The results show that the silicone rubber has an obvious temperature and frequency dependence, and it has a strong strain rate correlation considering that the strain rate effect indexes that are under high strain is 29.331. At the same time, clearly the viscoelastic dynamic constitutive behavior has phased characteristics that are in line with the scientific assumption of the distribution order. The fitting accuracy of DFKV model is higher than the existing contrast models, which reflects DFKV model and favorably represents the dynamic mechanical properties of viscoelastic materials under wide temperature, frequency and strain rate. The model is highly accurate, has fewer parameters, and the physical meaning of its parameters is clearer. It can provide a theoretical reference for the research and design of viscoelastic damping materials.