Fractional visco-hyperelastic modeling for dynamic behaviors of elastomers

To develop a high-performance numerical method for simulating dynamic behaviors of elastomers, it is necessary and urgent to investigate the influences of nonlinearity and thermodynamics-based stability of hyperelastic strain energy density function on the numerical predictions of dynamic properties of elastomers. To this end, this paper proposed a fractional visco-hyperelastic constitutive modeling approach for the dynamic behaviors of elastomers, in which two-parameter Mooney-Rivlin, Stumpf-Marczak and Hoss-Marczak hyperelastic models were harnessed. In this model, dependences of dynamic properties of elastomers on the frequency, dynamic strain amplitude (Payne effect), and prestrain were considered. Stress-strain constitutive relations were derived in the domain of an intrinsic time variable, which satisfies the thermodynamic consistency in the form of Clausius-Duhem inequality. Afterwards, the constitutive model was geometrically linearized in the neighborhood of a temporally constant predeformation. To determine the constitutive parameters, a linear formulation highlighting the prestrain effect was particularized in the derivations of the storage and the loss modulus. An inverse identification procedure was carried out for the experimental data. The prediction results revealed that the model using a nonlinear and thermodynamically stable strain energy density function with merely one fractional Maxwell element could achieve a remarkable accuracy and reliability in representing the dynamic behaviors of different elastomers under different dynamic loading conditions. Projection of constitutive relations in the intrinsic time domain facilitates the constitutive modeling within the dynamic regime. This work could provide a fundamental guidance for the assessment, optimization and design of elastomers with superior vibration isolation performance.